improper fraction problem solving

• Home   |  
• About   |  
• Contact Us   |  
• Privacy   |  
• Newsletter   |  
• Shop   |  
• 🔍 Search Site
• Easter Color By Number Sheets
• Printable Easter Dot to Dot
• Easter Worksheets for kids
• Kindergarten
• All Generated Sheets
• Place Value Generated Sheets
• Addition Generated Sheets
• Subtraction Generated Sheets
• Multiplication Generated Sheets
• Division Generated Sheets
• Money Generated Sheets
• Negative Numbers Generated Sheets
• Fraction Generated Sheets
• Place Value Zones
• Number Bonds
• Addition & Subtraction
• Times Tables
• Fraction & Percent Zones
• All Calculators
• Fraction Calculators
• Percent calculators
• Area & Volume Calculators
• Age Calculator
• Height Calculator
• Roman Numeral Calculator
• Coloring Pages
• Fun Math Sheets
• Math Puzzles
• Mental Math Sheets
• Online Times Tables
• Online Addition & Subtraction
• Math Grab Packs
• All Math Quizzes
• 1st Grade Quizzes
• 2nd Grade Quizzes
• 3rd Grade Quizzes
• 4th Grade Quizzes
• 5th Grade Quizzes
• 6th Grade Math Quizzes
• Place Value
• Rounding Numbers
• Comparing Numbers
• Number Lines
• Prime Numbers
• Negative Numbers
• Roman Numerals
• Subtraction
• Add & Subtract
• Multiplication
• Fraction Worksheets
• Learning Fractions
• Fraction Printables
• Percent Worksheets & Help
• All Geometry
• 2d Shapes Worksheets
• 3d Shapes Worksheets
• Shape Properties
• Geometry Cheat Sheets
• Printable Shapes
• Coordinates
• Measurement
• Math Conversion
• Statistics Worksheets
• Bar Graph Worksheets
• Venn Diagrams
• All Word Problems
• Finding all possibilities
• Logic Problems
• Ratio Word Problems
• All UK Maths Sheets
• Year 1 Maths Worksheets
• Year 2 Maths Worksheets
• Year 3 Maths Worksheets
• Year 4 Maths Worksheets
• Year 5 Maths Worksheets
• Year 6 Maths Worksheets
• All AU Maths Sheets
• Kindergarten Maths Australia
• Year 1 Maths Australia
• Year 2 Maths Australia
• Year 3 Maths Australia
• Year 4 Maths Australia
• Year 5 Maths Australia
• Meet the Sallies
• Certificates

Improper Fraction Worksheets

Welcome to our Improper Fraction Worksheets page. Here you will find a wide range of free printable Fraction Worksheets which will help your child understand and practice how to convert improper fractions to mixed numbers.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

Improper fractions are fractions with an absolute value greater than 1.

We have more information about what proper and improper fractions are with some examples below.

There are also a range of sheets to help develop the skill of converting improper fractions - both easier sheets with visual models and harder sheets without any visual aids.

Using these sheets will help your child to:

• understand what improper fractions are;
• convert improper fractions to mixed numbers;
• convert mixed numbers to improper fractions.

Want to test yourself to see how well you have understood this skill?

• Try our NEW quick quiz at the bottom of this page.

Quicklinks to...

What are proper, improper and mixed fractions.

• Converting Improper Fractions Support
• All Converting Improper Fractions Worksheets
• Converting Improper Fractions Visual Worksheets
• Converting Improper Fractions Trickier Worksheets
• More related Math resources

Convert Improper Fractions Online Quiz

A fraction is a number with the form: \[ {n \over d} \]

• If the numerator is smaller than the denominator (if n < d), then the fraction is called a proper fraction , and its value is less than 1.
• If the numerator is greater than the denominator (if n > d), then the fraction is called an improper fraction , and its value is greater than 1.
• If the numerator is equal to the denominator (if n = d), then the fraction's value is equal to 1.
• A mixed fraction (or mixed number) is a number that has a whole number part to it, and a fraction part to it.
• Please note: if the value of n or d is negative, then we compare the absolute values of the numerator and denominator.

Types of Fractions Examples

\[{3 \over 7} \; , \; {2 \over 10} \; and \; {17 \over 26} \] are all proper fractions.

\[ {31 \over 5} \; , \; {15 \over 10} \; , \; -{7 \over 4} \; and \; {37 \over 23} \] are all improper fractions.

\[ 3{1 \over 5} \; , \; 2 {5 \over 8} \; and \; 4 {1 \over 2} \] are all mixed numbers or mixed fractions.

Improper Fractions Support

Here you will find the support page on how to find equivalent fractions if you get stuck or want some support.

• Convert Improper Fractions Support

Converting Improper Fraction Worksheets

Here you will find a selection of Fraction worksheets designed to help your child to understand and practice converting improper fractions.

The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one.

We have split the sheets into two sections with the first section looking at improper fractions visually.

The sheets in the second sections are more abstract (with no visual models) and tricky!

These sheets are aimed at students at 4th and 5th grade, with the more abstract worksheets for 5th graders.

Converting Improper Fraction VISUAL Worksheets

Improper fraction worksheets to mixed numbers visual fractions.

These sheets are all about using circles to create visual fractions to aid understanding of improper fractions and mixed numbers.

• Improper Fractions to Mixed Numbers Sheet 1
• PDF version
• Improper Fractions to Mixed Numbers Sheet 2

Mixed Numbers to Improper Fraction Worksheets Visual Fractions

• Mixed Numbers to Improper Fractions Sheet 1
• Mixed Numbers to Improper Fractions Sheet 2

Convert Improper Fraction Worksheets - Visual Fractions

These sheets involve both converting improper fractions to mixed numbers, and also converting mixed numbers to improper fractions.

• Convert Improper Fractions Sheet 1
• Convert Improper Fractions Sheet 2
• Convert Improper Fractions Sheet 3
• Convert Improper Fractions Sheet 4
• Convert Improper Fractions Sheet 5

Converting Improper Fraction Trickier Worksheets

Convert improper fractions to mixed fractions trickier sheets.

These improper fraction worksheets are for students who are more confident working in a more abstract way.

• Convert Improper Fractions to Mixed Fractions 1
• Sheet 1 Answers
• Converting Improper Fractions to Mixed Fractions 2
• Sheet 2 Answers

Convert Mixed Numbers to Improper Fractions Trickier sheets

• Convert Mixed Numbers to Improper Fractions 1
• Convert Mixed Numbers to Improper Fractions 2

Convert Mixed Numbers to Improper Fractions Walkthrough Video

This short video walkthrough shows several problems from our Convert Mixed Numbers to Improper Fractions Sheet 1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

More Recommended Math Resources

Take a look at some more of our worksheets and resources similar to these.

• Improper Fraction Calculator

If you just want a calculator to do the hard work for you, then try our Improper Fraction Calculator.

The calculator will convert any mixed number to an improper fraction, or an improper fraction into a mixed number.

The great thing is that it will also show you all the working out - job done!

What is a Mixed Number

This support page introduces mixed numbers with some examples and an interactive teaching app.

There are also some practice worksheets to help you identify and write mixed numbers.

• What is a Mixed Number Support page

Simplifying Fractions

Take a look at our Simplifying Fractions Practice Zone or try our worksheets for finding the simplest form for a range of fractions.

You can choose from proper fractions, improper fractions or both.

You can print out your results or benchmark your scores against future achievements.

Good for practising equivalent fractions as well as converting to simplest form.

Great for using with a group of children as well as individually.

• Simplify Fractions Practice Zone
• Simplifying Fractions Worksheet page

Comparing Fractions

We have some carefully graded worksheets on comparing and ordering fractions.

You can choose from supported sheets with diagrams for students who need extra help to harder worksheets for those more confident.

• Comparing Fractions Worksheet page

Are you looking for free fraction help or fraction support?

Here you will find a range of fraction help on a variety of fraction topics, from simplest form to converting fractions.

There are fraction videos, worked examples and practice fraction worksheets.

Fraction Riddles

Riddles are a great way to get children to apply their knowledge of fractions.

These riddles are a good way to start off a maths lesson, or also to use as a way of checking your child's understanding about fractions.

All the fraction riddles consist of 3 or 4 clues and a selection of 6 or 8 possible answers. Children have to read the clues and work out which is the correct answer.

The riddles can also be used as a template for the children to write their own clues for a partner to guess.

• Fraction Riddles for kids (easier)
• Free Printable Fraction Riddles (harder)

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skills at using improper fractions here.

Fun Quiz Facts

• This quiz was attempted 940 times.
• The average (mean) score was 12.1 out of 17 marks.
• Can you beat the mean score?

How to Print or Save these sheets 🖶

Need help with printing or saving? Follow these 3 steps to get your worksheets printed perfectly!

• How to Print support

Subscribe to Math Salamanders News

Sign up for our newsletter to get free math support delivered to your inbox each month. Plus, get a seasonal math grab pack included for free!

• Newsletter Signup

Return to 4th Grade Math Worksheets

Return to Fraction Worksheets

Return from Equivalent Fractions Worksheet to Math Salamanders Homepage

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

New! Comments

TOP OF PAGE

© 2010-2024 Math Salamanders Limited. All Rights Reserved.

• Privacy Policy
• Copyright Policy

Improper Fractions

Fractions were first used in Ancient Egypt around 1600 BC, which makes the concept quite old. Fractions are of different types. When the numerator is smaller than the denominator i.e. 1/2, it is a proper fraction. However, when the denominator is smaller than or equal to the numerator, then it is an improper fraction. An example of this is 16/15.

An improper fraction is one type of fraction in which the numerator is equal to or greater than the denominator. Its value is always one or greater than one. Improper fractions are usually written in mixed number form in a simplified manner, as mixed fractions are easier to comprehend.

What is an Improper Fraction?

An improper fraction is a type of fraction where the numerator is greater than or equal to the denominator. For example, 5/2 and 8/5, are improper fractions. Every fraction has two parts, numerator, and denominator. In mathematics, there are two main types of fractions based on the values of numerator and denominator, and those are proper fractions and improper fractions.

Improper Fraction Definition

A fraction whose numerator is greater than or larger than the denominator is defined as an improper fraction such as 7/3 and 12/5. Improper fractions are easier to solve using addition and subtraction compared to the type of fractions such as mixed fractions.

Improper Fraction and Mixed Fraction

An improper fraction is a fraction whose numerator is greater than or equal to its denominator. For example, 9/4, 4/3 are improper fractions. Numerically, they are always equal to or greater than 1. On the other hand, a mixed fraction is a fraction that is written as a combination of a natural number and a proper fraction. It is a simplified form of an improper fraction. For example, \( 21\dfrac{4}{5}, 16\dfrac{2}{3}\) are mixed fractions. Numerically, a mixed fraction is always greater than 1. Also, any mixed fraction can be written as an improper fraction.

Generally, in real life, mixed fractions are easier to interpret and compare, as compared to improper fractions. We can easily convert any improper fraction to a mixed number or mixed fraction to an improper fraction by following some basic steps that you will study in later sections on this page.

Converting Improper Fractions to Decimals

Fractions and decimals are two ways to represent numbers. Improper fractions can be converted to decimals easily by dividing the numerator with the denominator . Let’s look at a quick and easy example of how we can convert improper fractions to decimals . Let’s consider the following example.

Example: Convert the given improper fraction to a decimal: 10/4.

The first step is to divide 10 by 4. When we do so, we will get 10 ÷ 4 = 2.5.

Here, 10/4 is an improper fraction and 2.5 is a decimal. Similarly, the value of 3/2 is 1.5 in decimals and 5/2 is 2.5 in decimals. When we convert an improper fraction to a decimal, the decimal value is always greater than 1.

Converting Improper Fractions to Mixed Numbers

The denominator of the mixed fraction form of an improper fraction is always the same as that of the original fraction. Mixed numbers are considered as the simplified form of improper fractions, that is why it is important to learn this conversion. For converting an improper fraction to a mixed number, we have to follow the below-listed steps:

• Step 1- Divide the numerator with the denominator.
• Step 2- You will get values of quotient and remainder.
• Step 3- Arrange those values of the quotient, remainder, and divisor in the following manner to express a fraction as a mixed number: \(Quotient\dfrac{Remainder}{Divisor}\).

Let’s look at a quick and easy example of how we can convert improper fractions to mixed numbers. Let’s say you have an improper fraction, 13/4. The first step is to divide 13 by 4. We get 3 as the quotient with a remainder of 1. Next, we will place 1 as the numerator, 4 as the denominator, and 3 as the whole number . Thus, we get the mixed fraction: \( 3\dfrac{1}{4}\).

Similarly, let’s solve another example. Here, we have an improper fraction: 9/2. On dividing 9 by 2, we get 4 as the quotient with a remainder of 1. Again, we will repeat the same process. We will place 1 as the numerator, 2 as the denominator, and 4 as the whole number. Thus, we get the mixed fraction: \(4\dfrac{1}{2}\).

How to Solve Improper Fractions?

Solving improper fractions mean performing arithmetic operations on them and simplifying the value of the answer so obtained. There are mainly four arithmetic operators in mathematics and those are addition, subtraction, multiplication, and division. Solving an improper fraction is the same as solving any other proper fraction, the only difference is that, here, we have to simplify the answer and write it in mixed numbers.

Let's solve the improper fraction: 4/3 + 7/3.

Step 1: We have the same denominator for both the fractions. Therefore, we will directly add the numerators 4 and 7. We get 11. Thus, on adding improper fractions, we get 11/3.

Step 2: Simplifying the improper fraction (dividing 11 by 3), we will get 3 as a whole, 2 as a numerator, and 3 as the denominator.

The answer is \(3\dfrac{2}{3}\).

Related Articles on Improper Fractions

Check the following topics related to the concept of improper fractions.

• Improper Fraction to Mixed Number
• Mixed Number to Improper Fraction
• Improper Fraction to Mixed Number Calculator
• Types of Fractions

Improper Fraction Examples

Example 1: Identify improper fractions out of the following: 12/5, 3, 1/9, 4/2, 4/5.

Improper fractions are the ones in which the numerator is either equal to or greater than the denominator. Out of the given fractions, 12/5, 3, and 4/2 are improper fractions. As, in 12/5, 12 > 5, 3 can be written as 3/1 where 3 > 1, and 4/2 can be simplified as 2/1 where 2 > 1.

Example 2: There are five-fourth liters of plain milk in the refrigerator. Convert the given quantity into a mixed number.

To convert the given improper fraction 5/4 to a mixed number, we have to divide 5 by 4. By dividing, we will get 1 as the quotient, and 1 as the remainder. Therefore, the answer is \(1\dfrac{1}{4}\).

Example 3: What is 4 1/3 as an improper fraction?

To convert the given mixed number to an improper fraction, we have to first multiply the denominator and the whole number and then we need to add the numerator to the sum. ⇒ \(4\dfrac{1}{3}\) = (4 × 3 + 1)/3 ⇒ (12 + 1)/3 ⇒ 13/3 Therefore, \(4\dfrac{1}{3}\) is equivalent to 13/3.

go to slide go to slide go to slide

Book a Free trial Class

Practice Questions on Improper Fractions

go to slide go to slide

FAQs on Improper Fractions

Fractions in which the numerator is equal to or less than the denominator are known as improper fractions in math. 3/2, 6/5, 18/11 are a few examples of improper fractions.

What is Proper Fraction and Improper Fraction?

Proper fractions are those in which the numerator is less than the denominator, while improper fractions are opposite of proper fractions where numerator ≥ denominator.

Are Whole Numbers Examples of Improper Fraction?

Yes, whole numbers are examples of improper fractions, as we can write any whole number in the form of a fraction in which the numerator is greater than the denominator. For example, 3= 3/1, 5= 5/1, etc.

How can we Add Improper Fractions?

The addition of two like improper fractions is done by adding the values of their numerator and writing the common denominator as the denominator of the sum obtained. While, in the case of two unlike improper fractions, we first take the LCM of the denominators and convert them into like fractions. Then, we add those two fractions. Let's take an example of addition of improper fractions 5/4 and 7/4.

• Step 1: We have the same denominator in these fractions 5/4 + 7/4. Therefore, we will simply add the numerators 5 and 7. We get 12 as the sum. Thus, on adding, we have 12/4.
• Step 2: By simplifying the improper fraction (dividing 12 by 4), we get 3 as the answer.

How do we Simplify an Improper Fraction?

Simplification of improper fractions means finding the lowest value of the fraction by dividing the numerator with the denominator. Let us take an example to understand how to simplify an improper fraction. Consider the fraction 100/5. By dividing 100 by 5, we get 20 as the answer. Thus, 100/5 = 20 in the simplified form.

How to Subtract Improper Fractions?

Subtraction of two like improper fractions is done by subtracting the values of their numerator and writing the common denominator as the denominator of the difference obtained. While, in the case of two unlike improper fractions, we first take the LCM of the denominators and convert them into like fractions. Then, we subtract those two fractions.

How to Convert Improper Fraction to Mixed Numbers?

Improper fractions are converted to mixed numbers by dividing the numerator with the denominator and write the answer in this form: \(Quotient\dfrac{Remainder}{Divisor}\).

How to Multiply Improper Fractions?

The numerator and denominator of an improper fraction are multiplied with the numerator and denominator of the other fraction to find the product. After multiplying, we simplify the fraction so obtained. In this way, we multiply two improper fractions.

Improper Fractions – Definition, Conversion, Examples, FAQs

What is an improper fraction, fraction conversion, solved examples on improper fractions, practice problems on improper fractions, frequently asked questions on improper fractions.

Fractions are often referred to as numbers between numbers. Fractions are numerical values that represent a part or a portion of a whole. For example, look at the pizza below.

This pizza has been cut into 4 equal parts. So each piece of the pizza represents 1 out of 4 equal parts. So mathematically, we can represent each piece as  $\frac{1}{4}$. This number is called a fraction . 

The number below the bar that represents the total number of equal parts that the whole is divided into is called the denominator .

And the number on the top that represents the number of equal parts we are considering is called the numerator . 

Before discussing improper fraction, we first need to understand proper fractions.

Proper fractions: Fractions for which the numerator is less than the denominator are called proper fractions . For example, if you order a pizza and cut it into 4 equal parts, and then eat one slice out of it, the remaining pizza can be expressed as $\frac{3}{4}$ of the whole pizza. Here, since 3 is less than 4, the fraction is a proper fraction.

Improper fractions: Improper fractions are defined as fractions for which the numerator is greater than the denominator. Let us take an example of improper fraction, imagine you order a pizza that has 4 slices. Your friends eat all 4 slices. And you realize you didn’t get any. You order another pizza. After eating 1 slice from it, you realize you are done eating. So, how much of the pizza did your friends and you have in all?

Your friends first had all 4 slices of 1 pizza, and then you had 1 slice of the same size from the second pizza.

So, the total pizza eaten is $\frac{5}{4}$ slices of pizza. And that’s an improper fraction with a numerator greater than the denominator. 

Mixed numbers: Mixed numbers are just another way of writing fractions greater than a whole. A mixed number has a whole part and a fractional part, which is actually a proper fraction.

Let’s take the same example from above. You and your friends ate one whole pizza and one-fourth of a pizza. As a mixed fraction, we can write this as $1$ and $\frac{1}{4}$ of a pizza or $1\frac{1}{4}$ of a pizza.

Improper Fraction to Mixed Number

An improper fraction can be converted to a mixed fraction and a mixed fraction can be converted to an improper fraction.

Let’s say we want to convert the fraction $\frac{7}{2}$ into a mixed number. 

Step 1: Find the quotient and the remainder by dividing the numerator with the denominator.

Step 2: The quotient will be the number of wholes for the mixed number. The remainder will be the numerator of the fractional part and the denominator will remain the same.

So, the mixed number form of $\frac{7}{2}$will be:

Mixed Number to Improper Fraction

Any mixed number can be converted into an improper fraction.

Let’s say we want to convert the mixed number $1\frac{3}{4}$ into an improper fraction. 

Step 1: Multiply the denominator with the whole. And then add the numerator to the product.

Step 2: Keep the denominator same and solve for the numerator.

Therefore, the improper fraction for the mixed number $1\frac{3}{4}$ will be $\frac{7}{4}$. 

Related Worksheets

Example 1. Identify the improper fractions:

$\frac{1}{5}$, $2\frac{7}{5}$, $\frac{3}{2}$, $\frac{1}{3}$, $\frac{5}{4}$, $6 \frac{1}{6}$

Solution: $\frac{2}{3}$ and $\frac{5}{4}$ are improper fractions as the value of the numerator is greater than the value of the denominator for both of these fractions.

Example 2. Write $4\frac{2}{7}$ as an improper fraction.

Solution: Converting $4\frac{2}{7}$ into an improper fraction,

$4 \frac{2}{7}$ = $\frac{(7\times4) + 2}{7}$ = $\frac{30}{7}$

Example 3. Write $2\frac{9}{6}$ as an improper fraction.

Solution: While dividing 29 by 6, the quotient and remainder are 4 and 5 respectively. So  $\frac{29}{6}$ written as a mixed number is $ 4 \frac{5}{6}$ .

Converting $3\frac{1}{5}$ to an improper fraction:

What are Improper Fractions? Meaning, Definition, Examples

Attend this quiz & Test your knowledge.

What type of fraction is $\frac{11}{4}$?

Write the mixed number $3\frac{1}{5}$ as an improper fraction., identify the improper fraction., convert $\frac{5}{2}$ into a mixed fraction..

Which are easier for calculations: improper fractions or mixed fractions?

Improper fractions are easy for arithmetic operations of addition , subtraction , multiplication , and division . Mixed fractions are easier to understand and represent in figures.

Why are fractions important?

Every quantity cannot be expressed in whole numbers . Fractions are employed to indicate a certain part or portion of any item. They are a fundamental concept in computation and applied in algebra , ratios, and several other concepts in mathematics and other fields.

How are decimals related to fractions?

Fractions and decimals are both ways to represent quantities or numbers. Decimals are nothing but a different way to represent fractions whose denominator is 10 or powers of 10. For example, the fraction $\frac{15}{10}$ in decimal form is 1.5.

RELATED POSTS

• Volume of Hemisphere: Definition, Formula, Examples
• Reflexive Property – Definition, Equality, Examples, FAQs
• Dividend – Definition with Examples
• Cube Numbers – Definition, Examples, Facts, Practice Problems
• Quotient – Definition with Examples

Math & ELA | PreK To Grade 5

Kids see fun., you see real learning outcomes..

Make study-time fun with 14,000+ games & activities, 450+ lesson plans, and more—free forever.

Parents, Try for Free Teachers, Use for Free

Improper Fractions

These lessons, with videos, examples, and solutions, help Grade 4 students learn about Improper Fractions.

Related Pages Mixed Numbers & Improper Fractions More Lessons for Grade 4 Math Worksheets

Printable Fraction Worksheets

What is an improper fraction? An improper fraction is a fraction whose numerator is greater than the denominator. The fraction a/b is an improper fraction if a > b.

We can convert an improper fraction to a mixed number by dividing the numerator by the denominator.

The following diagram shows an example of improper fraction. Scroll down the page for more examples and solutions on how to convert between improper fraction and mixed number.

Improper Fractions & Mixed Numbers What’s an improper fraction? How to convert between improper fraction and mixed number?

Proper fractions, improper fractions, and mixed numbers Learn how to convert improper fractions to and from mixed number.

Improper fraction Song

Proper Fraction, Improper Fraction and Mixed Song song

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Improper Fractions, Mixed Numbers Practice Questions

Click here for questions, click here for answers, gcse revision cards.

5-a-day Workbooks

Solver Title

Generating PDF...

• Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode
• Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
• Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
• Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
• Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
• Linear Algebra Matrices Vectors
• Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
• Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
• Physics Mechanics
• Chemistry Chemical Reactions Chemical Properties
• Finance Simple Interest Compound Interest Present Value Future Value
• Economics Point of Diminishing Return
• Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time Volume
• Pre Algebra
• Two-step without parentheses
• Two-step with parentheses
• Three/four steps without parentheses
• Three/four steps with parentheses
• Multi-step without parentheses
• Multi-step with parentheses
• Prime Factorization
• Negative Factors
• Positive Factors
• Odd Factors
• Even Factors
• Biggest Factor
• Equivalent Fractions
• Add, Subtract
• Add, Subtract Like Denominators
• Add, Subtract Unlike Denominators
• Multiply with Whole Number
• Divide with Whole Number
• Mixed Numbers
• Complex Fractions
• Improper Fractions
• Long Addition
• Long Subtraction
• Long Multiplication
• Long Division
• Add/Subtract
• Multiplication
• Decimal to Fraction
• Fraction to Decimal
• Square Root
• Ratios & Proportions

Number Line

• Expanded Form
• Pre Calculus
• Linear Algebra
• Trigonometry
• Conversions

Most Used Actions

• \frac{16}{5}
• \frac{20}{3}
• \frac{101}{9}
• 14\frac{2}{3}
• 8\frac{1}{2}

improper-fractions-calculator

• My Notebook, the Symbolab way Math notebooks have been around for hundreds of years. You write down problems, solutions and notes to go back...

Please add a message.

Message received. Thanks for the feedback.

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Course: 4th grade   >   Unit 8

• Writing mixed numbers as improper fractions

Writing improper fractions as mixed numbers

• Write mixed numbers and improper fractions
• Mixed numbers and improper fractions review

Want to join the conversation?

• Upvote Button navigates to signup page
• Downvote Button navigates to signup page
• Flag Button navigates to signup page

Video transcript

Fraction Worksheets

Conversion :: Addition :: Subtraction :: Multiplication :: Division

Conversions

Fractions - addition, fractions - subtraction, fractions - multiplication, fractions - division.

[FREE] Fun Math Games & Activities Packs

Always on the lookout for fun math games and activities in the classroom? Try our ready-to-go printable packs for students to complete independently or with a partner!

In order to access this I need to be confident with:

Fraction word prob.

Fraction word problems

Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.

Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.

What are fraction word problems?

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.

To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.

After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.

For example,

Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?

You can follow these steps to solve the problem:

Step-by-step guide: Adding and subtracting fractions

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Multiplying and dividing fractions

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4 th grade math to 6 th grade math?

• Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
• Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
• Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
• Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
• Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?

[FREE] Fraction Operations Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

How to solve fraction word problems

In order to solve fraction word problems:

Determine what operation is needed to solve.

Write an equation.

Solve the equation.

State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators).

Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?

The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.

2 Write an equation.

3 Solve the equation.

To add fractions with like denominators, add the numerators and keep the denominators the same.

4 State your answer in a sentence.

The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.

Julia and her brother ate \cfrac{5}{8} of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?

The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.

To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.

\cfrac{5}{6}+\cfrac{1}{3}= \, ?

The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.

That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.

\cfrac{1 \times 2}{3 \times 2}=\cfrac{2}{6}

Now you can add the fractions and simplify the answer.

\cfrac{5}{6}+\cfrac{2}{6}=\cfrac{7}{6}=1 \cfrac{1}{6}

Tim ran a total of 1 \cfrac{1}{6} miles.

Example 3: subtracting fractions (like denominators)

Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?

The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.

To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.

\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}

Pia walked \cfrac{1}{7} of a mile farther to the park than back home.

Example 4: subtracting fractions (unlike denominators)

Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?

The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.

To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.

\cfrac{7}{8}-\cfrac{1}{3}= \, ?

The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.

That means both fractions will need to be changed so that their denominator is 24.

To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.

\begin{aligned}&\cfrac{7 \times 3}{8 \times 3}=\cfrac{21}{24} \\\\ &\cfrac{1 \times 8}{3 \times 8}=\cfrac{8}{24} \end{aligned}

Now you can subtract the fractions.

\cfrac{21}{24}-\cfrac{8}{24}=\cfrac{13}{24}

Henry has \cfrac{13}{24} of a pound of beef left.

Example 5: multiplying fractions

Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?

It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.

However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.

The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.

To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”

\cfrac{1}{2} \times \cfrac{3}{4}= \, ?

To multiply fractions, multiply the numerators and multiply the denominators.

\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}

Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.

Example 6: dividing fractions

Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?

The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.

To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.

To divide fractions, multiply the dividend by the reciprocal of the divisor.

\begin{aligned}& \cfrac{7}{8} \div \cfrac{1}{4}= \, ? \\\\ & \downarrow \downarrow \downarrow \\\\ &\cfrac{7}{8} \times \cfrac{4}{1}=\cfrac{28}{8} \end{aligned}

You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.

Nia can make 3 \cfrac{1}{2} cup servings.

Teaching tips for fraction word problems

• Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
• Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
• Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
• As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
• Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
• There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.

Easy mistakes to make

• Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
• Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
• Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.

Related fractions operations lessons

• Fractions operations
• Multiplicative inverse
• Reciprocal math
• Fractions as divisions

Practice fraction word problem questions

1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?

Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.

Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.

Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.

Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.

To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.

\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.

Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”

2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?

The area of the garden is 1\cfrac{23}{36} square meters.

The area of the garden is \cfrac{27}{32} square meters.

The area of the garden is \cfrac{2}{3} square meters.

The perimeter of the garden is \cfrac{2}{3} meters.

To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.

\cfrac{24}{36} can be simplified to \cfrac{2}{3}. 

Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”

3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?

Zoe ate \cfrac{3}{64} more of the cake than Liam.

Zoe ate \cfrac{1}{4} more of the cake than Liam.

Zoe ate \cfrac{1}{8} more of the cake than Liam.

Liam ate \cfrac{1}{4} more of the cake than Zoe.

To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.

\cfrac{2}{8} can be simplified to \cfrac{1}{4}. 

Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”

4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?

Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.

Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.

Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.

Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.

To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}.  Then you can add.

\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}. 

Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”

5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?

Killian used \cfrac{2}{10} gallons of paint in all.

Killian used \cfrac{1}{5} gallons of paint in all.

Killian used \cfrac{63}{100} gallons of paint in all.

Killian used 1 \cfrac{3}{5} gallons of paint in all.

To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.

\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.

Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”

6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.

He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?

Evan filled \cfrac{2}{25} cups.

Evan filled 8 cups.

Evan filled \cfrac{9}{10} cups.

Evan filled 7 cups.

To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

\cfrac{40}{5} can be simplifed to 8.

Therefore, the correct answer is “Evan filled 8 cups.”

Fraction word problems FAQs

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.

To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.

Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.

The next lessons are

Still stuck.

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

Find out how we can help your students achieve success with our math tutoring programs .

[FREE] Common Core Practice Tests (Grades 3 to 6)

Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

Privacy Overview

Improper fraction

Improper fractions may be used as a counting system, and can also be used in cryptography. See improper fractional base .

This article is a stub. Help us out by expanding it .

Something appears to not have loaded correctly.

Click to refresh .

Special April offer - 7 days free unlimited access to all premium content Try Premium

• Fifth Grade

Improper fractions

Fifth grade improper fractions.

Filter by Grade:

Filter by subject:, smart practice.

Comparing Fractions

Simplifying Fractions

Adding Fractions

• International
• Schools directory
• Resources Jobs Schools directory News Search

improper fraction/mixed number word problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

20 January 2015

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Creative Commons "Sharealike"

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

terible word porblems becuse i dont like it

Empty reply does not make any sense for the end user

marie_teach

I was unfamiliar with the low, moderate, and high achiever acronym, but Google works.

ozzyshortstop34

This is just what I was looking for, word problems for application. Thank you.

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource: