homework and practice 4 10

• Skip to main content
• Skip to primary sidebar
• Skip to footer

Additional menu

Khan Academy Blog

Free Math Worksheets — Over 100k free practice problems on Khan Academy

Looking for free math worksheets.

You’ve found something even better!

That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!

Just choose your grade level or topic to get access to 100% free practice questions:

Kindergarten, basic geometry, pre-algebra, algebra basics, high school geometry.

• Trigonometry

Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

• Addition and subtraction
• Place value (tens and hundreds)
• Addition and subtraction within 20
• Addition and subtraction within 100
• Addition and subtraction within 1000
• Measurement and data
• Counting and place value
• Measurement and geometry
• Place value
• Measurement, data, and geometry
• Add and subtract within 20
• Add and subtract within 100
• Add and subtract within 1,000
• Money and time
• Measurement
• Intro to multiplication
• 1-digit multiplication
• Addition, subtraction, and estimation
• Intro to division
• Understand fractions
• Equivalent fractions and comparing fractions
• More with multiplication and division
• Arithmetic patterns and problem solving
• Quadrilaterals
• Represent and interpret data
• Multiply by 1-digit numbers
• Multiply by 2-digit numbers
• Factors, multiples and patterns
• Add and subtract fractions
• Multiply fractions
• Understand decimals
• Plane figures
• Measuring angles
• Area and perimeter
• Units of measurement
• Decimal place value
• Add decimals
• Subtract decimals
• Multi-digit multiplication and division
• Divide fractions
• Multiply decimals
• Divide decimals
• Powers of ten
• Coordinate plane
• Algebraic thinking
• Converting units of measure
• Properties of shapes
• Ratios, rates, & percentages
• Arithmetic operations
• Negative numbers
• Properties of numbers
• Variables & expressions
• Equations & inequalities introduction
• Data and statistics
• Negative numbers: addition and subtraction
• Negative numbers: multiplication and division
• Fractions, decimals, & percentages
• Rates & proportional relationships
• Expressions, equations, & inequalities
• Numbers and operations
• Solving equations with one unknown
• Linear equations and functions
• Systems of equations
• Geometric transformations
• Data and modeling
• Volume and surface area
• Pythagorean theorem
• Transformations, congruence, and similarity
• Arithmetic properties
• Factors and multiples
• Reading and interpreting data
• Negative numbers and coordinate plane
• Ratios, rates, proportions
• Equations, expressions, and inequalities
• Exponents, radicals, and scientific notation
• Foundations
• Algebraic expressions
• Linear equations and inequalities
• Graphing lines and slope
• Expressions with exponents
• Quadratics and polynomials
• Equations and geometry
• Algebra foundations
• Solving equations & inequalities
• Working with units
• Linear equations & graphs
• Forms of linear equations
• Inequalities (systems & graphs)
• Absolute value & piecewise functions
• Exponents & radicals
• Exponential growth & decay
• Quadratics: Multiplying & factoring
• Quadratic functions & equations
• Irrational numbers
• Performing transformations
• Transformation properties and proofs
• Right triangles & trigonometry
• Non-right triangles & trigonometry (Advanced)
• Analytic geometry
• Conic sections
• Solid geometry
• Polynomial arithmetic
• Complex numbers
• Polynomial factorization
• Polynomial division
• Polynomial graphs
• Rational exponents and radicals
• Exponential models
• Transformations of functions
• Rational functions
• Trigonometric functions
• Non-right triangles & trigonometry
• Trigonometric equations and identities
• Analyzing categorical data
• Displaying and comparing quantitative data
• Summarizing quantitative data
• Modeling data distributions
• Exploring bivariate numerical data
• Study design
• Probability
• Counting, permutations, and combinations
• Random variables
• Sampling distributions
• Confidence intervals
• Significance tests (hypothesis testing)
• Two-sample inference for the difference between groups
• Inference for categorical data (chi-square tests)
• Advanced regression (inference and transforming)
• Analysis of variance (ANOVA)
• Scatterplots
• Data distributions
• Two-way tables
• Binomial probability
• Normal distributions
• Displaying and describing quantitative data
• Inference comparing two groups or populations
• Chi-square tests for categorical data
• More on regression
• Prepare for the 2020 AP®︎ Statistics Exam
• AP®︎ Statistics Standards mappings
• Polynomials
• Composite functions
• Probability and combinatorics
• Limits and continuity
• Derivatives: definition and basic rules
• Derivatives: chain rule and other advanced topics
• Applications of derivatives
• Analyzing functions
• Parametric equations, polar coordinates, and vector-valued functions
• Applications of integrals
• Differentiation: definition and basic derivative rules
• Differentiation: composite, implicit, and inverse functions
• Contextual applications of differentiation
• Applying derivatives to analyze functions
• Integration and accumulation of change
• Applications of integration
• AP Calculus AB solved free response questions from past exams
• AP®︎ Calculus AB Standards mappings
• Infinite sequences and series
• AP Calculus BC solved exams
• AP®︎ Calculus BC Standards mappings
• Integrals review
• Integration techniques
• Thinking about multivariable functions
• Derivatives of multivariable functions
• Applications of multivariable derivatives
• Integrating multivariable functions
• Green’s, Stokes’, and the divergence theorems
• First order differential equations
• Second order linear equations
• Laplace transform
• Vectors and spaces
• Matrix transformations
• Alternate coordinate systems (bases)

Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

What do Khan Academy’s interactive math worksheets look like?

Here’s an example:

What are teachers saying about Khan Academy’s interactive math worksheets?

“My students love Khan Academy because they can immediately learn from their mistakes, unlike traditional worksheets.”

Is Khan Academy free?

Khan Academy’s practice questions are 100% free—with no ads or subscriptions.

What do Khan Academy’s interactive math worksheets cover?

Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

Is Khan Academy a company?

Khan Academy is a nonprofit with a mission to provide a free, world-class education to anyone, anywhere.

Want to get even more out of Khan Academy?

Then be sure to check out our teacher tools . They’ll help you assign the perfect practice for each student from our full math curriculum and track your students’ progress across the year. Plus, they’re also 100% free — with no subscriptions and no ads.

Get Khanmigo

The best way to learn and teach with AI is here. Ace the school year with our AI-powered guide, Khanmigo. 

For learners     For teachers     For parents

Does Homework Really Help Students Learn?

A conversation with a Wheelock researcher, a BU student, and a fourth-grade teacher

“Quality homework is engaging and relevant to kids’ lives,” says Wheelock’s Janine Bempechat. “It gives them autonomy and engages them in the community and with their families. In some subjects, like math, worksheets can be very helpful. It has to do with the value of practicing over and over.” Photo by iStock/Glenn Cook Photography

Do your homework.

If only it were that simple.

Educators have debated the merits of homework since the late 19th century. In recent years, amid concerns of some parents and teachers that children are being stressed out by too much homework, things have only gotten more fraught.

“Homework is complicated,” says developmental psychologist Janine Bempechat, a Wheelock College of Education & Human Development clinical professor. The author of the essay “ The Case for (Quality) Homework—Why It Improves Learning and How Parents Can Help ” in the winter 2019 issue of Education Next , Bempechat has studied how the debate about homework is influencing teacher preparation, parent and student beliefs about learning, and school policies.

She worries especially about socioeconomically disadvantaged students from low-performing schools who, according to research by Bempechat and others, get little or no homework.

BU Today  sat down with Bempechat and Erin Bruce (Wheelock’17,’18), a new fourth-grade teacher at a suburban Boston school, and future teacher freshman Emma Ardizzone (Wheelock) to talk about what quality homework looks like, how it can help children learn, and how schools can equip teachers to design it, evaluate it, and facilitate parents’ role in it.

BU Today: Parents and educators who are against homework in elementary school say there is no research definitively linking it to academic performance for kids in the early grades. You’ve said that they’re missing the point.

Bempechat : I think teachers assign homework in elementary school as a way to help kids develop skills they’ll need when they’re older—to begin to instill a sense of responsibility and to learn planning and organizational skills. That’s what I think is the greatest value of homework—in cultivating beliefs about learning and skills associated with academic success. If we greatly reduce or eliminate homework in elementary school, we deprive kids and parents of opportunities to instill these important learning habits and skills.

We do know that beginning in late middle school, and continuing through high school, there is a strong and positive correlation between homework completion and academic success.

That’s what I think is the greatest value of homework—in cultivating beliefs about learning and skills associated with academic success.

You talk about the importance of quality homework. What is that?

Quality homework is engaging and relevant to kids’ lives. It gives them autonomy and engages them in the community and with their families. In some subjects, like math, worksheets can be very helpful. It has to do with the value of practicing over and over.

What are your concerns about homework and low-income children?

The argument that some people make—that homework “punishes the poor” because lower-income parents may not be as well-equipped as affluent parents to help their children with homework—is very troubling to me. There are no parents who don’t care about their children’s learning. Parents don’t actually have to help with homework completion in order for kids to do well. They can help in other ways—by helping children organize a study space, providing snacks, being there as a support, helping children work in groups with siblings or friends.

Isn’t the discussion about getting rid of homework happening mostly in affluent communities?

Yes, and the stories we hear of kids being stressed out from too much homework—four or five hours of homework a night—are real. That’s problematic for physical and mental health and overall well-being. But the research shows that higher-income students get a lot more homework than lower-income kids.

Teachers may not have as high expectations for lower-income children. Schools should bear responsibility for providing supports for kids to be able to get their homework done—after-school clubs, community support, peer group support. It does kids a disservice when our expectations are lower for them.

The conversation around homework is to some extent a social class and social justice issue. If we eliminate homework for all children because affluent children have too much, we’re really doing a disservice to low-income children. They need the challenge, and every student can rise to the challenge with enough supports in place.

What did you learn by studying how education schools are preparing future teachers to handle homework?

My colleague, Margarita Jimenez-Silva, at the University of California, Davis, School of Education, and I interviewed faculty members at education schools, as well as supervising teachers, to find out how students are being prepared. And it seemed that they weren’t. There didn’t seem to be any readings on the research, or conversations on what high-quality homework is and how to design it.

Erin, what kind of training did you get in handling homework?

Bruce : I had phenomenal professors at Wheelock, but homework just didn’t come up. I did lots of student teaching. I’ve been in classrooms where the teachers didn’t assign any homework, and I’ve been in rooms where they assigned hours of homework a night. But I never even considered homework as something that was my decision. I just thought it was something I’d pull out of a book and it’d be done.

I started giving homework on the first night of school this year. My first assignment was to go home and draw a picture of the room where you do your homework. I want to know if it’s at a table and if there are chairs around it and if mom’s cooking dinner while you’re doing homework.

The second night I asked them to talk to a grown-up about how are you going to be able to get your homework done during the week. The kids really enjoyed it. There’s a running joke that I’m teaching life skills.

Friday nights, I read all my kids’ responses to me on their homework from the week and it’s wonderful. They pour their hearts out. It’s like we’re having a conversation on my couch Friday night.

It matters to know that the teacher cares about you and that what you think matters to the teacher. Homework is a vehicle to connect home and school…for parents to know teachers are welcoming to them and their families.

Bempechat : I can’t imagine that most new teachers would have the intuition Erin had in designing homework the way she did.

Ardizzone : Conversations with kids about homework, feeling you’re being listened to—that’s such a big part of wanting to do homework….I grew up in Westchester County. It was a pretty demanding school district. My junior year English teacher—I loved her—she would give us feedback, have meetings with all of us. She’d say, “If you have any questions, if you have anything you want to talk about, you can talk to me, here are my office hours.” It felt like she actually cared.

Bempechat : It matters to know that the teacher cares about you and that what you think matters to the teacher. Homework is a vehicle to connect home and school…for parents to know teachers are welcoming to them and their families.

Ardizzone : But can’t it lead to parents being overbearing and too involved in their children’s lives as students?

Bempechat : There’s good help and there’s bad help. The bad help is what you’re describing—when parents hover inappropriately, when they micromanage, when they see their children confused and struggling and tell them what to do.

Good help is when parents recognize there’s a struggle going on and instead ask informative questions: “Where do you think you went wrong?” They give hints, or pointers, rather than saying, “You missed this,” or “You didn’t read that.”

Bruce : I hope something comes of this. I hope BU or Wheelock can think of some way to make this a more pressing issue. As a first-year teacher, it was not something I even thought about on the first day of school—until a kid raised his hand and said, “Do we have homework?” It would have been wonderful if I’d had a plan from day one.

Explore Related Topics:

• Share this story

Senior Contributing Editor

Sara Rimer A journalist for more than three decades, Sara Rimer worked at the Miami Herald , Washington Post and, for 26 years, the New York Times , where she was the New England bureau chief, and a national reporter covering education, aging, immigration, and other social justice issues. Her stories on the death penalty’s inequities were nominated for a Pulitzer Prize and cited in the U.S. Supreme Court’s decision outlawing the execution of people with intellectual disabilities. Her journalism honors include Columbia University’s Meyer Berger award for in-depth human interest reporting. She holds a BA degree in American Studies from the University of Michigan. Profile

She can be reached at [email protected] .

Comments & Discussion

Boston University moderates comments to facilitate an informed, substantive, civil conversation. Abusive, profane, self-promotional, misleading, incoherent or off-topic comments will be rejected. Moderators are staffed during regular business hours (EST) and can only accept comments written in English. Statistics or facts must include a citation or a link to the citation.

There are 81 comments on Does Homework Really Help Students Learn?

Insightful! The values about homework in elementary schools are well aligned with my intuition as a parent.

when i finish my work i do my homework and i sometimes forget what to do because i did not get enough sleep

same omg it does not help me it is stressful and if I have it in more than one class I hate it.

Same I think my parent wants to help me but, she doesn’t care if I get bad grades so I just try my best and my grades are great.

I think that last question about Good help from parents is not know to all parents, we do as our parents did or how we best think it can be done, so maybe coaching parents or giving them resources on how to help with homework would be very beneficial for the parent on how to help and for the teacher to have consistency and improve homework results, and of course for the child. I do see how homework helps reaffirm the knowledge obtained in the classroom, I also have the ability to see progress and it is a time I share with my kids

The answer to the headline question is a no-brainer – a more pressing problem is why there is a difference in how students from different cultures succeed. Perfect example is the student population at BU – why is there a majority population of Asian students and only about 3% black students at BU? In fact at some universities there are law suits by Asians to stop discrimination and quotas against admitting Asian students because the real truth is that as a group they are demonstrating better qualifications for admittance, while at the same time there are quotas and reduced requirements for black students to boost their portion of the student population because as a group they do more poorly in meeting admissions standards – and it is not about the Benjamins. The real problem is that in our PC society no one has the gazuntas to explore this issue as it may reveal that all people are not created equal after all. Or is it just environmental cultural differences??????

I get you have a concern about the issue but that is not even what the point of this article is about. If you have an issue please take this to the site we have and only post your opinion about the actual topic

This is not at all what the article is talking about.

This literally has nothing to do with the article brought up. You should really take your opinions somewhere else before you speak about something that doesn’t make sense.

we have the same name

so they have the same name what of it?

lol you tell her

totally agree

What does that have to do with homework, that is not what the article talks about AT ALL.

Yes, I think homework plays an important role in the development of student life. Through homework, students have to face challenges on a daily basis and they try to solve them quickly.I am an intense online tutor at 24x7homeworkhelp and I give homework to my students at that level in which they handle it easily.

More than two-thirds of students said they used alcohol and drugs, primarily marijuana, to cope with stress.

You know what’s funny? I got this assignment to write an argument for homework about homework and this article was really helpful and understandable, and I also agree with this article’s point of view.

I also got the same task as you! I was looking for some good resources and I found this! I really found this article useful and easy to understand, just like you! ^^

i think that homework is the best thing that a child can have on the school because it help them with their thinking and memory.

I am a child myself and i think homework is a terrific pass time because i can’t play video games during the week. It also helps me set goals.

Homework is not harmful ,but it will if there is too much

I feel like, from a minors point of view that we shouldn’t get homework. Not only is the homework stressful, but it takes us away from relaxing and being social. For example, me and my friends was supposed to hang at the mall last week but we had to postpone it since we all had some sort of work to do. Our minds shouldn’t be focused on finishing an assignment that in realty, doesn’t matter. I completely understand that we should have homework. I have to write a paper on the unimportance of homework so thanks.

homework isn’t that bad

Are you a student? if not then i don’t really think you know how much and how severe todays homework really is

i am a student and i do not enjoy homework because i practice my sport 4 out of the five days we have school for 4 hours and that’s not even counting the commute time or the fact i still have to shower and eat dinner when i get home. its draining!

i totally agree with you. these people are such boomers

why just why

they do make a really good point, i think that there should be a limit though. hours and hours of homework can be really stressful, and the extra work isn’t making a difference to our learning, but i do believe homework should be optional and extra credit. that would make it for students to not have the leaning stress of a assignment and if you have a low grade you you can catch up.

Studies show that homework improves student achievement in terms of improved grades, test results, and the likelihood to attend college. Research published in the High School Journal indicates that students who spent between 31 and 90 minutes each day on homework “scored about 40 points higher on the SAT-Mathematics subtest than their peers, who reported spending no time on homework each day, on average.” On both standardized tests and grades, students in classes that were assigned homework outperformed 69% of students who didn’t have homework. A majority of studies on homework’s impact – 64% in one meta-study and 72% in another – showed that take home assignments were effective at improving academic achievement. Research by the Institute for the Study of Labor (IZA) concluded that increased homework led to better GPAs and higher probability of college attendance for high school boys. In fact, boys who attended college did more than three hours of additional homework per week in high school.

So how are your measuring student achievement? That’s the real question. The argument that doing homework is simply a tool for teaching responsibility isn’t enough for me. We can teach responsibility in a number of ways. Also the poor argument that parents don’t need to help with homework, and that students can do it on their own, is wishful thinking at best. It completely ignores neurodiverse students. Students in poverty aren’t magically going to find a space to do homework, a friend’s or siblings to help them do it, and snacks to eat. I feel like the author of this piece has never set foot in a classroom of students.

THIS. This article is pathetic coming from a university. So intellectually dishonest, refusing to address the havoc of capitalism and poverty plays on academic success in life. How can they in one sentence use poor kids in an argument and never once address that poor children have access to damn near 0 of the resources affluent kids have? Draw me a picture and let’s talk about feelings lmao what a joke is that gonna put food in their belly so they can have the calories to burn in order to use their brain to study? What about quiet their 7 other siblings that they share a single bedroom with for hours? Is it gonna force the single mom to magically be at home and at work at the same time to cook food while you study and be there to throw an encouraging word?

Also the “parents don’t need to be a parent and be able to guide their kid at all academically they just need to exist in the next room” is wild. Its one thing if a parent straight up is not equipped but to say kids can just figured it out is…. wow coming from an educator What’s next the teacher doesn’t need to teach cause the kid can just follow the packet and figure it out?

Well then get a tutor right? Oh wait you are poor only affluent kids can afford a tutor for their hours of homework a day were they on average have none of the worries a poor child does. Does this address that poor children are more likely to also suffer abuse and mental illness? Like mentioned what about kids that can’t learn or comprehend the forced standardized way? Just let em fail? These children regularly are not in “special education”(some of those are a joke in their own and full of neglect and abuse) programs cause most aren’t even acknowledged as having disabilities or disorders.

But yes all and all those pesky poor kids just aren’t being worked hard enough lol pretty sure poor children’s existence just in childhood is more work, stress, and responsibility alone than an affluent child’s entire life cycle. Love they never once talked about the quality of education in the classroom being so bad between the poor and affluent it can qualify as segregation, just basically blamed poor people for being lazy, good job capitalism for failing us once again!

why the hell?

you should feel bad for saying this, this article can be helpful for people who has to write a essay about it

This is more of a political rant than it is about homework

I know a teacher who has told his students their homework is to find something they are interested in, pursue it and then come share what they learn. The student responses are quite compelling. One girl taught herself German so she could talk to her grandfather. One boy did a research project on Nelson Mandela because the teacher had mentioned him in class. Another boy, a both on the autism spectrum, fixed his family’s computer. The list goes on. This is fourth grade. I think students are highly motivated to learn, when we step aside and encourage them.

The whole point of homework is to give the students a chance to use the material that they have been presented with in class. If they never have the opportunity to use that information, and discover that it is actually useful, it will be in one ear and out the other. As a science teacher, it is critical that the students are challenged to use the material they have been presented with, which gives them the opportunity to actually think about it rather than regurgitate “facts”. Well designed homework forces the student to think conceptually, as opposed to regurgitation, which is never a pretty sight

Wonderful discussion. and yes, homework helps in learning and building skills in students.

not true it just causes kids to stress

Homework can be both beneficial and unuseful, if you will. There are students who are gifted in all subjects in school and ones with disabilities. Why should the students who are gifted get the lucky break, whereas the people who have disabilities suffer? The people who were born with this “gift” go through school with ease whereas people with disabilities struggle with the work given to them. I speak from experience because I am one of those students: the ones with disabilities. Homework doesn’t benefit “us”, it only tears us down and put us in an abyss of confusion and stress and hopelessness because we can’t learn as fast as others. Or we can’t handle the amount of work given whereas the gifted students go through it with ease. It just brings us down and makes us feel lost; because no mater what, it feels like we are destined to fail. It feels like we weren’t “cut out” for success.

homework does help

here is the thing though, if a child is shoved in the face with a whole ton of homework that isn’t really even considered homework it is assignments, it’s not helpful. the teacher should make homework more of a fun learning experience rather than something that is dreaded

This article was wonderful, I am going to ask my teachers about extra, or at all giving homework.

I agree. Especially when you have homework before an exam. Which is distasteful as you’ll need that time to study. It doesn’t make any sense, nor does us doing homework really matters as It’s just facts thrown at us.

Homework is too severe and is just too much for students, schools need to decrease the amount of homework. When teachers assign homework they forget that the students have other classes that give them the same amount of homework each day. Students need to work on social skills and life skills.

I disagree.

Beyond achievement, proponents of homework argue that it can have many other beneficial effects. They claim it can help students develop good study habits so they are ready to grow as their cognitive capacities mature. It can help students recognize that learning can occur at home as well as at school. Homework can foster independent learning and responsible character traits. And it can give parents an opportunity to see what’s going on at school and let them express positive attitudes toward achievement.

Homework is helpful because homework helps us by teaching us how to learn a specific topic.

As a student myself, I can say that I have almost never gotten the full 9 hours of recommended sleep time, because of homework. (Now I’m writing an essay on it in the middle of the night D=)

I am a 10 year old kid doing a report about “Is homework good or bad” for homework before i was going to do homework is bad but the sources from this site changed my mind!

Homeowkr is god for stusenrs

I agree with hunter because homework can be so stressful especially with this whole covid thing no one has time for homework and every one just wants to get back to there normal lives it is especially stressful when you go on a 2 week vaca 3 weeks into the new school year and and then less then a week after you come back from the vaca you are out for over a month because of covid and you have no way to get the assignment done and turned in

As great as homework is said to be in the is article, I feel like the viewpoint of the students was left out. Every where I go on the internet researching about this topic it almost always has interviews from teachers, professors, and the like. However isn’t that a little biased? Of course teachers are going to be for homework, they’re not the ones that have to stay up past midnight completing the homework from not just one class, but all of them. I just feel like this site is one-sided and you should include what the students of today think of spending four hours every night completing 6-8 classes worth of work.

Are we talking about homework or practice? Those are two very different things and can result in different outcomes.

Homework is a graded assignment. I do not know of research showing the benefits of graded assignments going home.

Practice; however, can be extremely beneficial, especially if there is some sort of feedback (not a grade but feedback). That feedback can come from the teacher, another student or even an automated grading program.

As a former band director, I assigned daily practice. I never once thought it would be appropriate for me to require the students to turn in a recording of their practice for me to grade. Instead, I had in-class assignments/assessments that were graded and directly related to the practice assigned.

I would really like to read articles on “homework” that truly distinguish between the two.

oof i feel bad good luck!

thank you guys for the artical because I have to finish an assingment. yes i did cite it but just thanks

thx for the article guys.

Homework is good

I think homework is helpful AND harmful. Sometimes u can’t get sleep bc of homework but it helps u practice for school too so idk.

I agree with this Article. And does anyone know when this was published. I would like to know.

It was published FEb 19, 2019.

Studies have shown that homework improved student achievement in terms of improved grades, test results, and the likelihood to attend college.

i think homework can help kids but at the same time not help kids

This article is so out of touch with majority of homes it would be laughable if it wasn’t so incredibly sad.

There is no value to homework all it does is add stress to already stressed homes. Parents or adults magically having the time or energy to shepherd kids through homework is dome sort of 1950’s fantasy.

What lala land do these teachers live in?

Homework gives noting to the kid

Homework is Bad

homework is bad.

why do kids even have homework?

Comments are closed.

Latest from Bostonia

American academy of arts & sciences welcomes five bu members, com’s newest journalism grad took her time, could boston be the next city to impose congestion pricing, alum has traveled the world to witness total solar eclipses, opening doors: rhonda harrison (eng’98,’04, grs’04), campus reacts and responds to israel-hamas war, reading list: what the pandemic revealed, remembering com’s david anable, cas’ john stone, “intellectual brilliance and brilliant kindness”, one good deed: christine kannler (cas’96, sph’00, camed’00), william fairfield warren society inducts new members, spreading art appreciation, restoring the “black angels” to medical history, in the kitchen with jacques pépin, feedback: readers weigh in on bu’s new president, com’s new expert on misinformation, and what’s really dividing the nation, the gifts of great teaching, sth’s walter fluker honored by roosevelt institute, alum’s debut book is a ramadan story for children, my big idea: covering construction sites with art, former terriers power new professional women’s hockey league.

• 888-309-8227
• 732-384-0146

New User Registration

Forgot Password

Go Math! 4 Common Core, Grade: 4 Publisher: Houghton Mifflin Harcourt

Go math 4 common core, title : go math 4 common core, publisher : houghton mifflin harcourt, isbn : 054758783x, isbn-13 : 9780547587837, use the table below to find videos, mobile apps, worksheets and lessons that supplement go math 4 common core., textbook resources.

• Call us toll-free
• FAQs – Frequently Asked Questions
• Contact Lumos Learning – Proven Study Programs by Expert Teachers

Follow us: Lumos Learning -->

• 2024 © Lumos Learning
• Privacy Policy - Terms of Service - Disclaimers

PARCC® is a registered trademark of PARCC, Inc. Lumos Learning, is not owned by or affiliated in any fashion with PARCC, Inc... Read More

PARCC® is a registered trademark of PARCC, Inc. Lumos Learning, is not owned by or affiliated in any fashion with PARCC, Inc., the Partnership for the Assessment of Readiness for College and Careers, nor any state of the Union. Neither PARCC, Inc., nor The Partnership for the Assessment of Readiness for College and Careers, nor any member state has endorsed this product. No portion of any fees or charges paid for any products or services Lumos Learning offers will be paid or inure to the benefit of PARCC, Inc., or any state of the Union

SBAC is a copyright of The Regents of the University of California – Smarter Balanced Assessment Consortium, which is not aff... Read More

SBAC is a copyright of The Regents of the University of California – Smarter Balanced Assessment Consortium, which is not affiliated to Lumos Learning. The Regents of the University of California – Smarter Balanced Assessment Consortium, was not involved in the production of, and does not endorse these products or this site.

ACT® Aspire™ is a registered trademark of ACT Aspire LLC., which is not affiliated to Lumos Learning. ACT Aspire LLC, was not... Read More

ACT® Aspire™ is a registered trademark of ACT Aspire LLC., which is not affiliated to Lumos Learning. ACT Aspire LLC,was not involved in the production of, and does not endorse these products or this site.

Florida Department of Education is not affiliated to Lumos Learning. Florida department of education, was not involved in the... Read More

Florida Department of Education is not affiliated to Lumos Learning. Florida department of education, was not involved in the production of, and does not endorse these products or this site.

Indiana Department of Education is not affiliated to Lumos Learning. Indiana department of education, was not involved in the... Read More

Indiana Department of Education is not affiliated to Lumos Learning. Indiana department of education, was not involved in the production of, and does not endorse these products or this site.

Mississippi Department of Education is not affiliated to Lumos Learning. Mississippi department of education, was not involved... Read More

Mississippi Department of Education is not affiliated to Lumos Learning. Mississippi department of education, was not involved in the production of, and does not endorse these products or this site.

Ohio Department of Education is not affiliated to Lumos Learning. Ohio department of education, was not involved in the prod... Read More

Ohio Department of Education is not affiliated to Lumos Learning. Ohio department of education, was not involved in the production of, and does not endorse these products or this site.

Tennessee Department of Education is not affiliated to Lumos Learning. Tennessee department of education, was not involved... Read More

Tennessee Department of Education is not affiliated to Lumos Learning. Tennessee department of education, was not involved in the production of, and does not endorse these products or this site.

Georgia Department of Education is not affiliated to Lumos Learning. Georgia department of education, was not involved... Read More

Georgia Department of Education is not affiliated to Lumos Learning. Georgia department of education, was not involved in the production of, and does not endorse these products or this site.

Missouri Department of Education is not affiliated to Lumos Learning. Missouri department of education, was not involved... Read More

Missouri Department of Education is not affiliated to Lumos Learning. Missouri department of education, was not involved in the production of, and does not endorse these products or this site.

Louisiana Department of Education is not affiliated to Lumos Learning. Louisiana department of education, was not involved... Read More

Louisiana Department of Education is not affiliated to Lumos Learning. Louisiana department of education, was not involved in the production of, and does not endorse these products or this site.

• Texas Go Math
• Big Ideas Math
• Engageny Math
• McGraw Hill My Math
• enVision Math
• 180 Days of Math
• Math in Focus Answer Key
• Math Expressions Answer Key
• Privacy Policy

Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals

Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals: If you are an avid student and curious about Maths then take the help of the Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals. You can explore Questions from Practice Tests, Cumulative Practice, Chapter Test, Performance Tests, and seek the Homework Help required. Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals provided will enhance the Overall Maths Skills.

Big Ideas Math Book 4th Grade Answer Key Chapter 10 Relate Fractions and Decimals

In order to help you guys, we have provided the solutions in pdf format. So Download Big Ideas Math Book 4th Grade Answer Key Chapter 10 Relate Fractions and Decimals pdf for free. Access the topicwise Grade 4 Big Ideas Math Answer Key available via quick links and use them as a reference whenever you have any queries.

Lesson: 1 Understand Tenths

Lesson 10.1 Understand Tenths

Understand tenths homework & practice 10.1.

Lesson: 2 Understand Hundredths

Lesson 10.2 Understand Hundredths

Understand hundredths homework & practice 10.2.

Lesson: 3 Fractions and Decimals

Lesson 10.3 Fractions and Decimals

Fractions and decimals homework & practice 10.3.

Lesson: 4 Compare Decimals

Lesson 10.4 Compare Decimals

Compare decimals homework & practice 10.4.

Lesson: 5 Add Decimal Fractions and Decimals

Lesson 10.5 Add Decimal Fractions and Decimals

Add decimal fractions and decimals homework & practice 10.5.

Lesson: 6 Fractions, Decimals and Money

Lesson 10.6 Fractions, Decimals and Money

Fractions, decimals and money homework & practice 10.6.

Lesson: 7 Operations with Money

Lesson 10.7 Operations with Money

Operations with money homework & practice 10.7.

Performance Task

Relate Fractions and Decimals Performance Task 10

Relate fractions and decimals activity, relate fractions and decimals chapter practice 10.

Explore and Grow

One dime is what fraction of one dollar? Write your answer in words and as a fraction.

Answer: We know that, 1 dollar = 10 dimes So, The representation of one dime in the fraction of 1 dollar is: \(\frac{1}{10}\) In terms of words, one Dime is equal to one-tenth of the Dollar

Think and Grow: Understand Tenths

Show and Grow

Write the fraction or mixed number as a decimal.

Apply and Grow: Practice

Shade the model to represent the fraction or mixed number. Then write the fraction or mixed number as a decimal.

Explanation: The given mixed fraction is:5\(\frac{1}{10}\) So, The improper fraction of 5\(\frac{1}{10}\) is: \(\frac{51}{10}\) In 5\(\frac{1}{10}\), 5 represents the ones position and 1 represents the tenths position. The formula for converting fraction to a decimal is Decimal = Numerator ÷ Denominator Hence, The representation of 5\(\frac{1}{10}\) in the decimal form is: 5.1

Explanation: The given mixed fraction is: 24\(\frac{3}{10}\) So, The improper fraction of 24\(\frac{3}{10}\) is: \(\frac{243}{10}\) In 24\(\frac{3}{10}\), 2 represents the tens position 4 represents the one’s position 3 represents the tenths position The formula for converting fraction to a decimal is Decimal = Numerator ÷ Denominator Hence, The representation of 24\(\frac{3}{10}\) in the decimal form is: 24.3

Write the number as a fraction or mixed number and as a decimal.

Explanation: The given fraction is: \(\frac{6}{10}\) In \(\frac{6}{10}\), 6 represents the tenth’s position The formula for converting fraction to a decimal is Decimal = Numerator ÷ Denominator Hence, The representation of \(\frac{6}{10}\) in the Decimal form is: 0.6

Explanation: The given mixed fraction is: 11\(\frac{5}{10}\) So, The improper fraction of 11\(\frac{5}{10}\) is: \(\frac{115}{10}\) In 11\(\frac{5}{10}\), 1 represents Ten’s and 1 represents the one’s position 5 represents the tenth’s position The formula for converting fraction to a decimal is Decimal = Numerator ÷ Denominator Hence, the representation of 11\(\frac{5}{10}\) in the decimal form is: 11.5

Question 13. Writing Do 0.5 and 5.0 have the same value? Explain. Answer: 0.5 and 5.0 does not have the same value because the place-value of 5 is different in both 0.5 and 5.0

Think and Grow: Modeling Real Life

Question 15. DIG DEEPER! You have 10 apps on your tablet. Six of the apps are games. What portion of the apps on your tablet are not games? Write your answer as a decimal. Answer: The portion of the apps on your tablet that is not games in the fraction form is: \(\frac{4}{10}\)

Question 16. DIG DEEPER! You make 3 pans of lasagna for a party. You cut each pan of lasagna into10 equal pieces. The guests eat 22 pieces. Write the fraction and decimal that represent how many pans of lasagna the guests eat. Answer: The representation of the pans of lasagna the guests eat in the fraction form is: \(\frac{22}{30}\)

Write the fraction or mixed number as a decimal. Answer: The representation of 1\(\frac{8}{10}\) in the decimal form is: 1.8

Question 3. \(\frac{1}{10}\) Answer: The representation of \(\frac{1}{10}\) in the decimal form is: 0.1

Question 4. \(\frac{5}{10}\) Answer: The representation of \(\frac{5}{10}\) in the decimal form is: 0.5

Question 5. \(\frac{2}{10}\) Answer: The representation of \(\frac{2}{10}\) in the decimal form is: 0.2

Question 6. \(\frac{8}{10}\) Answer: The representation of \(\frac{8}{10}\) in the decimal form is: 0.8

Question 7. 4\(\frac{3}{10}\) Answer: The representation of 4\(\frac{3}{10}\) in the decimal form is: 4.3

Question 8. 1\(\frac{4}{10}\) Answer: The representation of 1\(\frac{4}{10}\) in the decimal form is: 1.4

Question 9. 31\(\frac{7}{10}\) Answer: The representation of 31\(\frac{7}{10}\) in the decimal form is: 31.7

Question 10. 40\(\frac{6}{10}\) Answer: The representation of 40\(\frac{6}{10}\) in the decimal form is: 40.6

Question 11. three tenths Answer: The representation of the three-tenths in the decimal form is: 0.3

Question 12. fourteen and nine-tenths Answer: The representation of fourteen and nine-tenths in the decimal form is: 14.9

Question 13. You knock down 5 out of 10 bowling pins. What portion of the bowling pins do you knockdown? Write your answer as a decimal. Answer: The portion the bowling pins did you knockdown is: \(\frac{5}{10}\) = 0.6

Answer:  The representation of 8\(\frac{7}{10}\) in the decimal form is: 8.7

Use the table. Answer: The number- cards represented by the model are: 1\(\frac{3}{10}\) and 1.3

Answer: The portion of the framed photographs that are of mammals in the decimal form is: 0.6

Question 17. DIG DEEPER! What portion of the framed not photographs are of mammals? Write your answer as a decimal. Answer: THe portion of the photographs that are not mammals in the decimal form is: 0.4

Review & Refresh

Find the product.

Explanation: By using the partial products method, 47 × 6 = ( 40 + 7 ) × 6 = ( 40 × 6 ) + ( 7 × 6 ) = 240 + 42 = 282 Hence, 47 × 6 = 282

Explanation: By using the partial products method, 961 × 3 = ( 900 + 60 + 1 ) × 3 = ( 900 × 3 ) + ( 60 × 3 ) + ( 1 × 3 ) = 2,700 + 180 + 3 = 2,883 Hence, 961 × 3 = 2,883

Explanation: By using the partial products method, 2,405 × 8 = ( 2,400 + 5 ) × 8 = ( 2,400 × 8 ) + ( 5 × 8 ) = 19,200 + 40 = 19,240 Hence, 2,405 × 8 = 19,240

One penny is what fraction of one dollar? Write your answer in words and as a fraction.

Answer: The representation of one penny into the dollar in the fraction form is: 0.01

Structure How is one-tenth related to one hundredth? How do you think you can write \(\frac{1}{100}\) in a place value chart?

Answer: The one-tenth is related to the one-hundredth as: \(\frac{1}{10}\)

Think and Grow: Understand Hundredths

The representation of 1\(\frac{34}{100}\) in the decimal form is: 1.34

Question 5. \(\frac{42}{100}\) Answer: The representation of \(\frac{42}{100}\) in the form of decimal number is: 0.42

Question 6. \(\frac{7}{100}\) Answer: The representation of \(\frac{7}{100}\) in the form of decimal number is: 0.07

Question 7. 4\(\frac{56}{100}\) Answer: The representation of 4\(\frac{56}{100}\) in the form of a decimal number is: 4.56

Question 8. 23\(\frac{9}{100}\) Answer: The representation of 23\(\frac{9}{100}\) in the form of a decimal number is: 23.09

Question 9. sixty-one hundredths Answer: The representation of sixty-one hundredths in the fraction form is: \(\frac{61}{100}\) The representation of sixty-one hundredths in the decimal form is: 0.61

Question 10. twelve and eighty-three hundredths Answer: The representation of twelve and eighty-three hundredths in the fraction form is: 12\(\frac{83}{100}\) The representation of twelve and eighty-three hundredths in the decimal form is: 12.83

Question 14. A book fair has 100 books. 60 of the books are chapter books. What portion of the books in the book fair are chapter books? Write your answer as a decimal. Answer: The portion of the chapter books out of the total number of books in the decimal form is: 0.60

Question 3. \(\frac{12}{100}\) Answer: The representation of \(\frac{12}{100}\) in the decimal form is: 0.12

Question 4. \(\frac{24}{100}\) Answer: The representation of \(\frac{24}{100}\) in the decimal form is: 0.24

Question 5. \(\frac{2}{100}\) Answer: The representation of \(\frac{2}{100}\) in the decimal form is: 0.02

Question 6. \(\frac{8}{100}\) Answer: The representation of \(\frac{8}{100}\) in the decimal form is: 0.08

Question 7. 2\(\frac{59}{100}\) Answer: The representation of 2\(\frac{59}{100}\) in the form of a decimal number is: 2.59

Question 8. 48\(\frac{31}{100}\) Answer: The representation of 48\(\frac{31}{100}\) in the form of a decimal number is: 48.31

Question 9. 6\(\frac{7}{100}\) Answer: The representation of 6\(\frac{7}{100}\) in the form of a decimal number is: 6.07

Question 10. 31\(\frac{6}{100}\) Answer: The representation of 31\(\frac{6}{100}\) in the form of a decimal number is: 31.06

Question 11. seventy-four hundredths Answer: The representation of seventy-four hundredths in the fraction form is: \(\frac{74}{100}\) The representation of seventy-four hundredths in the decimal form is: 0.74

Question 12. sixteen and thirty-one hundredths Answer: The representation of sixteen and thirty-one hundredths in the fraction form is: 16\(\frac{31}{100}\) The representation of sixteen and thirty-one hundredths in the decimal form is: 16.31

Write the value of the underlined digit.

Question 13. 5. 8 4 Answer: The value of 8 in 5.84 is: 0.8

Question 14. 2 1.03 Answer: The value of 2 in 21.03 is: 20

Question 15. 67.3 2 Answer: The value of 2 in 67.32 is: 0.02

Question 16. 5 06.19 Answer: The value of 5 in 506.19 is: 500

Question 19. YOU BE THE TEACHER Descartes writes 2\(\frac{40}{100}\) as 2.04. Is he correct? Explain. Answer: The representation of 2\(\frac{40}{100}\) in the form of a decimal number is: 2.40 So, Descartes is wrong.

Divide. Then check your answer.

Explanation: By using the partial quotients method, 1,308 ÷ 5 = ( 1,000 + 300 + 5 ) ÷ 5 = ( 1,000 ÷ 5 ) + ( 300 ÷ 5 ) + ( 5 ÷ 5 ) = 200 + 60 + 1 = 261 R 3 Hence, 1,308 ÷ 5 = 261 R 3

Explanation: By using the partial quotients method, 67 ÷ 4 = ( 56 + 8 ) ÷ 4 = ( 56 ÷ 4 ) + ( 8 ÷ 4 ) = 14 + 2 = 16 R 3 Henec, 67 ÷ 4 = 1 R 3

Explanation: By using the partial quotients method, 725 ÷ 2 = ( 720 + 4 ) ÷ 2 = ( 720 ÷ 2 ) + ( 4 ÷ 2 ) = 360 + 2 = 362 R 1 Hence, 75 ÷ 2 = 362 R 1

Reasoning What do you notice about the locations of the points? What can you conclude about the numbers?

Answer: From the above plots, we can see that the number of lines between any two numbers is the same whether the given number is in fraction form or in the decimal form So, from the above plots, we can conclude that the location of the numbers and the gap between the two numbers is the same.

Think and Grow: Fractions and Decimals

Question 1. Write \(\frac{9}{10}\) as hundredths in fraction form and decimal form. Answer: The representation of \(\frac{9}{10}\) as hundredths in the fraction form is: \(\frac{90}{100}\) The representation of \(\frac{90}{100}\) in the decimal form is: 0.90

Question 2. Write 0.20 as tenths in decimal form and fraction form. Answer: The representation of 0.20 as tenths in the fraction form is: \(\frac{2}{10}\) The representation of \(\frac{2}{10}\) in the decimal form is: 0.2

Write the number as tenths in fraction form and decimal form.

Question 3. \(\frac{80}{100}\) Answer: The representation of \(\frac{80}{100}\) as tenths in the fraction form is: \(\frac{8}{10}\) The representation of \(\frac{8}{10}\) in the decimal form is: 0.8

Question 4. \(\frac{50}{100}\) Answer: The representation of \(\frac{50}{100}\) as tenths in the fraction form is: \(\frac{5}{10}\) The representation of \(\frac{5}{10}\) in the decimal form is: 0.5

Question 5. 0.30 Answer: The representation of 0.30 as tenths in the fraction form is: \(\frac{3}{10}\) The representation of \(\frac{3}{10}\) in the decimal form is: 0.3

Write the number as hundredths in fraction form and decimal form.

Question 6. \(\frac{2}{10}\) Answer: The representation of \(\frac{2}{10}\) as hundredths in the fraction form is: \(\frac{20}{100}\) The representation of \(\frac{20}{100}\) in the decimal form is: 0.20

Question 7. 0.7 Answer: The representation of 0.7 as hundredths in the fraction form is: \(\frac{70}{100}\) The representation of \(\frac{70}{100}\) in the decimal form is: 0.70

Question 8. 2\(\frac{1}{10}\) Answer: The representation of 2\(\frac{1}{10}\) as hundredths in the fraction form is: 2\(\frac{10}{100}\) The representation of 2\(\frac{10}{100}\) in the decimal form is: 2.10

Question 9. A Answer: From the above number line, ‘A’ is: 0.4 The representation of 0.4 as hundredths in the fraction form is: \(\frac{40}{100}\) The representation of \(\frac{40}{100}\) in the decimal form is: 0.40

Question 10. B Answer: From the above number line, ‘B’ is: 0.9 The representation of 0.9 as hundredths in the fraction form is: \(\frac{90}{100}\) The representation of \(\frac{90}{100}\) in the decimal form is: 0.90

Question 11. C Answer: From the above number line, ‘C’ is: 1.5 The representation of 1.5 as hundredths in the fraction form is: \(\frac{150}{100}\) The representation of \(\frac{150}{100}\) in the decimal form is: 1.50

Question 1. \(\frac{40}{100}\) Answer: The representation of \(\frac{40}{100}\) as tenths in the fraction form is: \(\frac{4}{10}\) The representation of \(\frac{4}{10}\) in the decimal form is: 0.4

Question 2. \(\frac{70}{100}\) Answer: The representation of \(\frac{70}{100}\) as tenths in the fraction form is: \(\frac{7}{10}\) The representation of \(\frac{7}{10}\) in the decimal form is: 0.7

Question 3. 0.20 Answer: The representation of 2.20 as tenths in the fraction form is: \(\frac{2}{10}\) The representation of \(\frac{2}{10}\) in the decimal form is: 0.2

Write the number as hundredths in fraction form and decimal form

Question 4. \(\frac{8}{10}\) Answer: The representation of \(\frac{8}{10}\) as hundredths in the fraction form is: \(\frac{80}{100}\) The representation of \(\frac{80}{100}\) in the decimal form is: 0.80

Question 5. 0.5 Answer: The representation of 0.5 as hundredths in the fraction form is: \(\frac{50}{100}\) The representation of \(\frac{50}{100}\) in the decimal form is: 0.50

Question 6. 9\(\frac{6}{10}\) Answer: The representation of 9\(\frac{6}{10}\) as hundredths in the fraction form is: 9\(\frac{60}{100}\) The representation of 9\(\frac{60}{100}\) in the decimal form is: 9.60

Question 7. A Answer: From the above number line, ‘A’ is: 0.3 The representation of 0.3 as hundredths in the fraction form is: \(\frac{30}{100}\) The representation of \(\frac{30}{100}\) in the decimal form is: 0.30

Question 8. B Answer: From the above number line, ‘A’ is: 0.6 The representation of 0.6 as hundredths in the fraction form is: \(\frac{60}{100}\) The representation of \(\frac{60}{100}\) in the decimal form is: 0.60

Question 9. C Answer: From the above number line, ‘A’ is: 1.8 The representation of 1.8 as hundredths in the fraction form is: 1\(\frac{80}{100}\) The representation of 1\(\frac{80}{100}\) in the decimal form is: 1.80

Explanation: The given numbers are: 80 and 0.8 When we compare 80 and 0.8, We can say that 0.8 is the number that we can obtain when we divide 80 with 100 So, We can observe that 80 is the whole number and 0.8 is the decimal number We know that, The whole number is always greater than the decimal number. Hence, from the above, We can conclude that 80 is greater than 0.8 as 80 is greater than 8 according to Newton

Question 14.

Find the equivalent fraction

Explanation: The given fraction is \(\frac{4}{6}\) From the above fraction, the numerator and denominator are: 4 and 6 4 and 6 are the multiples of 2.  ( Since the  the numerator and the denominator are the even numbers ) So, We have to divide the \(\frac{4}{6}\) with 2 So, \(\frac{4}{6}=\frac{4 \div 2}{6 \div 2}=\frac{2}{3}\) Hence, The equivalent fraction of \(\frac{4}{6}\) is: \(\frac{2}{3}\)

Explanation: The given fraction is \(\frac{25}{100}\) From the above fraction, the numerator and denominator are: 25 and 100 25 and 100 are the multiples of 5.  ( Since the  the numerator and the denominator are the multiples of 5 ) So, We have to divide the \(\frac{25}{100}\) with 5 So, \(\frac{25}{100}=\frac{25 \div 5}{100 \div 5}=\frac{5}{20}\) Hence, The equivalent fraction of \(\frac{25}{100}\) is: \(\frac{5}{20}\)

Explanation: The given fraction is \(\frac{14}{8}\) From the above fraction, the numerator and denominator are: 14 and 8 14 and 8 are the multiples of 2.  ( Since the  the numerator and the denominator are the even numbers ) So, We have to divide the \(\frac{14}{8}\) with 2 So, \(\frac{14}{8}=\frac{14 \div 2}{8 \div 2}=\frac{7}{4}\) Hence, The equivalent fraction of \(\frac{14}{8}\) is: \(\frac{7}{4}\)

By using the models, we can compare the number of boxes for the comparison of the decimal numbers. Each box represents 1 unit out of 100 total units. So, The denominator will be the same i.e., the total number of boxes will be the same. So, we have to compare only numerators i.e., the number of colored boxes so that we can compare the decimal numbers

Reasoning How did you use your models to determine which decimal is greater?

Answer: For the comparison of the decimals, equate either the numerator or the denominator so that we can compare the numerators. If we compare the numerators, then we have to make the denominators equal If we compare the denominators, then we have to make the numerators equal Hence, in this way, we can compare the decimal numbers.

Think and Grow: Compare Decimals

Example Compare 0.7 and 0.07. Answer: 0.7 is greater than 0.07

Explanation: The given decimal numbers are: 0.7 and 0.07 The representation of 0.7 in the fraction form is: \(\frac{7}{10}\) The representation of 0.07 in the fraction form is: \(\frac{7}{100}\) So, for comparison, we have to make the denominators equal. So, Multiply \(\frac{7}{10}\) with 10 So for \(\frac{7}{10}\), The numerator is 7 and denominator is 10 So, The numerator 7 is multiplied by 10 and the denominator is also multiplied by 10 to make the denominators equal. So, The representation of \(\frac{7}{10}\) in the hundredth’s form is: \(\frac{70}{100}\) Hence, from the above, We can conclude that 0.7 is greater than 0.07 by comparing their fraction forms.

Example Compare 0.25 and 0.3.

Explanation:

Open-Ended Complete the statement to make it true.

Question 14. 9.43 < ____ Answer: Let the missing number be: 9.53 So, 9.43 < 9.53

Question 15. Precision Write the number that is halfway between 3.6 and 3.7. Explain how you found your answer. Answer: The number that is halfway between 3.6 and 3.7 is 3.65

Explanation: The given decimal numbers are: 3.6 and 3.7 We know that, The middle number between two numbers = (The given first number + The given second number) ÷ 2 So, The number that is halfway between 3.6 and 3.7 = (3.6 + 3.7) ÷ 2 = 7.3 ÷ 2 = 3.65 Hence, from the above, we can conclude that the number that is halfway between 3.6 and 3.7 is: 3.65

DIG DEEPER! Write whether the statement is true or false. If false, explain why

Explanation: The given numbers are: \(\frac{1}{10}\) and 0.07 The representation of 0.07 in the fraction form is: \(\frac{7}{100}\) So, for comparison, we have to convert \(\frac{1}{10}\) into hundredths form by multiplying \(\frac{1}{10}\) with 10. So, The representation of \(\frac{1}{10}\) as hundredths in the fraction form is: \(\frac{10}{100}\) The representation of 0.07 in the fraction form is: \(\frac{7}{100}\) Hence, from the above, we can conclude that \(\frac{1}{10}\) is greater than 0.07

Explanation: The given numbers are: 0.6 and \(\frac{36}{100}\) The representation of 0.6 in the fraction form is: \(\frac{6}{10}\) So, for comparison, we have to convert \(\frac{6}{10}\) into hundredths form by multiplying \(\frac{6}{10}\) with 10. So, The representation of \(\frac{6}{10}\) as hundredths in the fraction form is: \(\frac{60}{100}\) The representation of 0.36 in the fraction form is: \(\frac{36}{100}\) Hence, from the above, we can conclude that 0.6 is greater than \(\frac{36}{100}\)

Question 20. DIG DEEPER! Your water bottle is 0.25 full. Your friend’s water bottle is 0.5 full. You have more water than your friend. Explain how this is possible. Answer: This is not possible.

Explanation: It is given that your water bottle is 0.25 full and your friend’s water bottle is 0.5 full. So, we have to compare 0.25 and 0.5 The representation of 0.5 in the fraction form is: \(\frac{5}{10}\) The representation of 0.25 in the fraction form is: \(\frac{25}{100}\) So, for comparison, we have to convert \(\frac{5}{10}\) as hundredths by multiplying \(\frac{5}{10} \) with 10. So, The representation of \(\frac{5}{10}\) as hundredths in the fraction form is: \(\frac{50}{100}\) Hence, from the above, we can conclude that your friend’s water bottle has more water than you.

Explanation: The given decimal numbers are: 0.13 and 0.19 The given number line is:

Explanation: The given decimal numbers are: 4.70 and 4.7 The representation of 4.70 in the fraction form is: 4\(\frac{70}{100}\) The representation of 4.7 in the fraction form is: 4\(\frac{7}{10}\) So, to compare, we have to make the denominators equal. So, multiply 4\(\frac{7}{10}\) with 10 So, The representation of 4\(\frac{7}{10}\) as hundredth’s in the fraction form is: 4\(\frac{70}{100}\) Hence, from the above, We can conclude that 4.70 is equal to 4.7

Question 15. Precision Explain how to compare 0.46 and 0.48. Answer: 0.46 is less than 0.48

Explanation: Given that my number is greater than 0.6 and less than 0.7. So, The numbers might be: 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69 It is also given that the greatest digit in the number is in the tenths place. So, The numbers might be: 0.61, 0.62, 0.63, 0.64, 0.65 Hence, from the above, We can conclude that Descartes’s number might be: 0.61, 0.62, 0.63, 0.64, 0.65

Question 17. Modeling Real Life A traffic light is red for 23.4 seconds and green for 23.6 seconds. Does the traffic light stay red or green longer? Answer: The traffic light stay green for a long time

Round the number to the nearest hundred thousand

Question 19. 695,023 Answer: The nearest hundred thousand of 695,023 is: 700,000

Explanation: The given number is: 695,023 We know that, The value of a digit depends on the position of the digit So, The value of the nearest hundred thousand in 695,023 is: 700,000

Question 20. 246,947 Answer: The value of the nearest hundred thousand in 246,947 is: 200,000

Explanation: The given number is: 246,947 We know that, The value of a digit depends on the position of the digit So, The value of the nearest hundred thousand in 246,947 is: 200,000

Answer: The representation of the sum in the fraction form is: \(\frac{7}{10}\) + \(\frac{25}{100}\) = \(\frac{95}{100}\) The representation of the sum in the decimal form is: 0.25 + 0.7 = 0.95

Reasoning How can you add two decimal fractions with a denominator of 10? How can you add two decimal fractions with denominators of 10 and 100?

Answer: We add the two fractions only if their numerator or denominators are equal If there are fractions with different denominators, then we will make the denominators equal either by multiplying or by dividing the fractions and add the different fractions.

Think and Grow: Add Decimal Fractions and Decimals

Find the sum.

Explanation: The given fractions are: \(\frac{36}{100}\) and \(\frac{1}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{1}{10}\) as the hundredths, we have to multiply \(\frac{1}{10}\) by 10 So, The representation of \(\frac{1}{10}\) as hundredths in the fraction form is: \(\frac{10}{100}\) So, \(\frac{10}{100}\) + \(\frac{36}{100}\) = \(\frac{10 + 36}{100}\) = \(\frac{46}{100}\) The representation of \(\frac{46}{100}\) in the decimal form is: 0.46 Hence from the above, We can conclude that \(\frac{1}{10}\) + \(\frac{36}{100}\) = \(\frac{46}{100}\) The representation of \(\frac{46}{100}\) in the decimal for is: 0.46

Question 2. 0.5 + 0.25 = ____ Answer: The representation of the sum in the fraction form is: \(\frac{5}{10}\) + \(\frac{25}{100}\) = \(\frac{75}{100}\) The representation of 0.25 + 0.5 in the decimal form is: 0.75

Explanation: The given decimal numbers are: 0.5 and 0.25 So, convert the two decimal numbers in to respective fractions. So, The given fractions are: \(\frac{25}{100}\) and \(\frac{5}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{5}{10}\) as the hundredths, we have to multiply \(\frac{5}{10}\) by 10 So, The representation of \(\frac{5}{10}\) as hundredths in the fraction form is: \(\frac{50}{100}\) So, \(\frac{50}{100}\) + \(\frac{25}{100}\) = \(\frac{50 + 25}{100}\) = \(\frac{75}{100}\) The representation of \(\frac{75}{100}\) in the decimal form is: 0.75 Hence from the above, We can conclude that \(\frac{5}{10}\) + \(\frac{25}{100}\) = \(\frac{75}{100}\) The representation of \(\frac{75}{100}\) in the decimal for is: 0.75

Explanation: The given fractions are: \(\frac{37}{100}\) and \(\frac{4}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{4}{10}\) as the hundredths, we have to multiply \(\frac{4}{10}\) by 10 So, The representation of \(\frac{4}{10}\) as hundredths in the fraction form is: \(\frac{40}{100}\) So, \(\frac{40}{100}\) + \(\frac{37}{100}\) = \(\frac{40 + 37}{100}\) = \(\frac{77}{100}\) The representation of \(\frac{77}{100}\) in the decimal form is: 0.77 Hence from the above, We can conclude that \(\frac{4}{10}\) + \(\frac{37}{100}\) = \(\frac{77}{100}\) The representation of \(\frac{77}{100}\) in the decimal for is: 0.77

Explanation: The given fractions are: \(\frac{23}{100}\) and \(\frac{2}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{2}{10}\) as the hundredths, we have to multiply \(\frac{2}{10}\) by 10 So, The representation of \(\frac{2}{10}\) as hundredths in the fraction form is: \(\frac{20}{100}\) So, \(\frac{20}{100}\) + \(\frac{23}{100}\) = \(\frac{20 + 23}{100}\) = \(\frac{43}{100}\) The representation of \(\frac{43}{100}\) in the decimal form is: 0.43 Hence from the above, We can conclude that \(\frac{2}{10}\) + \(\frac{23}{100}\) = \(\frac{43}{100}\) The representation of \(\frac{43}{100}\) in the decimal for is: 0.43

Explanation: The given fractions are: \(\frac{19}{100}\) and \(\frac{7}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{7}{10}\) as the hundredths, we have to multiply \(\frac{7}{10}\) by 10 So, The representation of \(\frac{7}{10}\) as hundredths in the fraction form is: \(\frac{70}{100}\) So, \(\frac{70}{100}\) + \(\frac{19}{100}\) = \(\frac{70 + 19}{100}\) = \(\frac{89}{100}\) The representation of \(\frac{89}{100}\) in the decimal form is: 0.89 Hence from the above, We can conclude that \(\frac{7}{10}\) + \(\frac{19}{100}\) = \(\frac{89}{100}\) The representation of \(\frac{89}{100}\) in the decimal for is: 0.89

Question 6. 0.35 + 0.1 = ____ Answer: The representation of the sum in the fraction form is: \(\frac{1}{10}\) + \(\frac{35}{100}\) = \(\frac{45}{100}\) The representation of 0.35 + 0.1 in the decimal for is: 0.45

Explanation: The given decimal numbers are: 0.1 and 0.35 So, convert the two decimal numbers in to respective fractions. So, The given fractions are: \(\frac{35}{100}\) and \(\frac{1}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{1}{10}\) as the hundredths, we have to multiply \(\frac{1}{10}\) by 10 So, The representation of \(\frac{1}{10}\) as hundredths in the fraction form is: \(\frac{10}{100}\) So, \(\frac{10}{100}\) + \(\frac{35}{100}\) = \(\frac{10 + 35}{100}\) = \(\frac{45}{100}\) The representation of \(\frac{45}{100}\) in the decimal form is: 0.45 Hence from the above, We can conclude that \(\frac{1}{10}\) + \(\frac{35}{100}\) = \(\frac{45}{100}\) The representation of \(\frac{45}{100}\) in the decimal for is: 0.45

Question 7. 0.8 + 0.15 = ____ Answer: The representation of the sum in the fraction form is: \(\frac{8}{10}\) + \(\frac{15}{100}\) = \(\frac{95}{100}\) The representation of 0.15 + 0.8 in the decimal for is: 0.95

Explanation: The given decimal numbers are: 0.8 and 0.15 So, convert the two decimal numbers in to respective fractions. So, The given fractions are: \(\frac{15}{100}\) and \(\frac{8}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{8}{10}\) as the hundredths, we have to multiply \(\frac{8}{10}\) by 10 So, The representation of \(\frac{8}{10}\) as hundredths in the fraction form is: \(\frac{80}{100}\) So, \(\frac{80}{100}\) + \(\frac{15}{100}\) = \(\frac{80 + 15}{100}\) = \(\frac{95}{100}\) The representation of \(\frac{95}{100}\) in the decimal form is: 0.95 Hence from the above, We can conclude that \(\frac{8}{10}\) + \(\frac{15}{100}\) = \(\frac{95}{100}\) The representation of \(\frac{95}{100}\) in the decimal for is: 0.95

Question 8. 0.50 + 0.4 = __ Answer: The representation of the sum in the fraction form is: \(\frac{4}{10}\) + \(\frac{50}{100}\) = \(\frac{90}{100}\) The representation of 0.50 + 0.4 in the decimal for is: 0.90

Explanation: The given decimal numbers are: 0.4 and 0.50 So, convert the two decimal numbers in to respective fractions. So, The given fractions are: \(\frac{50}{100}\) and \(\frac{4}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{4}{10}\) as the hundredths, we have to multiply \(\frac{4}{10}\) by 10 So, The representation of \(\frac{4}{10}\) as hundredths in the fraction form is: \(\frac{40}{100}\) So, \(\frac{40}{100}\) + \(\frac{50}{100}\) = \(\frac{50 + 40}{100}\) = \(\frac{90}{100}\) The representation of \(\frac{90}{100}\) in the decimal form is: 0.90 Hence from the above, We can conclude that \(\frac{4}{10}\) + \(\frac{50}{100}\) = \(\frac{90}{100}\) The representation of \(\frac{90}{100}\) in the decimal for is: 0.90

Explanation: The given fractions are: \(\frac{48}{100}\), \(\frac{16}{100}\) and \(\frac{2}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{2}{10}\) as the hundredths, we have to multiply \(\frac{2}{10}\) by 10 So, The representation of \(\frac{2}{10}\) as hundredths in the fraction form is: \(\frac{20}{100}\) So, \(\frac{48}{100}\) + \(\frac{16}{100}\) + \(\frac{20}{100}\) = \(\frac{48 + 16 + 20}{100}\) = \(\frac{84}{100}\) The representation of \(\frac{84}{100}\) in the decimal form is: 0.84 Hence from the above, We can conclude that \(\frac{2}{10}\) + \(\frac{48}{100}\) + \(\frac{16}{100}\) = \(\frac{84}{100}\) The representation of \(\frac{84}{100}\) in the decimal for is: 0.84

Question 10. 0.3 + 0.25 + 0.1 = ___ Answer: The representation of the sum in the fraction form is: \(\frac{3}{10}\) + \(\frac{1}{10}\) + \(\frac{25}{100}\) = \(\frac{65}{100}\) The representation of 0.25 + 0.1 + 0.3 in the decimal for is: 0.65

Explanation: The given decimal numbers are: 0.3, 0.1 and 0.25 So, convert the three decimal numbers in to respective fractions. So, The given fractions are: \(\frac{25}{100}\) , \(\frac{3}{10}\) and \(\frac{1}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{1}{10}\) and \(\frac{3}{10}\) as the hundredths, we have to multiply \(\frac{5}{10}\) and \(\frac{3}{10}\) by 10 So, The representation of \(\frac{1}{10}\) as hundredths in the fraction form is: \(\frac{10}{100}\) The representation of \(\frac{3}{10}\) as hundredths in the fraction form is: \(\frac{30}{100}\) So, \(\frac{10}{100}\) + \(\frac{25}{100}\) + \(\frac{30}{100}\) = \(\frac{10 + 25 + 30}{100}\) = \(\frac{65}{100}\) The representation of \(\frac{65}{100}\) in the decimal form is: 0.65 Hence from the above, We can conclude that \(\frac{1}{10}\) + \(\frac{25}{100}\) + \(\frac{3}{10}\) = \(\frac{65}{100}\) The representation of \(\frac{65}{100}\) in the decimal for is: 0.65

Number Sense Find the sum.

Explanation: The given numbers are: 0.5 and \(\frac{29}{100}\) So, convert the decimal number in to respective fractions. So, The given fractions are: \(\frac{5}{10}\) and \(\frac{29}{100}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{5}{10}\) as the hundredths, we have to multiply \(\frac{5}{10}\) by 10 So, The representation of \(\frac{5}{10}\) as hundredths in the fraction form is: \(\frac{50}{100}\) So, \(\frac{50}{100}\) + \(\frac{29}{100}\) = \(\frac{50 + 29}{100}\) = \(\frac{79}{100}\) The representation of \(\frac{79}{100}\) in the decimal form is: 0.79 Hence from the above, We can conclude that \(\frac{5}{10}\) + \(\frac{29}{100}\) = \(\frac{79}{100}\) The representation of \(\frac{79}{100}\) in the decimal for is: 0.79

Explanation: The given numbers are: 0.75 and \(\frac{8}{10}\) So, convert the decimal number in to respective fractions. So, The given fractions are: \(\frac{8}{10}\) and \(\frac{75}{100}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{8}{10}\) as the hundredths, we have to multiply \(\frac{8}{10}\) by 10 So, The representation of \(\frac{8}{10}\) as hundredths in the fraction form is: \(\frac{80}{100}\) So, \(\frac{80}{100}\) + \(\frac{75}{100}\) = \(\frac{80 + 75}{100}\) = \(\frac{155}{100}\) The representation of \(\frac{155}{100}\) in the decimal form is: 1.55 Hence from the above, We can conclude that \(\frac{8}{10}\) + \(\frac{75}{100}\) = \(\frac{155}{100}\) The representation of \(\frac{155}{100}\) in the decimal for is: 1.55

Explanation: The representation of the sum in the fraction form is: \(\frac{5}{10}\) + \(\frac{5}{100}\) + \(\frac{55}{100}\) = \(\frac{110}{100}\) The representation of 0.55 + 0.5 + 0.05 in the decimal for is: 1.10

Explanation: The given decimal numbers are: 0.05, 0.5 and 0.55 So, convert the three decimal numbers in to respective fractions. So, The given fractions are: \(\frac{55}{100}\) , \(\frac{5}{10}\) and \(\frac{5}{100}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{5}{10}\)  as the hundredths, we have to multiply \(\frac{5}{10}\) by 10 So, The representation of \(\frac{5}{10}\) as hundredths in the fraction form is: \(\frac{50}{100}\) So, \(\frac{50}{100}\) + \(\frac{55}{100}\) + \(\frac{5}{100}\) = \(\frac{50 + 55 + 5}{100}\) = \(\frac{110}{100}\) The representation of \(\frac{110}{100}\) in the decimal form is: 1.10 Hence from the above, We can conclude that \(\frac{5}{10}\) + \(\frac{55}{100}\) + \(\frac{5}{100}\) = \(\frac{110}{100}\) The representation of \(\frac{110}{100}\) in the decimal for is: 1.10 or 1.1

Question 15. Each morning, you walk \(\frac{25}{100}\) mile to your friend’s house and then \(\frac{5}{10}\) mile to school. What fraction of a mile do you walk each morning? Answer: The fraction of a mile you walk each morning is: \(\frac{25}{100}\) + \(\frac{5}{10}\) = \(\frac{75}{100}\)

Explanation: It is given that each morning, you walk \(\frac{25}{100}\) mile to your friend’s house and then \(\frac{5}{10}\) mile to school. So, To find the portion of a mile you walk in the morning, you have to add the fractions. So, Now, first, we have to convert \(\frac{5}{10}\) as hundredths so that we can add both the fractions because denominators have to be equal for the addition. So, Multiply \(\frac{5}{10}\) with 10 to convert it as hundredths So, The representation of \(\frac{5}{10}\) as hundredths in the fraction form is: \(\frac{50}{100}\) So, \(\frac{25}{100}\) + \(\frac{50}{100}\) = \(\frac{75}{100}\) Hence, from the above, We can conclude that the portion of a mile you walk in the morning is: \(\frac{75}{100}\)

Explanation: It is given that you ride a zip line that is mile-long \(\frac{15}{100}\) mile long. You ride another zip line that is \(\frac{3}{10}\) mile long and your friend rides a total of \(\frac{40}{100}\) mile on zip lines. So, the given three fractions are: \(\frac{15}{100}\), \(\frac{3}{10}\) and \(\frac{40}{100}\) So, for the comparison of the three fractions, we have to make the denominators equal. So, we have to convert \(\frac{3}{10}\) as hundredths. So, We have to multiply \(\frac{3}{10}\) with 10 So, The representation of \(\frac{3}{10}\) as hundredths in the fraction form is: \(\frac{30}{100}\) Now, As the denominators are equal, compare the numerators. So, we have to compare 15, 30, and 40 By comparing, we can observe that 40 > 30 > 15 Hence, from the above, We can conclude that your friend rides farther on zip lines than you.

Question 17. DIG DEEPER! You ship a package that weighs 0.8 pounds. Your package is 0.75 pounds lighter than your friend’s package. How much does your friend’s package weigh? Write your answer in decimal form. Answer: The weight of your friend’s package is: 1.55 pounds

Explanation: The two given decimal numbers are: 0.8 and 0.75 It is given that your package is 0.75 pounds lighter than your friend’s package. So, The weight of your friend’s package = 0.8 + 0.75 Now, first, convert the given decimal numbers into fractions. So, The representation of 0.8 and 0.75 in the fraction forms is: \(\frac{8}{10}\) and \(\frac{75}{100}\) Now, for addition, we have to make the denominators of the two fractions equal. So, We have to multiply \(\frac{3}{10}\) with 10, to make the denominator equal to 100 So, The representation of \(\frac{3}{10}\) as hundredths in the fraction form is: \(\frac{30}{100}\) So, \(\frac{30}{100}\) + \(\frac{75}{100}\) = \(\frac{105}{100}\) The representation of \(\frac{105}{100}\) in the decimal form is: 1.05 Hence, from the above, We can conclude that the weight of your friend’s package in the decimal form is: 1.05 pounds

Explanation: The given fractions are: \(\frac{32}{100}\) and \(\frac{4}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{4}{10}\) as the hundredths, we have to multiply \(\frac{4}{10}\) by 10 So, The representation of \(\frac{4}{10}\) as hundredths in the fraction form is: \(\frac{40}{100}\) So, \(\frac{40}{100}\) + \(\frac{32}{100}\) = \(\frac{40 + 32}{100}\) = \(\frac{72}{100}\) The representation of \(\frac{72}{100}\) in the decimal form is: 0.72 Hence from the above, We can conclude that \(\frac{4}{10}\) + \(\frac{32}{100}\) = \(\frac{72}{100}\) The representation of \(\frac{72}{100}\) in the decimal for is: 0.72

Explanation: The given fractions are: \(\frac{3}{100}\) and \(\frac{8}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{8}{10}\) as the hundredths, we have to multiply \(\frac{8}{10}\) by 10 So, The representation of \(\frac{8}{10}\) as hundredths in the fraction form is: \(\frac{80}{100}\) So, \(\frac{80}{100}\) + \(\frac{3}{100}\) = \(\frac{80 + 3}{100}\) = \(\frac{83}{100}\) The representation of \(\frac{83}{100}\) in the decimal form is: 0.83 Hence from the above, We can conclude that \(\frac{8}{10}\) + \(\frac{3}{100}\) = \(\frac{83}{100}\) The representation of \(\frac{83}{100}\) in the decimal for is: 0.83

Explanation: The given fractions are: \(\frac{15}{100}\) and \(\frac{2}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{2}{10}\) as the hundredths, we have to multiply \(\frac{2}{10}\) by 10 So, The representation of \(\frac{2}{10}\) as hundredths in the fraction form is: \(\frac{20}{100}\) So, \(\frac{20}{100}\) + \(\frac{15}{100}\) = \(\frac{20 + 15}{100}\) = \(\frac{35}{100}\) The representation of \(\frac{35}{100}\) in the decimal form is: 0.35 Hence from the above, We can conclude that \(\frac{2}{10}\) + \(\frac{15}{100}\) = \(\frac{35}{100}\) The representation of \(\frac{35}{100}\) in the decimal for is: 0.35

Explanation: The given fractions are: \(\frac{45}{100}\) and \(\frac{1}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{1}{10}\) as the hundredths, we have to multiply \(\frac{1}{10}\) by 10 So, The representation of \(\frac{1}{10}\) as hundredths in the fraction form is: \(\frac{10}{100}\) So, \(\frac{10}{100}\) + \(\frac{45}{100}\) = \(\frac{10 + 45}{100}\) = \(\frac{55}{100}\) The representation of \(\frac{55}{100}\) in the decimal form is: 0.55 Hence from the above, We can conclude that \(\frac{1}{10}\) + \(\frac{45}{100}\) = \(\frac{55}{100}\) The representation of \(\frac{55}{100}\) in the decimal for is: 0.55

Explanation: The given fractions are: \(\frac{22}{100}\) and \(\frac{7}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{7}{10}\) as the hundredths, we have to multiply \(\frac{7}{10}\) by 10 So, The representation of \(\frac{7}{10}\) as hundredths in the fraction form is: \(\frac{70}{100}\) So, \(\frac{70}{100}\) + \(\frac{22}{100}\) = \(\frac{70 + 22}{100}\) = \(\frac{92}{100}\) The representation of \(\frac{92}{100}\) in the decimal form is: 0.92 Hence from the above, We can conclude that \(\frac{7}{10}\) + \(\frac{22}{100}\) = \(\frac{92}{100}\) The representation of \(\frac{92}{100}\) in the decimal for is: 0.92

Explanation: The given fractions are: \(\frac{17}{100}\) and \(\frac{5}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{5}{10}\) as the hundredths, we have to multiply \(\frac{5}{10}\) by 10 So, The representation of \(\frac{5}{10}\) as hundredths in the fraction form is: \(\frac{50}{100}\) So, \(\frac{50}{100}\) + \(\frac{17}{100}\) = \(\frac{50 + 17}{100}\) = \(\frac{67}{100}\) The representation of \(\frac{67}{100}\) in the decimal form is: 0.67 Hence from the above, We can conclude that \(\frac{5}{10}\) + \(\frac{17}{100}\) = \(\frac{67}{100}\) The representation of \(\frac{67}{100}\) in the decimal for is: 0.67

Question 7. 0.6 + 0.25 = ___ Answer: The representation of the sum in the fraction form is: \(\frac{6}{10}\) + \(\frac{25}{100}\) = \(\frac{85}{100}\) The representation of 0.25 + 0.6 in the decimal form is: 0.85

Explanation: The given decimal numbers are: 0.6 and 0.25 So, convert the two decimal numbers in to respective fractions. So, The given fractions are: \(\frac{25}{100}\) and \(\frac{6}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{6}{10}\) as the hundredths, we have to multiply \(\frac{6}{10}\) by 10 So, The representation of \(\frac{6}{10}\) as hundredths in the fraction form is: \(\frac{60}{100}\) So, \(\frac{60}{100}\) + \(\frac{25}{100}\) = \(\frac{60 + 25}{100}\) = \(\frac{85}{100}\) The representation of \(\frac{85}{100}\) in the decimal form is: 0.85 Hence from the above, We can conclude that \(\frac{6}{10}\) + \(\frac{25}{100}\) = \(\frac{85}{100}\) The representation of \(\frac{85}{100}\) in the decimal for is: 0.85

Question 8. 0.3 + 0.40 = ___ Answer: The representation of the sum in the fraction form is: \(\frac{3}{10}\) + \(\frac{40}{100}\) = \(\frac{70}{100}\) The representation of 0.40 + 0.3 in the decimal form is: 0.70

Explanation: The given decimal numbers are: 0.3 and 0.40 So, convert the two decimal numbers in to respective fractions. So, The given fractions are: \(\frac{40}{100}\) and \(\frac{3}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{3}{10}\) as the hundredths, we have to multiply \(\frac{3}{10}\) by 10 So, The representation of \(\frac{3}{10}\) as hundredths in the fraction form is: \(\frac{30}{100}\) So, \(\frac{30}{100}\) + \(\frac{40}{100}\) = \(\frac{30 + 40}{100}\) = \(\frac{70}{100}\) The representation of \(\frac{70}{100}\) in the decimal form is: 0.70 Hence from the above, We can conclude that \(\frac{3}{10}\) + \(\frac{40}{100}\) = \(\frac{70}{100}\) The representation of \(\frac{70}{100}\) in the decimal for is: 0.70

Question 9. 0.05 + 0.9 = ___ Answer: The representation of the sum in the fraction form is: \(\frac{9}{10}\) + \(\frac{5}{100}\) = \(\frac{95}{100}\) The representation of 0.05 + 0.9 in the decimal form is: 0.95

Explanation: The given decimal numbers are: 0.05 and 0.9 So, convert the two decimal numbers in to respective fractions. So, The given fractions are: \(\frac{5}{100}\) and \(\frac{9}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{9}{10}\) as the hundredths, we have to multiply \(\frac{9}{10}\) by 10 So, The representation of \(\frac{9}{10}\) as hundredths in the fraction form is: \(\frac{90}{100}\) So, \(\frac{5}{100}\) + \(\frac{90}{100}\) = \(\frac{5 + 90}{100}\) = \(\frac{95}{100}\) The representation of \(\frac{95}{100}\) in the decimal form is: 0.95 Hence from the above, We can conclude that \(\frac{9}{10}\) + \(\frac{5}{100}\) = \(\frac{95}{100}\) The representation of \(\frac{95}{100}\) in the decimal for is: 0.95

Explanation: The given fractions are: \(\frac{41}{100}\), \(\frac{22}{100}\) and \(\frac{3}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{3}{10}\) as the hundredths, we have to multiply \(\frac{3}{10}\) by 10 So, The representation of \(\frac{3}{10}\) as hundredths in the fraction form is: \(\frac{30}{100}\) So, \(\frac{41}{100}\) + \(\frac{22}{100}\) + \(\frac{30}{100}\) = \(\frac{41 + 22 + 30}{100}\) = \(\frac{93}{100}\) The representation of \(\frac{93}{100}\) in the decimal form is: 0.93 Hence from the above, We can conclude that \(\frac{3}{10}\) + \(\frac{41}{100}\) + \(\frac{22}{100}\) = \(\frac{93}{100}\) The representation of \(\frac{93}{100}\) in the decimal for is: 0.93

Question 11. 0.8 + 0.25 + 0.75 = ___ Answer: The representation of the sum in the fraction form is: \(\frac{8}{10}\) + \(\frac{75}{100}\) + \(\frac{25}{100}\) = \(\frac{180}{100}\) The representation of 0.25 + 0.75 + 0.8 in the decimal for is: 1.80

Explanation: The given decimal numbers are: 0.8, 0.75 and 0.25 So, convert the three decimal numbers in to respective fractions. So, The given fractions are: \(\frac{25}{100}\) , \(\frac{8}{10}\) and \(\frac{75}{100}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{8}{10}\)  as the hundredths, we have to multiply \(\frac{}{10}\) by 10 So, The representation of \(\frac{8}{10}\) as hundredths in the fraction form is: \(\frac{80}{100}\) So, \(\frac{80}{100}\) + \(\frac{25}{100}\) + \(\frac{75}{100}\) = \(\frac{80 + 25 + 75}{100}\) = \(\frac{180}{100}\) The representation of \(\frac{180}{100}\) in the decimal form is: 1.80 Hence from the above, We can conclude that \(\frac{8}{10}\) + \(\frac{25}{100}\) + \(\frac{75}{100}\) = \(\frac{180}{100}\) The representation of \(\frac{180}{100}\) in the decimal for is: 1.80

Answer: The representation of the sum in the fraction form is: \(\frac{1}{10}\) + \(\frac{9}{100}\) = \(\frac{19}{100}\) The representation of \(\frac{19}{100}\) in the decimal for is: 0.19

The representation of the sum in the fraction form is: \(\frac{2}{10}\) + \(\frac{18}{100}\) = \(\frac{38}{100}\) The representation of \(\frac{38}{100}\) in the decimal for is: 0.38

The representation of the sum in the fraction form is: \(\frac{3}{10}\) + \(\frac{27}{100}\) = \(\frac{57}{100}\) The representation of \(\frac{114}{100}\) in the decimal for is: 0.57 Now, Whwn we add all the three results, we will get The last result’s representation in the fraction form is: \(\frac{19}{100}\) + \(\frac{38}{100}\) + \(\frac{57}{100}\) = \(\frac{114}{100}\) The last result’s representation in the decimal form is: 0.19 + 0.38 + 0.57 = 1.14

Question 14. Modeling Real Life In an aquarium, \(\frac{5}{10}\) of the fish are red and \(\frac{3}{100}\) of the fish are yellow. What fraction of the fish is more? Answer: The fraction of the fish that is red is more in the aquarium

Explanation: It is given that in the aquarium, There are \(\frac{5}{10}\) of the fish are red and \(\frac{3}{100}\) of the fish are yellow. So, for comparison, we have to equal the denominators So, \(\frac{5}{10}\) has to be multiplied by 10 to make the denominator of \(\frac{5}{10}\) as hundredths So, The representation of \(\frac{5}{10}\) as hundredths in the fraction form is: \(\frac{50}{100}\) So, when we compare the fishes that are red and yellow, We will get that Red fishes > Yellow fishes hence, from the above, We can conclude that the red fishes are more than yellow fishes in the aquarium

Explanation: It is given that The total length of Leopard Gecko is: 0.05 + 0.06 = 0.11 m = \(\frac{11}{100}\) The length of Adult Electric Blue Gecko is: \(\frac{7}{100}\) So, from the above, We can say that the numerators of both the fractions are equal. So, when we compare, We can see that leopard gecko is longer than adult Electric Blue Gecko Hence, from the above, We can conclude that the Leopard Gecko is longer than the Adult Electric Blue Gecko

Question 16. 38 ÷ 4 Answer: 38 ÷ 4 = 9 R 2

Explanation: By using the partial quotients method, 38 ÷ 4 = ( 32 + 4 ) ÷ 4 = ( 32 ÷ 4 ) + ( 4 ÷ 4 ) = 8 + 1 = 9 R 2 Hence, 38 ÷ 4 = 9 R 2

Question 17. 641 ÷ 9 Answer: 641 ÷ 9 = 71 R 2

Explanation: By using the partial quotients method, 641 ÷ 9 = ( 630 + 9 ) ÷ 9 = ( 630 ÷ 9 ) + ( 9 ÷ 9 ( = 70 + 1 = 71 R 2 Hence, 641 ÷ 9 = 71 R 2

Question 18. 52 ÷ 7 Answer: 52 ÷ 7 = 7 R 3

Explanation: By using the partial quotients method, 52 ÷ 7 = (42 + 7 ) ÷ 7 = ( 42 ÷ 7 ) + ( 7 ÷ 7 ) = 6 + 1 = 7 R 3 Hence, 52 ÷ 7 = 7 R 3

Shade the model to show each money moment.

Answer: Here, we have taken the reference of 1 dollar and find out the amount by them that is equal to 1 dollar

Explanation: We know that, 1 Quarter = 0.25 dollar 1 dime = 0.1 dollar 1 nickel = 0.05 dollar 1 penny = 0.01 dollar Hence, the above values are marked in the above-given model.

How can you write each money amount as a fraction and a decimal in terms of dollars?

Answer: The representation of the Quarter, in the dollar in the fraction form is: \(\frac{25}{100}\) dollar The representation of the Quarter, in the dollar in the decimal form is: 0.25

The representation of the dime, in the dollar in the fraction form is: \(\frac{10}{100}\) dollar The representation of the dime, in the dollar in the decimal form is: 0.10

The representation of the nickel, in the dollar in the fraction form is: \(\frac{5}{100}\) dollar The representation of the nickel, in the dollar in the decimal form is: 0.05

The representation of the penny, in the dollar in the fraction form is: \(\frac{1}{100}\) dollar The representation of the penny, in the dollar in the decimal form is: 0.01

Explanation: We know that, 1 Quarter = 0.25 dollar 1 dime = 0.1 dollar 1 nickel = 0.05 dollar 1 penny = 0.01 dollar So, all the money moments are represented in the terms of dollars. So, the representation of all the money moments in terms of dollars in the fraction and the decimal forms is: The representation of the Quarter, in the dollar in the fraction form is: \(\frac{25}{100}\) dollar The representation of the Quarter, in the dollar in the decimal form is: 0.25

Think and Grow: Fractions, Decimals, and Money

Find the total money amount. Then write the amount as a fraction or mixed number and as a decimal.

Explanation: We know that, 1 Quarter = $0.25 1 nickel = $0.05 1 penny = $0.01 The given money is: 2 Quarters, 3 nickels, and 1 penny So, The total amount of money = ( 2 × 0.25 ) + ( 3 × 0.05 ) + ( 1 × 0.01 ) = 0.50 + 0.15 + 0.01 = 0.06 Hence, The total amount of money is: $0.06 The representation of $0.06 in the fraction form is: \(\frac{6}{100}\) dollar The representation of $0.06 in the decimal form is: $0.06

Explanation: We know that, 1 Quarter = $0.25 1 nickel = $0.05 The given money is: 2 dollars, 1 Quarter, and 1 nickel So, The total amount of money = ( 2 × 1 ) + ( 1 × 0.25 ) + ( 1 × 0.05 ) = 2 + 0.25 + 0.05 = 2.30 Hence, The total amount of money is: $2.30 The representation of $2.30 in the fraction form is: 2\(\frac{30}{100}\) dollar The representation of $2.30 in the decimal form is: $2.30

Explanation: We know that, 1 Quarter = $0.25 1 nickel = $0.05 1 dime = $0.10 1 penny = $0.01 The given money is: 6 pennies, 1 Quarter, 1 dime, and 1 nickel So, The total amount of money = ( 6 × 0.01 ) + ( 1 × 0.25 ) + ( 1 × 0.05 ) + ( 1 × 0.10 ) = 0.06 + 0.25 + 0.05 + 0.10 = 0.46 Hence, The total amount of money is: $0.46 The representation of $0.46 in the fraction form is: \(\frac{46}{100}\) dollar The representation of $0.46 in the decimal form is: $0.46

Explanation: We know that, 1 Quarter = $0.25 1 nickel = $0.05 4 Quarters = 1 dollar The given money is: 4 Quarters, 1 dollar, and 1 nickel So, The total amount of money = ( 1 × 1 ) + ( 4 × 0.25 ) + ( 1 × 0.05 ) = 1 + 1 + 0.05 = 2.05 Hence, The total amount of money is: $2.05 The representation of $2.05 in the fraction form is: 2\(\frac{5}{100}\) dollar The representation of $2.05 in the decimal form is: $2.05

Write the fraction or mixed number as a money amount and as a decimal.

Question 5. \(\frac{53}{100}\) Answer: The representation of \(\frac{53}{100}\) as the total amount of money is: $0.53

Explanation: The given fraction is: \(\frac{53}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $0.53

Question 6. \(\frac{4}{100}\) Answer: The representation of \(\frac{4}{100}\) as the total amount of money is: $0.04

Explanation: The given fraction is: \(\frac{4}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $0.04

Question 7. \(\frac{100}{100}\) Answer: The representation of \(\frac{100}{100}\) as the total amount of money is: $1

Explanation: The given fraction is: \(\frac{100}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $1

Question 8. 1\(\frac{22}{100}\) Answer: The representation of 1\(\frac{22}{100}\) as the total amount of money is: $1.22

Explanation: The given fraction is: 1\(\frac{22}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $1.22

Question 9. 1\(\frac{18}{100}\) Answer: The representation of 1\(\frac{18}{100}\) as the total amount of money is: $1.18

Explanation: The given fraction is: 1\(\frac{18}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $1.18

Question 10. 1\(\frac{70}{100}\) Answer: The representation of 1\(\frac{70}{100}\) as the total amount of money is: $1.70

Explanation: The given fraction is: 1\(\frac{70}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $1.70

Question 11. You find 1 dime, 3 nickels, and 2 pennies on the ground. How much money do you find? Write your answer in three different ways. Answer: The total amount of money you find on the ground is: $0.27

Explanation: The given amount that you find on the ground is: 1 dime, 3 nickels, and 2 pennies We know that, 1 dime = 0.10 dollars 1 nickel = $0.05 dollars 1 penny = $0.01 dollars So, The total amount of money you find on the ground = ( 1 × 0.10 ) + ( 3 × 0.05 ) + (2 × 0.01 ) = 0.10 + 0.15 + 0.02 = 0.27 Hence from the above, We can conclude that the three ways of representing the total amount of money is: The total amount of money you find on the ground is: $0.27 The representation of the total amount of money in the fraction form is: \(\frac{27}{100}\) dollar The representation of the total amount of money in the decimal form is: $0.27

Question 12. YOU BE THE TEACHER Your friend has three $1 bills and 2 pennies. Your friend writes, “I have $ 3.2.” Is your friend correct? Explain. Answer: No, your friend is wrong

Explanation: It is given that your friend has three $1 bills and 2 pennies. So, The given amount your friend has: 3 $1 bills and 2 pennies We know that, 1 penny = 0.01 dollars So, The total amount of money your friend has = ( 3 × 1 ) + ( 2 × 0.01 ) = 3 + 0.02 = 3.02 Hence, The total amount of money your friend has: $3.02 dollars or 3 dollars and 2 pennies But, your friend has written $3.02 as $3.20 which means 3 dollars and 2 dimes Hence, from the above, We can conclude that your friend is wrong

Question 13. DIG DEEPER! You have \(\frac{1}{4}\) dollar in coins. Draw two possible groups of coins that you could have. Answer: The possible group of coins that you could have for \(\frac{1}{4}\) is: Quarter

Explanation: It is given that you have \(\frac{1}{4}\) dollar in coins. But, we have al, the money moments in terms of 100. So, to make the denominator of \(\frac{1}{4}\) 100, multiply \(\frac{1}{4}\) by 25 So, The representation of \(\frac{1}{4}\) as hundredths in the fraction form is: \(\frac{25}{100}\) We know that, 1 Quarter = $0.25 Hence, from the above, We can conclude that the possible group of coins that you could have for \(\frac{1}{4}\) is: Quarter

Explanation: It is given that Newton has \(\frac{85}{100}\) dollar So, The amount of money that Newton has in the decimal form is: $0.85 But, it is also given that The cost of spinning toy is: \(\frac{99}{100}\) dollar So, for comparison, we have to make either the numerators or the denominators equal. Here, both the denominators are equal. So, we can compare both the fractions directly. So, by comparing, we get, 0.85 < 0.99 Hence, We can conclude that Newton can’t buy the spinning toy.

Explanation: It is given that Descartes has \(\frac{76}{100}\) dollar So, The amount of money that Descartes has in the decimal form is: $0.76 But, it is also given that The cost of bouncy ball is: \(\frac{50}{100}\) dollar So, for comparison, we have to make either the numerators or the denominators equal. Here, both the denominators are equal. So, we can compare both the fractions directly. So, by comparing, we get, 0.76 > 0.50 Hence, We can conclude that Descartes can buy the bouncy ball.

Question 15. You throw 3 dimes, 3 nickels, and 8 pennies into a fountain. Your friend throws 1 quarter, 4 nickels, and 5 pennies. Who throws a greater amount of money into the fountain? Answer: You throw a greater amount of money into the fountain when compared to your friend.

Explanation: It is given that you throw 3 dimes, 3 nickels, and 8 pennies and your friend throws 1 quarter, 4 nickels, and 5 pennies So, The amount that you have is: 3 dimes, 3 nickels, and 8 pennies The amount that your friend has is: 1 quarter, 4 nickels, and 5 pennies We know that, 1 quarter = $0.25 1 dime = $0.10 1 nickel = $0.05 1 penny = $0.01 So, The total amount of money you have = ( 3 × 0.10 ) + ( 3 × 0.05 ) + ( 8 × 0.01 ) = 0.30 + 0.15 + 0.08 = $0.53 The total amount of money your friend has = ( 1 × 0.25 ) + ( 4 × 0.05 ) + ( 5 × 0.01 ) = 0.25 + 0.20 + 0.05 = $0.50 Now, The representation of the amount of money you have in the fraction form is: \(\frac{53}{100}\) dollars The representation of the amount of money your friend has in the fraction form is: \(\frac{50}{100}\) dollars So, by comparing these two amounts, We can conclude that you have a greater amount of money than your friend

Write the money amount as a fraction or mixed number and as a decimal.

Question 1. $ 0.53 Answer: The representation of $0.53 as the total amount of money in the fraction form is: \(\frac{53}{100}\) dollar

Explanation: The given amount of money in the decimal form is: $0.53 The given decimal form will be given as an amount in dollars. So, The total amount of money in the fraction form is: \(\frac{53}{100}\) dollars The total amount of money in the decimal form is: $0.53

Question 2. $ 0.40 Answer: The representation of $0.40 as the total amount of money in the fraction form is: \(\frac{40}{100}\) dollar

Explanation: The given amount of money in the decimal form is: $0.40 The given decimal form will be given as an amount in dollars. So, The total amount of money in the fraction form is: \(\frac{40}{100}\) dollars The total amount of money in the decimal form is: $0.40

Question 3. $1.01 Answer: The representation of $1.01 as the total amount of money in the fraction form is: 1\(\frac{1}{100}\) dollar

Explanation: The given amount of money in the decimal form is: $1.01 The given decimal form will be given as an amount in dollars. So, The total amount of money in the fraction form is: 1\(\frac{1}{100}\) dollars The total amount of money in the decimal form is: $1.01

Explanation: We know that, 1 Quarter = $0.25 1 nickel = $0.05 1 dime = $0.10 The given money is: 1 Quarter, 2 dimes, and 4 nickel So, The total amount of money = ( 1 × 0.25 ) + ( 4 × 0.05 ) + ( 2 × 0.10 ) =  0.25 + 0.20 + 0.20 = 0.65 Hence, The total amount of money is: $0.65 The representation of $0.65 in the fraction form is: \(\frac{65}{100}\) dollar The representation of $0.65 in the decimal form is: $0.65

Explanation: We know that, 1 dime = $0.10 1 penny = $0.01 The given money is: 3 pennies, 1 dime, and 2 dollars So, The total amount of money = ( 3 × 0.01 ) + ( 2 × 1 ) + ( 1 × 0.10 ) = 0.03 + 2 + 0.10 = 2.13 Hence, The total amount of money is: $2.13 The representation of $2.13 in the fraction form is: 2\(\frac{13}{100}\) dollar The representation of $2.13 in the decimal form is: $2.13

Explanation: We know that, 1 Quarter = $0.25 1 dime = $0.10 1 penny = $0.01 The given money is: 2 pennies, 2 Quarters, 4 dimes So, The total amount of money = ( 2 × 0.01 ) + ( 2 × 0.25 ) + ( 4 × 0.10 ) = 0.02 +0.50 + 0.40 = 0.92 Hence, The total amount of money is: $0.92 The representation of $0.92 in the fraction form is: \(\frac{92}{100}\) dollar The representation of $0.92 in the decimal form is: $0.92

Explanation: We know that, 1 Quarter = $0.25 1 nickel = $0.05 1 dime = $0.10 The given money is: 4 Quarters, 2 dollars, 1 dime, and 1 nickel So, The total amount of money = ( 2 × 1 ) + ( 4 × 0.25 ) + ( 1 × 0.05 ) + ( 1 × 0.10 ) = 2 + 1 + 0.05 + 0.10 = 3.15 Hence, The total amount of money is: $3.15 The representation of $3.15 in the fraction form is: 3\(\frac{15}{100}\) dollar The representation of $3.15 in the decimal form is: $3.15

Question 8. \(\frac{87}{100}\) Answer: The representation of \(\frac{87}{100}\) as the total amount of money is: $0.87

Explanation: The given fraction is: \(\frac{87}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $0.87

Question 9. \(\frac{12}{100}\) Answer: The representation of \(\frac{12}{100}\) as the total amount of money is: $0.12

Explanation: The given fraction is: \(\frac{12}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $0.12

Question 10. 1\(\frac{9}{100}\) Answer: The representation of 1\(\frac{9}{100}\) as the total amount of money is: $1.09

Explanation: The given fraction is: 1\(\frac{9}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $1.09

Question 11. You find 3 quarters, 2 nickels, and 1 penny in your backpack. How much money do you find? Write your answer in three different ways. Answer: The amount of money you find is: $0.86

Explanation: It is given that you find 3 quarters, 2 nickels, and 1 penny in your backpack So, The amount of money you have is: 3 quarters, 2 nickels, and 1 penny We know that, 1 quarter = $0.25 1 nickel = $0.05 1 penny = $0.01 So, The total amount of money you have = ( 3 × 0.25 ) + ( 2 × 0.05 ) + ( 1 × 0.01 ) = 0.75 + 0.10 + 0.01 = 0.86 Hence, The total amount of money you have is: $0.86 The total amount of money you have in the fraction form is: \(\frac{86}{100}\) The total amount of money you have in the decimal form is: $0.86

Explanation: Le the amounts named as A, B, C, and D Now, A) 3 pennies  B) \(\frac{3}{10}\)  C) 0.30 dollars  D) \(\frac{30}{100}\) We know that, 1 penny = $0.01 So, 3 pennies = $0.03 Hence, from the above, we can conclude that A) does not belong to the other three.

Question 13. Reasoning Would you rather have \(\frac{2}{10}\) of a dollar or 6 nickels? Explain. Answer: You would rather have 6 nickels

Explanation: The given fraction is: \(\frac{2}{10}\) of a dollar So, The representation of \(\frac{2}{10}\) as hundredths in the fraction form is: \(\frac{20}{100}\) The representation of \(\frac{20}{100}\) in the decimal form is: 0.20 We know that, 1 nickel = $0.05 So, 6 nickels = 6 × 0.05 = $0.30 Now, When we compare the given fraction and 6 nickels, w can observe that 6 nickels > \(\frac{2}{10}\) of a dollar Hence, from the above, we can conclude that you would have to rather have 6 nickels than \(\frac{2}{10}\) of a dollar

Explanation: It is given that Newton has \(\frac{46}{10}\) dollar So, The representation of \(\frac{46}{10}\) in the decimal form is: $0.46 It is also given that, The cost of the key chain is: $0.49 Now, When we compare the fractions, we have to equate either the numerators or the denominators. Here, both the denominators are equal. So, When we compare, we will observe 0.46 < 0.49 Hence, from the above, We can conclude that Newton can’t buy the key chain

Question 15. DIG DEEPER! Descartes has $1. Can he buy 2 key chains? Explain how you know without calculating. Answer: Yes, Descartes can buy 2 key chains

Explanation: From the above problem, The cost of 1 key chain is: $0.49 It is given that Descartes has $1 and he wants to buy the 2 key chains So, The cost of 2 key chains = 0.49 + 0.49 = $0.98 But, Descartes has $1 So, The money that Descartes left = 1 – 0.98 = 0.02 Hence, from the above, We can conclude that Descartes can buy the 2 key chains

Explanation: The given fractions are: \(\frac{24}{100}\) and \(\frac{35}{100}\) So, for the addition of the fractions, we have to equate either both the numerators or both the denominators. Here, both the denominators are equal. Hence, \(\frac{24}{100}\) + \(\frac{35}{100}\) = \(\frac{59}{100}\)

Explanation: The given fractions are: \(\frac{10}{8}\) and \(\frac{3}{8}\) So, for the addition of the fractions, we have to see whether the denominators are equal or the numerators are equal. Here, both the denominators are equal. Hence, \(\frac{10}{8}\) + \(\frac{3}{8}\) = \(\frac{13}{8}\)

Explanation: The given fractions are: \(\frac{1}{10}\), \(\frac{3}{10}\) and \(\frac{6}{10}\) So, in addition, We have to equate either both the numerators or both the denominators. Here, The denominators of all the fractions are equal. Hence, \(\frac{1}{10}\) + \(\frac{3}{10}\) + \(\frac{6}{10}\) = \(\frac{10}{10}\)

• You pay for one of the toys with a $10 bill. What is your change?

Answer: Let the toy be an Action figure. Now, It is given that the cost of an Action figure is: $5.50 It is also given that you pay for one of the toys with a $10 bill So, Your change = 10 – 5.50 = $4.50 Hence, from the above, We can conclude that the change is: $4.50

2. You buy three of the same toys. How much do the toys cost in all?

3. You and your friend put your money together to buy some of the toys. The cashier gives you a $4.50 change. You want to share the change equally. How much money does each of you get?

Answer: It is given that you and your friend put your money together to buy some of the toys. It is also given that the cashier gives you a $4.50 change. So, The amount that should be shared equally between you and your friend = 4.50 ÷ 2 = (4 ÷ 2 ) + ( 0.50 ÷ 2 ) = 2 + 0.25 = 2.25 Hence, from the above, we can conclude that the amount that should be shared equally between you and your friend is: $2.25

Precision Compare your work to your partner’s.

Question 1. You pay a total of $2.25 for 3 granola bars. How much money does each bar cost? Draw bills and coins to solve. Answer: The amount of money does each bar cost is: $0.75

Explanation: It is given that you pay a total of $2.25 for 3 granola bars So, The amount of money that each bar cost = The total cost of 3 granola bars ÷ 3 = 2.25 ÷ 3 = 0.75 Hence, from the above, We can conclude that the amount of money does each ba cost is: $0.75

Question 2. You buy 2 stamps. Each stamp costs $0.49. How much money do you spend in all? Answer: The total amount of money you spend is: $0.98

Explanation: It is given that you buy 2 stamps and each stamp costs $0.49 So, The total amount of money you spent on buying stamps = The cost of each stamp × 2 = 0.49 × 2 = $0.98 Hence, from the above, we can conclude that the amount of money you spent on buying the 2 stamps is: $0.98

Question 3. Newton has $2.50. He spends $1.07 on a flying disk. How much money does Newton have left? Answer: The amount of money does Newton have left is: $1.43

Explanation: It is given that Newton has $2.50 and he spends $1.07 on a flying disk So, The amount of money does Newton have left = The amount of money that Newton has – The amount of money that Newton spent = 2.50 – 107 = $1.43 Hence, from the above, We can conclude that the amount of money does Newton have left is: $1.43

Question 4. A tube of toothpaste costs $2.71 and a toothbrush costs $1.62. How much more money does the toothpaste cost more than the toothbrush? Answer: The amount of money that the toothpaste cost more than the toothbrush is: $1.09

Explanation: It is given that a tube of toothpaste costs $2.71 and a toothbrush costs $1.62. So, The amount of money that the toothpaste cost more than the toothbrush = The cost of toothpaste -The cost of the toothbrush = 2.71 – 1.62 = $1.07 Hence, from the above, We can conclude that the more money does the toothpaste cost more than the toothbrush is: $1.07

Explanation: It is given that the two fingerboards cost a total of $7.20 It is also given that each fingerboard costs the same amount. So, The cost of each fingerboard = The cost of 2 fingerboards ÷ 2 = 7.20 ÷ 2 = ( 7 ÷ 2 ) + ( 0.2 ÷ 2 ) = 3.5 + 0.1 = 3.6 Hence, from the above, We can conclude that the cost of each fingerboard is: $0.36

Question 6. In Exercise 2, you pay for the stamps using a $1 bill. What is your change? Answer: From Exercise 2, The total cost of buying 2 stamps is: $0.98 In this exercise, it is given that you pay for the stamps using a $1 bill. So, The change = 1 – 0.98 = 0.02 Hence, from the above, We can conclude that The change after paying the $1 bill for paying the stamps is: $0.02

Question 7. You have four $1 bills and 3 dimes. Do you have enough money to buy the tube of toothpaste and the toothbrush in Exercise 4? Explain. Answer: No, you don’t have enough money to buy the tube of toothbrush and toothpaste which is explained in Exercise 4

Explanation: From Exercise 4, The total cost of money to buy the tube of toothpaste and the toothbrush = 2.71 + 1.62 = $4.33 It is given that you have 4 $1 bills and 3 dimes We know that, 1 dime = $0.10 So, The total amount of money you have = (4 × 1 ) + ( 3 × 0.10 ) = 4 + 0.30 = 4.30 Now, We have to compare 4.33 and 4.30 So, by comparing the 2 values, we will observe 4.33 > 4.30 Hence, from the above, We can conclude that you don’t have enough money to buy the toothpaste and the toothbrush

Question 9. You buy a gel pen that costs $1.10 and a school shirt that costs $5.85. You give the cashier $7. What is your change? Answer: The change is: $0.05

Explanation: It is given that you buy a gel pen that costs $1.10 and a school shirt that costs $5.85. So, The total cost of the gel pen and the school skirt = 5.85 + 1.10 = $ 6.95 It is also given that you give the cashier $7 So, the change = The money given to the cashier – The total cost of the gel pen and the school skirt = 7 – 6.95 = 0.05 Hence, from the above, We can conclude that the change is: $0.05

Question 10. You have $2.50. Your friend has 2 times as much money as you. How much money do you and your friend have altogether? Answer: The amount of money you and your friend have altogether is: $7.50

Explanation: It is given that you have $2.50 and your friend has 2 times as much money as you. So, The amount of money your friend has = 2.50 × 2 = $5 So, The amount of money you and your friend have altogether = The amount of money you have + The amount of money your friend has = 5 + 2.5 = $7.5 Hence, from the above, We can conclude that the amount of money you and your friend have altogether is: $7.50

Question 11. DIG DEEPER! You have $8.38. Your friend has $3.16. How much money can you give to your friend so that you each have the same amount? Answer: The amount of money you can give to your friend so that you each have the same amount = $5.22

Explanation: It is given that you have $8.38 and your friend has $3.16 So, The amount of money you can give to your friend so that you each have the same amount = The amount of money you have – The amount of money your friend has = 8.38 – 3.16 = $5.22 Hence, from the above, We can conclude that the amount of money you can give to your friend so that you each have the same amount is: $5.22

Draw bills and coins to solve.

Question 1. A sketch pad is $2.85 and a sketching pencil is $1.25. How much more money is the sketch pad than the sketching pencil? Answer: The amount of money the sketch pad needs more than the sketching pencil is: $1.60

Explanation: It is given that a sketch pad is $2.85 and a sketching pencil is $1.25. So, The cost of a sketch pad is: $2.85 The cost of a sketching pencil is: $1.25 So, the amount of money more than the sketching pencil = The cost of sketch pad – The cost of the sketching pencil = 2.85 – 1.25 = $1.60 Hence, from the above, We can conclude that the amount of money needed more than the sketching pencil is: $.1.60

Question 2. Descartes buys two toys for a total of $2.54. Each toy costs the same amount. How much does each toy cost? Answer: The cost of each boy is: $1.27

Explanation: It is given that Descartes buys 2 toys for a total of $2.54 and it is also given that each toy costs the same amount So, The cost of each toy = The total cost of the two toys ÷ 2 = 2.54 ÷ 2 = $1.27 Hence, from the above, We can conclude that the cost of each toy is: $1.27

Explanation: It is given that you have 4 bags of balloons and it is also given that the cost of each bag of balloon is $1.20 So, The total cost of the four bags of balloons = 4 × 1.20 = $4.80 hence, from the above, We can conclude that the cost of the four bags of balloons is: $4.80

Question 4. You have four $1 bills and 2 nickels. Do you have enough money to buy the sketch pad and the sketching pencil in Exercise 1? Explain. Answer: No, we have enough money to buy the sketch pad and the sketching pencil

Explanation: From Exercise 1, The total cost of the sketch pen and the sketching pencil = 2.85 + 1.25 = $4.10 In this exercise, it is given that you have 4 $1 bills and 2 nickels. We know that, 1 nickel = $0.05 So, The total amount of money = ( 4 × 1 ) + ( 2 × 0.05 ) =  + 0.1 = $4.1 So, The total amount from exercise 1 and the money you have are equal Hence, from the above, We can conclude that we have enough money to buy the sketch pen and the sketching pencil

Explanation: It is given that you have 3 jars, with $2.32 in each jar So, The total amount of money n the three jars = 3 × 2.32 = $6.96 It is also given that The cost of the model car is: $7.49 So, The amount of money needed more to buy the model car = The cost of the model car – The total amount of money in the three jars = 7.49 – 6.96 = $0.53 Hence, from the above, We can conclude that we don’t have enough money to buy the model car The amount of money needed more to buy the car is: $0.53

Question 6. DIG DEEPER! Descartes has 3 quarters, 1 dime, and 3 nickels. He wants to put the same amount of money into each of the two piggy banks. How can he do this with these coins? Answer: The amount of money in each of the two piggy banks is: $0.5

Explanation: It is given that Descartes has 3 quarters, 1 dime, and 3 nickels. So, The amount of money Descartes possess is: 3 quarters, 1 dime, and 3 nickels We know that, 1 quarter = $0.25 1 dime = $0.10 1 nickel = $0.05 So, The total amount of money Descartes possesses = ( 3 × 0.25 ) + ( 1 × 0.10 ) + ( 3 × 0.05 ) = 0.75 + 0.10 + 0.15 = $1.00 So, The amount of money in each of the two piggy banks = 1 ÷ 2 = $0.5 Hence, from the above, We can conclude that the amount of money in each of the two piggy banks is: $0.5

Explanation: It is given that you have bought some key chains as shown in the below figure.

Question 8. DIG DEEPER! Your class collects pennies and nickels in separate jars. Your class collects $5.87 in pennies and $2.65 in nickels. You divide the total amount of money collected between two charities. How many pennies do you put in the nickel jar so that both jars have the same amount of money? Answer: The total amount of money divided between the 2 charities is: $4.26 The number of pennies you need to put in the nickel jar is: $3.22

Explanation: It is given that your class collects pennies and nickels in separate jars. It is also given that your class collects $5.87 in pennies and $2.65 in nickels. It is given that you divide the total amount of money collected between two charities. So, The total amount of money collected by the class = 5.87 + 2.65 = $8.52 Now, The total amount of money divided between the 2 charities = 8.52 ÷ 2 = ( 8 ÷ 2 ) + ( 0.52 ÷ 2 ) = 4 + 0.26 = $ 4.26 Now, The amount of money needed more to add pennies into the nickel jars = 5.87 – 2.65 = $3.22 Hence, from the above, We can conclude that The total amount of money divided between the 2 charities is: $4.26 The number of pennies you need to put in the nickel jar is: $3.22

Write the product as a multiple of a unit fraction. Then find the product.

Explanation: The given fractions are: \(\frac{6}{1}\) and \(\frac{7}{12}\) For multiplication, Multiply numerators and denominators separately. So, \(\frac{6}{1}\) × \(\frac{7}{12}\) = \(\frac{6 × 7 }{1 × 12}\) = \(\frac{42}{12}\) For the simplified form of \(\frac{42}{12}\), divide \(\frac{42}{12}\) by 3 as 42 and 12 are the multiples of 3 Hence, \(\frac{7}{12}\) × \(\frac{6}{1}\) = \(\frac{42}{12}\) = \(\frac{14}{4}\)

Explanation: The given fractions are: \(\frac{2}{1}\) and \(\frac{5}{6}\) For multiplication, Multiply numerators and denominators separately. So, \(\frac{2}{1}\) × \(\frac{5}{6}\) = \(\frac{2 × 5 }{1 × 6}\) = \(\frac{10}{6}\) For the simplified form of \(\frac{10}{6}\), divide \(\frac{10}{6}\) by 2 as 10 and 6 are the multiples of 2 Hence, \(\frac{5}{6}\) × \(\frac{2}{1}\) = \(\frac{10}{6}\) = \(\frac{5}{3}\)

Explanation: The given fractions are: \(\frac{10}{1}\) and \(\frac{3}{8}\) For multiplication, Multiply numerators and denominators separately. So, \(\frac{10}{1}\) × \(\frac{3}{8}\) = \(\frac{10 × 3 }{1 × 8}\) = \(\frac{30}{8}\) For the simplified form of \(\frac{30}{8}\), divide \(\frac{30}{8}\) by 2 as 30 and 8 are the multiples of 2 Hence, \(\frac{5}{8}\) × \(\frac{10}{1}\) = \(\frac{30}{8}\) = \(\frac{15}{4}\)

You have a recipe to make one loaf of home made whole wheat bread. You want to make 8 loaves of bread.

Answer: The least amount of cups you need to add is: 3.25

Explanation: It is given that you need between 6.5 and 7 cups of whole wheat flour for one loaf of bread. It is given that you measured so far 3\(\frac{1}{4}\) cups of flour for one loaf So, The least number of cups you need to add to make one loaf of bread = 6.5 – 3\(\frac{1}{4}\) The representation of 3\(\frac{1}{4}\) in the decimal form is: 3.25 So, The least number of cups you need = 6.5 – 3.25 = 3.25 cups Hence, from the above, We can conclude that you need a minimum of 3.25 cups of wheat flour to make a loaf of bread

Answer: You should buy about 20 cups of flour to make all the bread

Explanation: It is given that we need about 4 cups of flour in 1 pound. So, The number of cups you need for five-pound bags = 4 × 5 = 20 cups Hence, from the above, We can conclude that we will need about 20 cups of flour to make all the bread

c. You use a $10 bill to buy enough bags of whole wheat flour for 8 loaves. What is your change? Answer: Your change is: $4.8

Explanation: It is given that you use a $10 bill to buy enough bags of whole wheat flour for 8 loaves. So, The total cost of wheat flour = 2.69 × 2 = $5.38 So, Your change = 10 – 5.38 = $4.62 Hence, from the above, We can conclude that the change is: $4.62

Answer: The number of cups of warm water you need for all the bread is: 18 cups

Explanation: It is given that you need to add 2\(\frac{1}{4}\) cups of warm water for one loaf of bread. But, it is given for the whole read, there are 8 loaves of bread. So, The total number of cups you need to make all the bread = 2\(\frac{1}{4}\) × 8 = 2.25 × 8 = 18 cups Hence, from the above, We can conclude that we will need 18 cups of warm water to make all the whole bread

b. You find the temperatures of 3 different samples of water. Which sample of water should you use? Explain. Answer: We will use a C sample of water

Decimal Boss

Directions:

• Divide the Decimal Boss Cards equally between both players.
• Each player flips a Decimal Boss Card.
• Players compare their numbers. The player with the greater number takes both cards.
• The player with the most cards at the end of the round wins!

10.1 Understand Tenths

Question 1. \(\frac{8}{10}\) Answer: The representation of \(\frac{8}{10}\) in the decimal form is: 0.8

Question 2. \(\frac{3}{10}\) Answer: The representation of \(\frac{3}{10}\) in the decimal form is: 0.3

Question 3. 6\(\frac{7}{10}\) Answer: The representation of 6\(\frac{7}{10}\) in the decimal form is: 6.7

Question 4. 15\(\frac{4}{10}\) Answer: The representation of 15\(\frac{4}{10}\) in the decimal form is: 15.4

Question 5. two tenths Answer: The representation of two-tenths in the fraction form is: \(\frac{2}{10}\) The representation of two-tenths in the decimal form is: 0.2

Question 6. thirteen and six tenths Answer: The representation of thirteen and six-tenths in the fraction form is: 13\(\frac{6}{10}\) The representation of thirteen and six-tenths in the decimal form is: 13.6

Explanation: It is given that you bake 2 loaves of banana bread and you cut each banana bread into 10 pieces So, The total number of pieces is: 20 pieces It is also given that the guests eat 18 pieces. So, The number of pieces eaten by guests is: 18 So, The representation of the loaves that the guests eat in the fraction form is: \(\frac{18}{20}\) The representation of the loaves that the guests eat in the decimal form is: 0.9

10.2 Understand Hundredths

Question 8. \(\frac{10}{100}\) Answer: The representation of \(\frac{10}{100}\) in the form of decimal number is: 0.10

Question 9. \(\frac{6}{100}\) Answer: The representation of \(\frac{6}{100}\) in the form of decimal number is: 0.06

Question 10. 8\(\frac{75}{100}\) Answer: The representation of 8\(\frac{75}{100}\) in the form of a decimal number is: 8.75

Question 11. 34\(\frac{2}{100}\) Answer: The representation of 34\(\frac{2}{100}\) in the form of a decimal number is: 34.02

Question 12. thirty-seven hundredths Answer: The representation of thirty-seven hundredths in the fraction form is: \(\frac{37}{100}\) The representation of thirty-seven hundredths in the decimal form is: 0.37

Question 13. nineteen and forty-one hundredths Answer: The representation of nineteen and forty-seven hundredths in the fraction form is: 19\(\frac{47}{100}\) The representation of nineteen and forty-seven hundredths in the decimal form is: 19.47

10.3 Fractions and Decimals

Question 14. \(\frac{30}{100}\) Answer: The representation of \(\frac{30}{100}\) as tenths in the fraction form is: \(\frac{3}{10}\) The representation of \(\frac{3}{10}\) in the decimal form is: 0.3

Question 15. \(\frac{90}{100}\) Answer: The representation of \(\frac{90}{100}\) as tenths in the fraction form is: \(\frac{39{10}\) The representation of \(\frac{39}{10}\) in the decimal form is: 0.9

Question 16. 0.50 Answer: The representation of 0.50 as tenths in the fraction form is: \(\frac{5}{10}\) The representation of \(\frac{5}{10}\) in the decimal form is: 0.5

Question 17. \(\frac{7}{10}\) Answer: The representation of \(\frac{7}{10}\) as hundredths in the fraction form is: \(\frac{70}{100}\) The representation of \(\frac{70}{100}\) in the decimal form is: 0.70

Question 18. \(\frac{4}{10}\) Answer: The representation of \(\frac{4}{10}\) as hundredths in the fraction form is: \(\frac{40}{100}\) The representation of \(\frac{40}{100}\) in the decimal form is: 0.40

Question 19. 0.6 Answer: The representation of 0.6 as hundredths in the fraction form is: \(\frac{60}{100}\) The representation of \(\frac{60}{100}\) in the decimal form is: 0.60

10.4 Compare Decimals

Question 25. ___ > 40.48 Answer: 40.58 is greater than 40.48

Explanation: It is given that Newton’s number will be between 0.2 and 0.3 So, Newton’s number might be: 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29 It is also given that the highest digit will be in the hundredth’s place Hence, Newton’s number might be: 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29

10.5 Add Decimal Fractions and Decimals

Explanation: The given fractions are: \(\frac{14}{100}\) and \(\frac{6}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{6}{10}\) as the hundredths, we have to multiply \(\frac{6}{10}\) by 10 So, The representation of \(\frac{6}{10}\) as hundredths in the fraction form is: \(\frac{60}{100}\) So, \(\frac{60}{100}\) + \(\frac{14}{100}\) = \(\frac{60 + 14}{100}\) = \(\frac{74}{100}\) The representation of \(\frac{74}{100}\) in the decimal form is: 0.74 Hence from the above, We can conclude that \(\frac{6}{10}\) + \(\frac{14}{100}\) = \(\frac{74}{100}\) The representation of \(\frac{74}{100}\) in the decimal for is: 0.74

Explanation: The given fractions are: \(\frac{52}{100}\) and \(\frac{3}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{3}{10}\) as the hundredths, we have to multiply \(\frac{3}{10}\) by 10 So, The representation of \(\frac{3}{10}\) as hundredths in the fraction form is: \(\frac{30}{100}\) So, \(\frac{30}{100}\) + \(\frac{52}{100}\) = \(\frac{30 + 52}{100}\) = \(\frac{82}{100}\) The representation of \(\frac{82}{100}\) in the decimal form is: 0.82 Hence from the above, We can conclude that \(\frac{3}{10}\) + \(\frac{52}{100}\) = \(\frac{82}{100}\) The representation of \(\frac{82}{100}\) in the decimal for is: 0.82

Question 29. 0.12 + 0.6 = ___ Answer: The representation of the sum in the fraction form is: \(\frac{6}{10}\) + \(\frac{12}{100}\) = \(\frac{72}{100}\) The representation of 012 + 0.6 in the decimal form is: 0.72

Explanation: The given decimal numbers are: 0.6 and 0.12 So, convert the two decimal numbers in to respective fractions. So, The given fractions are: \(\frac{12}{100}\) and \(\frac{6}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{6}{10}\) as the hundredths, we have to multiply \(\frac{6}{10}\) by 10 So, The representation of \(\frac{6}{10}\) as hundredths in the fraction form is: \(\frac{60}{100}\) So, \(\frac{60}{100}\) + \(\frac{12}{100}\) = \(\frac{60 + 12}{100}\) = \(\frac{72}{100}\) The representation of \(\frac{72}{100}\) in the decimal form is: 0.72 Hence from the above, We can conclude that \(\frac{6}{10}\) + \(\frac{12}{100}\) = \(\frac{72}{100}\) The representation of \(\frac{72}{100}\) in the decimal for is: 0.72

Question 30. 0.4 + 0.72 = ___ Answer: The representation of the sum in the fraction form is: \(\frac{4}{10}\) + \(\frac{72}{100}\) = \(\frac{112}{100}\) The representation of 0.4 + 0.72 in the decimal form is: 1.12

Explanation: The given decimal numbers are: 0.4 and 0.72 So, convert the two decimal numbers in to respective fractions. So, The given fractions are: \(\frac{72}{100}\) and \(\frac{4}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{4}{10}\) as the hundredths, we have to multiply \(\frac{4}{10}\) by 10 So, The representation of \(\frac{4}{10}\) as hundredths in the fraction form is: \(\frac{40}{100}\) So, \(\frac{40}{100}\) + \(\frac{72}{100}\) = \(\frac{72 + 40}{100}\) = \(\frac{112}{100}\) The representation of \(\frac{112}{100}\) in the decimal form is: 1.12 Hence from the above, We can conclude that \(\frac{4}{10}\) + \(\frac{72}{100}\) = \(\frac{112}{100}\) The representation of \(\frac{112}{100}\) in the decimal for is: 1.12

Explanation: The given fractions are: \(\frac{23}{100}\), \(\frac{36}{100}\) and \(\frac{2}{10}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{2}{10}\) as the hundredths, we have to multiply \(\frac{2}{10}\) by 10 So, The representation of \(\frac{2}{10}\) as hundredths in the fraction form is: \(\frac{20}{100}\) So, \(\frac{23}{100}\) + \(\frac{36}{100}\) + \(\frac{20}{100}\) = \(\frac{23 + 36 + 20}{100}\) = \(\frac{79}{100}\) The representation of \(\frac{79}{100}\) in the decimal form is: 0.79 Hence from the above, We can conclude that \(\frac{2}{10}\) + \(\frac{23}{100}\) + \(\frac{36}{100}\) = \(\frac{79}{100}\) The representation of \(\frac{79}{100}\) in the decimal for is: 0.79

Question 32. 0.18 + 0.2 + 0.07 = ___ Answer: The representation of the sum in the fraction form is: \(\frac{2}{10}\) + \(\frac{18}{100}\) + \(\frac{7}{100}\) = \(\frac{45}{100}\) The representation of 0.18 + 0.2 + 0.07 in the decimal for is: 0.45

Explanation: The given decimal numbers are: 0.18, 0.2 and 0.07 So, convert the three decimal numbers in to respective fractions. So, The given fractions are: \(\frac{18}{100}\) , \(\frac{2}{10}\) and \(\frac{7}{100}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{2}{10}\)  as the hundredths, we have to multiply \(\frac{2}{10}\)  by 10 So, The representation of \(\frac{2}{10}\) as hundredths in the fraction form is: \(\frac{20}{100}\) So, \(\frac{20}{100}\) + \(\frac{18}{100}\) + \(\frac{7}{100}\) = \(\frac{20 + 18 + 7}{100}\) = \(\frac{45}{100}\) The representation of \(\frac{45}{100}\) in the decimal form is: 0.45 Hence from the above, We can conclude that \(\frac{2}{10}\) + \(\frac{18}{100}\) + \(\frac{7}{100}\) = \(\frac{45}{100}\) The representation of \(\frac{45}{100}\) in the decimal for is: 0.45

Explanation: The given numbers are: 0.5 and \(\frac{48}{100}\) So, convert the decimal number in to respective fractions. So, The given fractions are: \(\frac{5}{10}\) and \(\frac{48}{100}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{5}{10}\) as the hundredths, we have to multiply \(\frac{5}{10}\) by 10 So, The representation of \(\frac{5}{10}\) as hundredths in the fraction form is: \(\frac{50}{100}\) So, \(\frac{50}{100}\) + \(\frac{48}{100}\) = \(\frac{50 + 48}{100}\) = \(\frac{98}{100}\) The representation of \(\frac{98}{100}\) in the decimal form is: 0.98 Hence from the above, We can conclude that \(\frac{5}{10}\) + \(\frac{48}{100}\) = \(\frac{98}{100}\) The representation of \(\frac{98}{100}\) in the decimal for is: 0.98

Explanation: The given numbers are: 0.25 and \(\frac{9}{10}\) So, convert the decimal number in to respective fractions. So, The given fractions are: \(\frac{9}{10}\) and \(\frac{25}{100}\) For addition, we have to make either denominators or the numerators equal. so, For making \(\frac{9}{10}\) as the hundredths, we have to multiply \(\frac{9}{10}\) by 10 So, The representation of \(\frac{9}{10}\) as hundredths in the fraction form is: \(\frac{90}{100}\) So, \(\frac{90}{100}\) + \(\frac{25}{100}\) = \(\frac{90 + 25}{100}\) = \(\frac{115}{100}\) The representation of \(\frac{115}{100}\) in the decimal form is: 1.15 Hence from the above, We can conclude that \(\frac{9}{10}\) + \(\frac{25}{100}\) = \(\frac{115}{100}\) The representation of \(\frac{115}{100}\) in the decimal for is: 1.15

10.6 Fractions, Decimals, and Money

Explanation: We know that, 1 Quarter = $0.25 1 nickel = $0.05 1 penny = $0.01 The given money is: 3 pennies, 4 Quarters, and 2 nickels So, The total amount of money =  ( 4 × 0.25 ) + ( 2 × 0.05 ) + ( 3 × 0.01 ) = 1 + 0.10 + 0.03 = 1.13 Hence, The total amount of money is: $1.13 The representation of $1.13 in the fraction form is: 1\(\frac{13}{100}\) dollar The representation of $1.13 in the decimal form is: 1.13

Explanation: We know that, 1 Quarter = $0.25 1 nickel = $0.05 1 penny = $0.01 The given money is: 1 penny, 4 Quarters, 1 dollar, and 2 nickels So, The total amount of money = ( 1 × 1 ) + ( 4 × 0.25 ) + ( 2 × 0.05 ) + ( 1 × 0.01 ) = 1 + 1 + 0.1 + 0.01 = 2.11 Hence, The total amount of money is: $2.11 The representation of $2.11 in the fraction form is: 2\(\frac{11}{100}\) dollar The representation if $2.11 in the decimal form is: 2.11

Question 37. Write \(\frac{18}{100}\) as a money amount and as a decimal. Answer: The representation of \(\frac{18}{100}\) as the total amount of money is: $0.18

Explanation: The given fraction is: \(\frac{18}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $0.18

Question 38. Write $0.94 as a fraction and as a decimal. Answer: The representation of 0.94 as the total amount of money is: $0.94

Explanation: The given decimal number is: 0.94 So, The representation of 0.94 in the fraction form is: \(\frac{94}{100}\) The given fraction will be given as an amount in dollars. So, The total amount of money in the decimal form is: $0.94

10.7 Operations with Money

Question 39. Bananas cost $0.29 per pound. You buy 3 pounds of bananas. How much money do you spend in all? Answer: The total amount of money you spent is: $0.87

Explanation: It is given that bananas cost $0.29 per pound and you bought 3 pounds of bananas So, The cost of bananas per pound is: $0.29 So, The cost of 3 pounds of bananas = 3 × 0.29 = $0.87 hence, from the above, We can conclude that the total amount of money you spent is: $0.89

Question 40. Descartes has $3.50. He spends $1.75 on a journal. How much money does Descartes have left? Answer: The amount of money Descartes left is: $1.75

Explanation: It is given that Descartes has $3.50 and he spent $1.75 on a journal So, The total amount of money Descartes has: $3.50 The amount of money Descartes spent is: $1.75 So, The amount of money Descartes left = The total amount of money Descartes has – The amount of money Descartes spent = 3.50 – 1.75 = $1.75 Hence, from the above, We can conclude that the amount of money Descartes left is: $1.75

Conclusion:

All detailed and step by step explanations are covered in the Big Ideas Math Answers Grade 4 Chapter 10 Relate Fractions and Decimals. The solutions are prepared by the highly experienced subject experts after the ample research. This will help you to score the highest marks in the exams. Keep in touch with us to get the solution key of all Big Ideas Math Grade 4 Chapters.

Leave a Comment Cancel Reply

You must be logged in to post a comment.

Please ensure that your password is at least 8 characters and contains each of the following:

• a special character: @$#!%*?&

• Privacy Policy
• Terms of Use

Processing Request...

U2.4 Imperfect Practice 2

Created by Profe Egashira

Charts & Printables

Be faster with shortcuts

Check answer:

Add accent:

Are you sure you want to restart your practice?

Your practice score will be lost. To save it, press NO and then click Record Score

500 attempts is the limit per practice. If you want to practice more, start a new practice

You are not logged in to record this score

• Instructions

When ready, press start.

Timer is set to 5 minutes by default.

Customize Your Practice

Here's how you did, your privacy.

We use cookies to improve your experience on our site. By pressing ACCEPT, you agree to our use of cookies to process your personal data to personalize your experience.

• Texas Go Math
• Big Ideas Math
• enVision Math
• EngageNY Math
• McGraw Hill My Math
• 180 Days of Math
• Math in Focus Answer Key
• Math Expressions Answer Key
• Privacy Policy

Texas Go Math Grade 3 Lesson 10.4 Answer Key Relate Subtraction and Division

Refer to our Texas Go Math Grade 3 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 3 Lesson 10.4 Answer Key Relate Subtraction and Division.

Essential Question How is division related to subtraction? Answer: Repeated Subtraction is a method that subtracts the equal number of items from a group, also known as division.

Unlock the Problem Serena and Mandy brought a total of 12 newspapers to school for the recycling program. Each girl brought in one newspaper each day. For how many days did the girls bring in newspapers?

• How many newspapers were brought in altogether? Answer: 12 newspapers Explanation: Serena and Mandy brought a total of 12 newspapers to school for the recycling program. Each girl brought in one newspaper each day. Total number of days girls bring the newspaper 12 ÷ 1 = 12

• How many newspapers did the two girls bring in altogether each day? Answer: 2 newspapers Explanation: Serena and Mandy brought a total of 12 newspapers to school for the recycling program. Total newspapers the two girls bring in altogether each day is 2

One Way Use repeated subtraction.

• Start with 12.
• Subtract 2 until you reach 0.
• Count the number times you subtract 2.

Error Alert Be sure to keep subtracting 2 until you are unable to subtract 2 anymore.

Read: Twelve divided by two equal six.

Another Way Count back on a number line.

• Start at 12.
• Count back by 2s as many times as you can. Draw the rest of the jumps on the number line.
• Count the number of times you jumped back 2.

Math Talk Mathematical Processes Explain in your own words how you found the answer.

Math Talk Mathematical Processes Explain how counting back on a number line is like using repeated subtraction. Answer: Repeated Subtraction is a method that subtracts the equal number of items from a group, also known as division

Write a division equation.

Problem Solving

Question 4. Matt puts his box tops in 2 equal piles. How many box tops are in each pile?

Go Math Lesson 10.4 3rd Grade Answer Key Question 6. Write Math What’s the Question? Dwayne puts all his box tops into bins. He puts an equal number in each bin. The answer is 5. What’s the question? Answer: 3 equal number of box tops in each bin. Explanation: Dwayne has 15 box tops. the answer is given as 5 So, 15 ÷ 5 = 3 He puts 3 equal numbers of box tops in each bin.

Question 7. H.O.T. Pose a Problem Write a word problem about collecting box tops that can be solved by using the division equation 28 ÷ 7 = 4. Then solve the problem. Answer: Paige adds 3 more box tops and puts in 7 equal piles. How many box tops are in each box? Each box has 4 box tops. Explanation: Paige have 25 box tops Paige adds 3 more box tops and puts in 7 equal piles. Total box tops in each box 28 ÷ 7 = 4. Each box has 4 box tops.

Daily Assessment Task

Fill in the bubble for the correct answer choice. You may use models or strategies to solve.

Question 8. Multi-Step There are 16 dolphins in a pod. Each pod has the same number of males and females. The female dolphins are swimming in pairs. How many pairs of female dolphins are there? (A) 8 (B) 4 (C) 6 (D) 2 Answer: Option(B) Explanation: There are 16 dolphins in a pod. Each pod has the same number of males and females 16 ÷ 8 = 2 So, 8 males and 8 females. The female dolphins are swimming in pairs. Total pairs of female dolphins 8 ÷ 2 = 4

Go Math Grade 3 Lesson 10.4 Subtraction and Division Question 10. Multi-Step Tim has 30 grapes. He keeps 9 grapes for himself. Then he gives 7 grapes each to some of his friends. To how many friends does Tim give grapes? (A) 3 (B) 4 (C) 10 (D) 7 Answer: Option(A) Explanation: Tim has 30 grapes. He keeps 9 grapes for himself. So, 30 – 9 = 21 Then he gives 7 grapes each to some of his friends. Tim gives grapes to his friends 21 ÷ 7 = 3

Texas Test Prep

Question 11. Renee has 18 photos. She wants to put the same number of photos on each of 6 pages in her photo album. How many photos will be on each page? (A) 4 (B) 3 (C) 2 (D) 5 Answer: Option(B) Explanation: Renee has 18 photos. She wants to put the same number of photos on each of 6 pages in her photo album. Number of photos on each page 18 ÷ 6 = 3

Texas Go Math Grade 3 Lesson 10.4 Homework and Practice Answer Key

Use the graph for 3-6.

Question 3. Beth sorts an equal number of her bottles into 3 bins. How many bottles are in each bin?

Go Math Lesson 10.4 Answer Key 3rd Grade Question 4. Malik and Kimi combine their bottles, then sort an equal number of each into 3 bins. How many bottles are in each bin? Answer: 9 bottles in each bin. Explanation: Malik and Kimi combine their bottles, 18 + 9 = 27 then sort an equal number of each into 3 bins. Number of bottles in each bin 27 ÷  3 = 9

Question 5. Kimi collects another 7 bottles and sorts an equal number into 4 bins. How many bottles are in each bin? Answer: 4 bottles in each bin. Explanation: Kimi has 9 bottles at first and then, collects another 7 bottles and sorts an equal number into 4 bins. Number of bottles in each bin 16 ÷ 4 = 4

Question 6. All of the students want to combine their bottles and sort an equal number into 6 bins. Can they do this? Explain. Answer: No, they cannot sort an equal number into 6 bins. Explanation: All of the students want to combine their bottles and sort an equal number into 6 bins. Total number of bottles altogether 12 + 18 + 9 = 39 No, they cannot sort an equal number into 6 bins, because when 39 ÷ 6, we get the remainder as 3.

Texas test Prep

Lesson Check

Fill in the bubble completely to show your answer.

Question 9. Key bakes 18 mini-pies. There are 6 pies on each tray. How many trays does Key use? (A) 12 (B) 6 (C) 4 (D) 3 Answer: Option(D) Explanation: Key bakes 18 mini-pies. There are 6 pies on each tray. Number of trays Key used 18 ÷ 6 = 3

Question 10. Keesha has 14 shoes in all. How many pairs of shoes does Keesha have? (A) 7 (B) 2 (C) 28 (D) 14 Answer: Option(A) Explanation: Keesha has 14 shoes in all. Total pairs of shoes Keesha have 14 ÷ 2 = 7

Question 11. Multi-Step Tara has 32 beads. She takes out 4 red heads, then sorts the rest into 4 equal groups. How many beads are in each group? (A) 7 (B) 4 (C) 8 (D) 9 Answer: Option (A) Explanation: Tara has 32 beads. She takes out 4 red beads, so, 32 – 4 = 28 then sorts the rest into 4 equal groups. Number of beads in each group 28 ÷ 4 = 7

Go Math Practice and Homework Lesson 10.4 Answer Key 3rd Grade Question 12. Multi-Step Jeff has a booklet of 30 stickers. He uses one page of stickers. If there are 6 stickers on each page, how many pages are left? (A) 4 (B) 24 (C) 5 (D) 6 Answer: Option (A) Explanation: Jeff has a booklet of 30 stickers. He uses one page of stickers. If there are 6 stickers on each page, Total pages of stickers 30 ÷  6 = 5 Number of pages left 5 – 1 = 4

Share this:

Leave a comment cancel reply.

You must be logged in to post a comment.

ChatGPT vs. ChatGPT Plus: Is a paid subscription still worth it?

When  GPT-4  was OpenAI's most powerful artificial intelligence large language model (LLM), paying for a subscription to ChatGPT Plus --  which costs $20 a month  -- made sense. But now that OpenAI announced the availability of GPT-4o, I'm not so sure. 

With this latest update, OpenAI revealed an omnimodel that makes GPT-4-level intelligence available for all, so you won't need a Plus subscription to access it. What's more, free users can now access features that were previously reserved for paid subscribers, including GPT Store access to use custom GPT bots; the Memory feature to give their conversations a sense of continuity; uploading photos and documents to discuss them with ChatGPT; browsing the web to give more current context; and advanced data analysis. 

Also: 6 ways OpenAI just supercharged ChatGPT for free users

These changes can make it hard to determine who will find free ChatGPT adequate and who should spring for a Plus subscription. As a ChatGPT Plus subscriber, I'll explain below in exactly which cases you should use one or the other. Once GPT-4o is widely available, I'll test it to see how it performs for free users and ChatGPT Plus subscribers and report if any further differences arise.

You should use ChatGPT Plus if...

1. you use chatgpt a lot more than the average user.

With GPT-4o giving free users many of the same capabilities that were only available behind a Plus subscription, the reasons to sign up for a monthly fee have dwindled but are not completely gone. Free ChatGPT users will be limited in the number of messages they can send with GPT-4o, depending on usage and demand; however, OpenAI doesn't specify exactly what that limit is. 

Also:  Microsoft Copilot vs. Copilot Pro: Is the subscription fee worth it?

OpenAI says ChatGPT will switch automatically to GPT-3.5 when free users reach their limit. ChatGPT Plus subscribers have five times the capacity of free users. Paid users will be able to ask GPT-4o five times as many questions as free users and will still have access to GPT-4 when they exceed their limit. We expect OpenAI will increase the limits for GPT-4o for both free and paid users. 

2. You can't wait

OpenAI says it is beginning to roll out GPT-4o to ChatGPT Plus, Team, and ChatGPT free users today, with Enterprise users coming soon. During the Spring Update live stream, OpenAI CTO Mira Murati announced that the new GPT-4o model and the rest of the updates will roll out iteratively to customers over the next few weeks. This means that only a fraction of ChatGPT users currently have access to the new features, with this number increasing shortly.

Also:  How to subscribe to ChatGPT Plus (and why you should)

If you don't want to wait until you get the new update in your account to use Plus features as a free subscriber, you can get a Plus subscription now to stave off the excitement. Note that you can cancel the subscription whenever you want.

ChatGPT Plus users also still get early access to new features that OpenAI rolls out, including the new ChatGPT desktop app for macOS. Soon, this early access will include the new Voice Mode that rolls out over the coming weeks. OpenAI also will launch a Windows version of the app later this year.

You should use free ChatGPT if...

1. you don't want to pay a monthly fee.

When GPT-4o is available, ChatGPT users will no longer need a Plus subscription to access most of the features that initially attracted subscribers. OpenAI is making GPT-4o available to all users, whether they are paying or not. 

ChatGPT free users will be able to access the multimodal GPT-4o with GPT-4-level intelligence, get responses from the web, use advanced data analysis, upload files and photos to discuss with the chatbot, access custom GPTs in the GPT Store, and have more helpful experience with Memory -- all of which used to be ChatGPT Plus benefits.

Although it's unclear whether free users can generate images natively in GPT-4o (OpenAI did not disclose this during the event), free users will have access to GPT bots in the GPT Store. If DALL-E access remains a Plus feature, free users can still access the DALL-E bot in the GPT Store. 

2. You're a casual ChatGPT user

There is no need to upgrade to a ChatGPT Plus membership if you're just a casual user who doesn't reach the usage limits of GPT-4o. The new GPT-4o model is rolling out to ChatGPT free users with usage limits beginning today, but OpenAI hasn't specified this limit. Plus users will have a message limit that is five times greater than that of free users, with Team and Enterprise users getting even higher limits.

Also:  ChatGPT vs. Bing Chat vs. Google Bard: Which is the best AI chatbot?

If you're a free user who doesn't use ChatGPT often and stays within the usage limit, you wouldn't get much benefit from a ChatGPT Plus subscription now. I expect OpenAI will amend the subscription benefits or the price as time passes and GPT-4o becomes widely available.

Artificial Intelligence

Microsoft copilot pro vs. openai's chatgpt plus: which is worth your $20 a month, chatgpt vs. copilot: which ai chatbot is better for you, how to use chatgpt (and what you can use it for).

Log in using your username and password

• Search More Search for this keyword Advanced search
• Latest content
• Current issue
• Browse by collection
• BMJ Journals More You are viewing from: Google Indexer

You are here

• Online First
• Best practice in myopia control: insights and innovations for myopia prevention and control – a round table discussion
• Article Text
• Article info
• Citation Tools
• Rapid Responses
• Article metrics

• http://orcid.org/0000-0002-5721-6051 Yanxian Chen 1 , 2 ,
• Andreas Mueller 3 ,
• http://orcid.org/0000-0002-4548-3574 Ian Morgan 4 ,
• Frank Larkin 5 ,
• http://orcid.org/0000-0002-1257-6635 Yan Wang 6 ,
• Junwen Zeng 7 ,
• Mingguang He 1 , 2 , 7
• 1 School of Optometry , The Hong Kong Polytechnic University , Hong Kong , Hong Kong SAR
• 2 Research Centre for SHARP Vision (RCSV) , The Hong Kong Polytechnic University , Hong Kong , Hong Kong SAR
• 3 Department of Noncommunicable Diseases , World Health Organization , Geneva , Switzerland
• 4 Research School of Biology , Australian National University , Canberra , Australian Capital Territory , Australia
• 5 Cornea and External Disease Department , Moorfields Eye Hospital NHS Foundation Trust , London , UK
• 6 Tianjin Eye Hospital & Eye Institute, Ophthalmology and Visual Development Key Laboratory, Tianjin Medical University , Tianjin , China
• 7 State Key Laboratory of Ophthalmology, Zhongshan Ophthalmic Center, Sun Yat-Sen University , Guangzhou , Guangdong , China
• Correspondence to Professor Mingguang He, The Hong Kong Polytechnic University, Hong Kong, Hong Kong; mingguang.he{at}polyu.edu.hk

https://doi.org/10.1136/bjo-2023-325112

Statistics from Altmetric.com

Request permissions.

If you wish to reuse any or all of this article please use the link below which will take you to the Copyright Clearance Center’s RightsLink service. You will be able to get a quick price and instant permission to reuse the content in many different ways.

• Optics and Refraction
• Child health (paediatrics)
• Epidemiology

In August 2023, BJO and the Zhongshan Ophthalmic Center co-hosted a round table discussion on Best Practices in Myopia Control. This gathering provided a platform for the exchange of insights and discussion of evidence-based strategies to respond to the rapid increase in myopia prevalence. Participants from China, Hong Kong, the UK and Australia met in Guangzhou, China, to discuss the global status and challenges associated with myopia control (see the ‘Acknowledgements’ section for the list of panel members). The event included panel discussions on (1) prevention and public education for myopia control and (2) individualised myopia control. This report summarises the topics in myopia prevention and control discussed.

Prevention and public education for myopia control

Over the past 50 years, there has been a striking increase in the prevalence of myopia, raising questions about its causes and potential future impact. 1 Early data indicate that the advent of the COVID-19 pandemic and associated lockdowns has accelerated the myopia trend. 2 3 It is not clear whether a reduction in the time spent outdoors during lockdowns has led to longer-term behavioural changes favouring indoor lifestyles and hence impacted myopia prevalence.

Reduction of the impact of myopia centres on two crucial elements: education intensity and outdoor activities. Strategies that merely broadcast knowledge about myopia have shown limited effectiveness. Singapore’s efforts, including teacher training and promoting good eye care habits in schools, yielded marginal reductions in myopia prevalence. 5 Though the use of social media, such as WeChat messages, may result in some noteworthy reduction in myopia incidence, 8 9 this effect may be diminished by the effect of parental myopia. Compared with children with myopic parents, online family health education was more effective in children with non-myopic parents. A more compulsive strategy to increase time outdoors may be more effective. The Taiwanese school-focused strategy allocated 2 hours of supervised time, unlike in Singapore, during which children engaged in outdoor activities. It led to a significant decrease in the prevalence of myopia 4 and has generated an L-shaped decline after 10-year promotion of outdoor activities in kindergartens. 10

In China, safety concerns commonly arise in the implementation of outdoor activities during school hours. For instance, from 2016 to 2018 in Shanghai, an additional 40 min of outdoor activity classes was introduced to primary schools, but teachers expressed apprehensions about potential accidents when students were outdoors. However, experiences in Australia and Taiwan have shown that, with necessary safety measures such as teacher supervision and wearing hats, the risks associated with outdoor activities at school are minimal. An alternative solution considered for schools in China is to consolidate short 10 min breaks between classes into longer periods. Based on evidence from Taiwan, a clear implementation strategy led by the government coupled with an adapted education programme is likely to be a successful implementation of outdoor activities during school time.

Individualised myopia control

For children already affected by myopia, the primary focus is on controlling its progression. Myopia is a condition that physically alters the shape of the eye. The concept that every dioptre of myopia matters significantly holds true; even a one-diopre increase comes with a substantial 67% higher risk of myopic macular degeneration. 11 Consequently, reducing myopia by even one dioptre can be significantly beneficial. Myopia control encompasses a range of established interventions, including orthokeratology and low-dose atropine eye-drops. 12 The effect on myopia of atropine is recognised to be concentration-dependent and age-dependent, which itself exemplifies the individualisation of myopia prevention and control. A history of myopia in one or both parents is known to have a significant influence on development of myopia. Is ethnicity important? Comparatively few high-quality trials have been reported outside East Asia. One of the largest such trials from the USA, in which only 11% of children were East Asian, reported no benefit of atropine 0.01% drops in low to moderate myopia compared with placebo. 13

Additional emerging interventions, including defocus incorporated multiple segments spectacle lenses, 14 15 high-add power multifocal contact lenses, 16 spectacles with highly aspherical lenses 17 and repeated low-level red light (RLRL) therapy, 18 19 are showing promise. These diverse interventions offer hope for effective myopia control.

However, it is important to acknowledge that available interventions come with their own advantages and disadvantages. For instance, specially designed spectacles may have limitations related to wearing time and the patient’s age. 14 15 The use of orthokeratology demands comprehensive support from both clinics and parents. RLRL, although effective with a low rate of complications, carries the potential risk of retinal damage that necessitates close monitoring. Thus, success in myopia control lies in individualisation, recognising that different parents have varying requests, capabilities and expectations. For young children or those with highly myopic parents, a more robust intervention may be advisable, such as a higher concentration of atropine drops, a greater magnitude of myopic defocus or red-light therapy.

In regions with limited resources, strategies for myopia prevention and control must be tailored to factors such as affordability and accessibility. While 0.05% atropine has shown the potential to prevent myopia onset by 50%, 20 and RLRL therapy boasts a 54% reduction rate, 21 the cost–benefit analysis for large-scale implementation of these interventions in myopia prevention still requires further research. Spectacle lenses, being relatively more accessible, cost-effective and effective in slowing myopia progression, 15 present an alternative for low-income areas, although their effectiveness in reducing incident myopia also warrants further investigation.

In conclusion, the escalating prevalence of myopia represents a greater challenge than previously anticipated. However, there is recent clear evidence of effective myopia control on a national level in some countries taking proactive measures through interventions and educational reforms. While the effectiveness of myopia control interventions has been extensively explored, the focus must now shift towards individualised strategies in clinical practice to achieve better outcomes. Significant challenges persist, particularly concerning the large-scale implementation of myopia interventions in resource-constrained areas. These challenges remain an essential area for ongoing research and development.

Ethics statements

Patient consent for publication.

Not applicable.

Acknowledgments

The following panelists participated in the ZOC-BJO Round Table Discussion on 'Best Practices in Myopia Control' (names in alphabetical order). Andreas Mueller, WHO; Chi-ho To, The Hong Kong Polytechnic University; Frank Larkin, Moorfields Eye Hospital (chairman); Ian Morgan, Australian National University, Zhongshan Ophthalmic Center, Sun Yat-sen University

Jason Yam, The Chinese University of Hong Kong; Junwen Zeng, Zhongshan Ophthalmic Center, Sun Yat-sen University; Kathryn Rose, University of Technology Sydney; Mingguang He, The Hong Kong Polytechnic University & Zhongshan Ophthalmic Center, Sun Yat-sen University; Ningli Wang, Beijing Tongren Hospital, Chinese Medical University; Stuart Keel, WHO; Xianggui He, Shanghai Eye Disease Prevention and Treatment Center; Xiangtian Zhou, Eye Hospital, Wenzhou Medical University; Xiao Yang, Zhongshan Ophthalmic Center, Sun Yat-sen University; Yan Wang, Tianjin Eye Hospital. We are grateful to Kangying Lai and Pai Zheng, BMJ China Office for their assistance in organisation of this round table.

• Morgan IG ,
• French AN ,
• Ashby RS , et al
• Yang X , et al
• Ding X , et al
• Chang L-C , et al
• Karuppiah V ,
• Tay V , et al
• Zhang J , et al
• Kang M-T , et al
• Wang CY , et al
• Bullimore MA ,
• Brennan NA ,
• Toubouti YM ,
• Cheng X , et al
• Chandler DL , et al
• Huang D , et al
• Tse DY-Y , et al
• Walline JJ ,
• Walker MK ,
• Mutti DO , et al
• Yin Z , et al
• Tan X , et al
• Chen X , et al
• Zhang Y , et al
• Zhu Z , et al

Contributors Drafting of manuscript: YC, JZ and MH. Review and revision of manuscript: AM, IM, FL and YW.

Funding The research was supported by PolyU - Rohto Centre of Research Excellence for Eye Care (Collaborative) (P0046333).

Competing interests MH is the director and shareholder in Eyerising and Eyerising International. The other authors have no proprietary interest in any aspect of this study.

Provenance and peer review Not commissioned; externally peer reviewed.

Read the full text or download the PDF: