problem solving maths 5th class

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CHALLENGE ZONE 5th Grade Math Problems

Welcome to our 5th Grade Math Problems. Here you will find our range of challenging math problem worksheets which are designed to give children the opportunity to apply their skills and knowledge to solve a range of longer problems.

These problems are also a great way of developing perseverance and getting children to try different approaches in their math.

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5th Grade Math Problems

Here you will find a range of problem solving worksheets.

The 5th grade math problems on the sheets are longer math problems designed to encourage children to use a range of math skills to solve them.

The skills the problems will help to develop include:

• systematic working
• logical thinking
• number fact knowledge
• fraction problems
• trial and improvement strategies
• working backwards
• working systematically
• searching for all possible answers.

At fifth grade, the problems are more advanced with children needing to become more systematic in their approach and experimenting using trial and improvement strategies.

Many of the problems have addition 'What if ...' questions with them to extend learning and get children looking for alternative solutions.

These sheets are great for extending learning for more able mathematicians, or using in a whole class problem solving lesson.

• 5th Grade Math Word Problems
• Bertie's Big Win

Bertie's Big Win is a problem involving both money and fractions which can be worked backwards. The aim of the problem is to work out how much money Bertie started with from the clue that are given.

• PDF version
• Fox vs Rabbit #2

Fox vs Rabbit is an activity involving mathematical modelling of a fox chasing a rabbit. The rabbit has a head-start, but the fox is faster. The aim is to find out when the fox will catch the rabbit, and whether or not the rabbit has time to reach his burrow.

• 1..2..3..4.. Challenge

The 1..2..3..4.. Challengs is a number problem involving using the numbers 1, 2, 3 and 4 along with arithmetic operators to make the numbers from 1 to 20. It is great for practicing PEMDAS and getting children to persevere and develop their mental arithmetic skills.

There are 2 versions of the problem sheet, one with a pre-prepared template for filling in, and a second blank version for children to show their own recording system.

• Blank version
• Frazer's Wall #2

Frazer's Wall #2 is a fraction problem solving activity which involves trying to work out the number of bricks that were laid in each day to find out how long it would take to make a wall. This problem is best solved by using a table or working it out one day at a time.

• Millenary Math

Millenary Math is a time problem involving what the time will be in a thousand years/weeks/hours/minutes, etc. It is a good activity for converting units of time and knowing facts like how many days are in each month. There is no answer sheet, as the activity involves using the current time.

• Sally's Fruit Punch #3

Sally's Fruit Punch is a money and scaling activity. The aim is to use the information to work out how much ingredients are needed. The ingredients then need to be priced to work out a total cost.

• Sally's Fruit Punch #3 UK Version
• Share the Treasure #5

Share the Treasure is a fraction sharing activity where the aim is to work backwards to find out how many bars of treasure the pirates had before they shared them all out. It is a good activity for developing fraction problem solving and working backwards.

• Something Fishy #2

Something Fishy is a money problem which involves working out exactly how many of each fish were bought in order to have spent a fixed amount of money on the fish. It is a good activity for using lists and tables to find all possibilities. It is also great for perseverance!

• Something Fishy #2 UK Version
• The Five Primes

The Five Primes is a number activity involving finding five primes with different totals. It is a good activity for learning prime numbers up to 30, and also for working systematically.

• The Rock Race #3

The Rock Race is a 5th grade math problem which needs some perseverance to complete. The aim of the activity is to try different routes around the 6 rocks to determine which route is the shortest.

• Who Chose Which?

Who Chose Which is a logical number activity where you need to use the clues to work out which numbers each of the salamanders chose.

• Birthday Bonanza

Birthday Bonanza is a logic problem which requires logical thinking to work out who got which present and how old each of them was.

• Number Totals Investigation

Number Totals Investigation is a PEMDAS number task which involves using 3 digits and operations to make the largest or smallest possible total.

Looking for some easier math problems?

We have a range of easier word problems on our 4th grade math problems page.

The problems on this page are at a simpler level than those here.

Many of the problems, e.g. Share the Treasure, The Rock Race, Something Fishy have easier versions on this page.

• 4th Grade Math Problems

Looking for some more fifth grade math word problems?

Here you will find our selection of free 5th grade math word problems.

Each sheet is availabel in both standard and metric units (where applicable).

Each sheet comes complete with a separate answer sheet.

All the problems are based around 'real life' such as the planets, heights of mountains, or length of rivers.

Using these sheet will help your child to:

• apply their addition, subtraction, multiplication and division skills;
• apply their knowledge of rounding and place value;
• solve a range of problems including "real life" problems and ratio problems.

All the worksheets help to support Elementary math benchmarks.

• 5th Grade Math Puzzles

Here you will find a range of printable 5th grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

• learn and practice their addition facts, including decimals;
• practice their subtraction facts, including decimals;
• practice and apply multiplication and division facts;
• develop problem solving skills and reasoning.

All the puzzles support elementary math benchmarks for 5th grade.

Fifth Grade Math Games

Here you will find a range of free printable 5th Grade Math games.

All children like to play Math games, and you will find a good range of Grade 5 Math Games here for your child to play and enjoy.

The following games involve different 5th Grade Math activities which you and your child can enjoy together.

All the free 5th Grade Math Worksheets in this section follow the Elementary Math Benchmarks for Grade 5.

• Math Games 5th Grade

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35 math problems for 5th graders

Here are 35 fifth-grade math problems that will help your child stay on track!

Author Amber Watkins

Published September 13, 2023

• Key takeaways
• 5th-grade math word problems help students apply mathematical concepts to real-world scenarios.
• In fifth-grade math, it’s important to master fractions, decimals, and order of operations.
• Hard problems for 5th graders can be simplified by drawing a picture or using a method that makes them easier to solve.

Table of contents

• Word problems

Numbers & place value

• Multiplication

If this math page has 5 sections of math problems for 5th graders with an average of 7 questions in each section, can you guess how many problems there will be in all? That’s right, there will be a total of 35 math problems for 5th graders for us to practice. Without realizing it, you just solved one of our first 5th-grade math word problems . Excellent work! Together we will review fifth-grade math problems with decimals, fractions, order of operations, and rounding. We will even consider hard math problems for 5th graders, like multiplying using square models and number lines. Don’t worry about getting the answers right the first time, each section includes math problems for 5th graders with answers if you need a sneak peek. So grab a pad and pencil and let’s begin.

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Select a year group

• Kindergarten

Measurement and data

Sample questions, word problems for 5th graders.

Let’s begin by covering math word problems for 5th graders.

Mia’s water bottle can hold 24 ounces of water. She drinks two full water bottles each day. How many total cups of water does Mia drink each day? [Conversions]

The playground is made up of four rectangular lots that are each 10 ft by 7 ft. What is the total area of the playground? [Finding area]

 Josh lives 2.5 miles away from the park. Josh rides his bike to the park and back home four days a week. How many miles does Josh ride his bike each week? [Calculations]

Place value

In this section, we will cover math problems for 5th graders that use place values, word form to standard form, standard form to word form, and expanded form.

Which digit in the number 245 is in the hundreds place?

Which digit in the number 4,602 is in the tens place?

Which digit in the number 752 is in the ones place?

Word form to standard form

Standard form to expanded form.

4,000 + 300 + 2 = 4,302

600 + 50 + 4 = 654

20,000 + 2,000 + 300 + 60 + 5 = 22,365

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In this section, we will cover fifth-grade math problems that include comparing decimals and rounding decimals to the nearest tenth, hundredth, and thousandths place. Let’s get started.

8.9 and 8.900 are the same.

Remember if the number to the right is 5 or larger, you can borrow and become one digit larger. If the number to the right is between 0 and 4, you can’t borrow and the number remains the same.

In this section, we will review math problems for fifth graders that cover the topics of adding and subtracting two and three-digit numbers using transformation, division using area models, and the order of operations .

Adding and subtracting whole numbers by transformation

A large portion of fifth-grade math problems can be made easier to solve by transformation or changing numbers to make the problem simpler. Let’s practice adding and subtracting two and three-digit numbers by transformation.

How to add numbers using transformation?

When adding or subtracting numbers, look for ways to round to make the problem simpler. Don’t forget what you do to one number, you have to do the opposite to the other. This makes sure the problem stays balanced. Let’s see how this is done. What is 48 + 52? 48 + 2 = 50

52 – 2 = 50 

50 + 50 = 100.

It may be difficult to add 48 + 52 in your head, so we round 48 to 50 by adding 2. Since we added 2 to the first number, we have to make sure to subtract 2 from the second number. So now the problem is 50 plus 50, which is much easier to calculate! 

32 – 2 = 30 68 + 2 = 70 30 + 70 = 100 The answer is 100.

208 – 8 = 200 432 + 8 = 440 200 + 440 = 640 The answer is 640.

321- 1 = 320 199 + 1 = 200 320 – 200 = 120 120 + 2 = 122 The answer is 122

Division using area models

Don’t know what an area model is? See our area model guide to help with these problems.

Using an area model find the quotient of 365 ፥ 5 =

Using an area model find the quotient of 504 ፥ 6 =

Using the area model below, find the quotient of 872 ፥ 2 =

Order of operations

Many people remember the Order of Operations with the acronym PEMDAS- “Please Excuse My Dear Aunt Sally”, with each letter representing an operation: Parentheses, Exponents, Multiply or Divide, Add or Subtract. Solve the following equations using the order of operations.

Hard multiplication math problems

Some of the hardest math problems for fifth graders involve multiplying: multiplying using square models, multiplying fractions and whole numbers using expanded form, and multiplying fractions using number lines. Let’s practice a few of each!

Multiplying using square models

Multiplying using square models is a method to help students “see” multiplication problems in a simpler way.

Multiply 42 x 35 using the square model below.

Multiply 55 x 76 using the square model below.

Multiply 98 x 42 using the square model below.

Multiplying fractions and whole numbers using expanded form

Multiply ½ x 5 using expanded form.

Multiply ⅔ x 6 using expanded form.

Multiply ⅙ x 7 using expanded form.

Multiplying fractions using a number line

Multiply ½ x 4/6 by using a number line.

For more math practice for 5th graders , our app for math help provides 5th-grade math help in a way that makes math fun, rewards effort over being correct, and scaffolds learning. Plus, you’ll get access to a dashboard that displays your child’s participation and progression on math topics they struggle with. Check it out today!

Parents, sign up for a DoodleMath subscription and see your child become a math wizard!

Word problem answer sheet

Mia drinks 6 cups of water each day. Explanation: There are 8 ounces in each cup. So 24 divided by 8 is equal to 3 cups each day.

280 square feet. Explanation: The area of one lot is 10 x 7 = 70 square feet. Take that area and times it by four, so 70 x 4 = 280 square feet.

Josh rides 20 miles on his bike each week. Explanation: Each day Josh rides 5 total miles: 2.5 miles to the park and 2.5 miles back home. If we multiply that number by 4 days a week, it equals 20 miles in all.

Writing numbers answer sheet

2 is in the hundreds place.

0 is in the tens place.

2 is in the ones place.

Division using area models answer sheet

Multiplying using square models answer sheet

Multiplying fractions and whole numbers using expanded form answer sheet

Multiplying fractions using a number line answer sheet

Explanation – First divide the number line into 6 equal parts and draw up a line up to 4/6. Then find the ½ way mark of that line you drew up to 4/6. You will now see the line is divided into three parts. So the answer would be ⅓. 

Lesson credits

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring elementary through college level math. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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5th Grade Math Word Problems: Free Worksheets with Answers

May 5, 2020 by Anthony Persico

Free 5th Grade Math Word Problems Worksheets!

Are you looking for engaging multi-step 5th grade math word problems with answers to add to your upcoming lesson plans? The following collection of free 5th grade maths word problems worksheets cover topics including mixed operations, estimation and rounding, fractions, and decimals.

These free 5th grade math word problem worksheets can be shared at home or in the classroom and they are great for warm-ups and cool-downs, transitions, extra practice, homework and credit assignments.

And if you’re looking for more free 5th grade math worksheets, check out this free library!

Mixed Operations 5th Grade Math Word Problems (PDF Download)

Click the link below to download your free 5th grade mixed operations word problems worksheet and answer key.

Looking for more free 5th grade math worksheets? Click here to access our full PDF library.

And click here to access our free library of 5th Grade Math Videos!

Estimation and Rounding 5th Grade Math Word Problems (PDF Download)

Click the link below to download your free 5th grade estimation and rounding PDF worksheet and answer key.

Click here to sign-up for our free weekly email newsletter!

Adding and Subtracting Fractions 5th Grade Math Word Problems (PDF Download)

Click the link below to download your free 5th grade adding and subtracting fractions PDF worksheet and answer key.

Multiplying Fractions 5th Grade Math Word Problems (PDF Download)

Click the link below to download your free 5th grade multiplying fractions PDF worksheet and answer key.

Decimals 5th Grade Math Word Problems (PDF Download)

Click the link below to download your free 5th grade decimals PDF worksheet and answer key.

Other 5th Grade Math Resources You Should Check Out:

This New Warm-Up Activity is a Game Changer (and a Time Saver!)

Check Out This Awesome Mean, Median, and Mode Activity!

How to Teach Multiplication Using Area Models

10 Super Fun Math Riddles for Kids (with Answers) 

Do you have any questions or anything to add? Share your thoughts in the comments below.

(Never miss a Mashup Math blog--click here to get our weekly newsletter!) 

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Fifth Grade Math Worksheets

Free & printable grade 5 math worksheets.

Our grade 5 math worksheets cover the 4 operations, fractions and decimals at a greater level of difficulty than previous grades. We also introduce variables and expressions into our word problem worksheets .  

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Add & Subtract

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Sample Grade 5 Math Worksheet

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• Maths Word Problems for Class 5

An Introduction to Maths Word Problems for Class 5

Word problems in mathematics refer to the information presented through ordinary storytelling, and students have to understand and transform it into mathematical equations. The level of difficulty of the exercises has been lowered, and mathematical ideas have been simplified to the greatest extent possible. To understand how concepts are used, each topic offers a substantial number of examples. We will focus on the four fundamental operations, fractions , decimals , etc. in fifth grade.

Word Problems on Addition and Subtraction for Class 5

Addition and subtraction word problems for Class 5 are necessary for students to build upon the basic addition and subtraction skill of arithmetic .

The benefit of addition and subtraction word problems is that students understand how to comprehend the given information in the word problems and write it in mathematical notation in order to solve it further.

Q1. Jerry had 87 marbles. He collected 74 more today. How many marbles does he have now?

Ans: Here from the question, it is given that Jerry had 87 marbles.

Since he collected 74 more,

So the total marble becomes 87 + 74

Jerry has a total of 161 marbles.

Q2. Mr. Sebastian had $257$. He bought an oven for $158$. How much money is left with him?

Ans: According to the question,

Mr. Sebastian had $257$. Out of $257$, he bought an oven for $158$.

So the money he had left will become:

= $257$ - $158$

Word Problems on Multiplication and Division for Class 5

Multiplication and division word problems for Class 5 will enhance the student's understanding of multiplication and division while solving real-life problems. Multiplication and division are one of the four basic arithmetic operations which find their use in our everyday lives.

Q1. A baseball team has 9 players. In a tournament, there are 6 teams. How many players are total in all?

Ans: In question, it is given that a baseball team has 9 players. If in a tournament there are 6 teams,

So the total players will become $9 \times 6$

= 54 players,

Therefore, 54 players are in total.

Q2. A farmer has to sow 500 seeds in 20 rows. How many seeds should be sown in each row?

Ans: According to the question, a farmer has to sow 500 seeds in 20 rows.

To find the number of seeds in each row, we need to divide the number of sown seeds by the rows.

Therefore, $\dfrac{500}{20}$ = 25

Hence, 25 seeds should be sown in each row.

Fraction Word Problems for Class 5

The fraction word problems for Class 5 help the students uncover fraction concepts and their usage in real-life situations. Fractions mean a part of the whole and they find their place everywhere making it an important topic to learn.

Q1. Sean buys 25 stickers on Monday and 17 on Tuesday. On Wednesday, he gives $\dfrac{5}{6}$ th of his stickers to James. How many does he have left?

Ans: Total stickers bought by Sean = Number of stickers bought on (Monday + Tuesday)

= 42 stickers.

Since he gave $\dfrac{5}{6}$ th of his stickers to James.

i.e. $\dfrac{5}{6}$ th of 42 stickers to James.

= $\dfrac{5}{6} \times 42$

= $5 \times 7$

So, he gave 35 stickers to James.

The number of stickers left for Sean is 42 - 35

Therefore, he has 7 stickers left.

Word Problems for Class 5 with Solution

Q1. Mr. Thomas sold 832 cookies in January and 917 cookies in February. How many cookies did he sell in these two months?

Mr. Thomas sold 832 cookies in January and 917 cookies in February.

So the total cookies he sold will become: 832 + 917

Q2. There are 40 pieces in a jigsaw puzzle. How many pieces are there in 3 such puzzles?

Ans: As per the question, there are 40 pieces in a jigsaw puzzle.

So to find the number of pieces in 3 puzzles, we have to multiply it by 40.

Therefore, $40 \times 3$

Hence, 120 pieces are in 3 puzzles.

Q3. The average rate of heartbeat per minute is 72. In how many minutes the heart would beat 1440 times?

Ans: Given,

The average rate of heartbeat per minute is 72.

So for 1440 times, $\dfrac{1440}{72}$

= 20 minutes.

Therefore, In 20 minutes the heart would beat 1440 times.

Q4. Hannah has 72 sweets in a bag. She keeps $\dfrac{1}{3}$rd of them for herself and shares the rest with friends. How many sweets will she give to her friends?

Ans: According to the question, Hannah has 72 sweets in a bag.

She keeps $\dfrac{1}{3}$rd of them for herself.

i.e. $\dfrac{1}{3}$rd of 72

= $\dfrac{1}{3} \times 72$

= $1 \times 24$

So she kept 24 for herself.

Therefore, Hannah has sweets = 72 - 24

Hence, she will give 48 sweets to her friends.

Practice Word Problems for Class 5

Q1. The population of the town is 78,384. If out of this, 38,400 are female, find the male population.

Ans: 39,984

Q2. Among every 5 bikes manufactured by a company, one bike is a special edition. If the company manufactures 150 bikes, how many bikes are special editions?

Ans: 30 bikes

For kids to master any topic, it is necessary to solve various problems within that topic. This article covered problems based on addition, subtraction , multiplication , division, and fraction. These problems will give insights and more clarity in day-to-day life while solving arithmetic problems. At the end of the article, we added solved examples and practice questions to get a better understanding.

FAQs on Maths Word Problems for Class 5

1. What are the tips and tricks for Class 5 Maths?

Create a connection between mathematical concepts and everyday tasks like working, playing, and buying. Allow your child to group or divide a few objects into different groups. There are two ways to learn tips and techniques in fifth grade, as follows:

Answer arithmetic problems

Apply maths to real-world situations.

2. What Maths concepts should I cover in Class 5?

Children learn to deal comfortably with numbers up to 1000 in Maths class five. They practise several approaches to number division, factoring, and multiple discoveries. As children study numbers up to 1000, they should also comprehend the idea of place value for numbers in the ones, tens, and hundreds range. Students advance their fundamental mathematical abilities in this first stage, including measuring quantities, and figuring out multiples, factors, and time. 

3. What distinguishes division from multiplication?

The numbers that are being multiplied are referred to as factors, and the outcome of the multiplication is referred to as the product. In division, the dividend is the number being divided, the divisor is the number dividing it, and the quotient is the outcome of the division. You will discover how to utilise arrays to illustrate how multiplication and division relate in this tutorial. 

NCERT Solutions for Class 5 Maths

The NCERT solutions for class 5 maths are customized for your learning needs, providing clear explanations and step-by-step approaches. These solutions are here to guide you through every step, from investigating the shapes and angles to disclosing the secrets of fractions with colourful practical examples, ensuring that math becomes not just a subject for kids but it is an exciting journey.

Are you ready to commence on a mathematical journey like no other? Let's begin the mathematical adventure together.

NCERT Solutions for Class 5 Maths PDF Download

Find a convenient way to excel in your class 5 maths through our NCERT solutions PDFs. These PDFs include chapter-wise solutions for NCERT maths of class 5 with step-by-step solutions. These solutions are diligently created by our math experts ensuring the enriched math learning experience of class 5 kids by providing all required visual elements.

Class 5 Maths NCERT Solutions Chapter 1 to 14

☛ Download Class 5 Maths NCERT Book

Class 5 NCERT Maths Chapters

Class 5 NCERT maths has 14 chapters. Here are the chapters and what they consist of in brief. This gives a better idea of what class 5 math is all about.

• Chapter 1 The Fish Tale:  This chapter involves solving real-life scenarios using addition , subtraction , multiplication , and division through an engaging story about fish.
• Chapter 2 Shapes and Angles:  This talks about different types of angles formed at the corners of different shapes . This chapter mainly talks about three types of angles: right angle , less than right angle, and more than right angle. 
• Chapter 3 How Many Squares?:  This chapter deals with counting squares to introduce the concept of the area of different shapes. Also, kids get an opportunity to play with the designs made of different tiles.
• Chapter 4 Parts and Wholes:  In this lesson, class 4 maths kids grasp the concept of fractions through vivid practical examples. 
• Chapter 5 Does it Look the Same?:  Throughout the chances students are provided with various examples to understand the mirror lines (symmetry) and their practice usage. Also, they are made to understand what are 1/2 turn, 1/4 turn, 1/3 turn, and 1/6 turn with many colourful drawings.
• Chapter 6 Be My Multiple, I'll Be Your Factor:  This lesson concentrates on multiples and factors . By the end of the lesson, kids will be able to understand the meaning of common multiples and common factors .
• Chapter 7 Can You See the Pattern:  Kids already are introduced to patterns in Class 4 NCERT maths. In this chapter, they will learn patterns of shapes and numbers in more depth.
• Chapter 8 Mapping Your Way:  This lesson is all about mapping and directions that help kids to enhance their spatial skills. 
• Chapter 9 Boxes and Sketches:  This chapter explains how to represent 3D object diagrams using 2D sketches. This talks about open drawings of a cube , floor maps of buildings and their deep drawings.
• Chapter 10 Tenths and Hundredths:  This lesson explains tenths and hundredths by using the concept of centimetres in terms of millimetres, metres in terms of centimetres, rupees in terms of paise, etc.
• Chapter 11 Area and Its Boundary:  In this chapter, students explore the concepts of perimeter and area of rectangles and squares by using different examples related to tokens, land, stamps, etc.
• Chapter 12 Smart Charts:  Through this chapter, kids will understand how to represent and read the data from visual representations like tally charts , pi charts , bar graphs , etc. 
• Chapter 13 Ways to Multiply and Divide:  As the name suggests, this lesson is all about different techniques of multiplication and division. The process of long division is introduced so nicely that any kid can understand the concept lying behind division.
• Chapter 14 How Big? How Heavy?:  This lesson introduces the concept of weight and capacity by comparing objects with small objects such as marbles, coins, cubes, matchboxes, etc. 

Importance of NCERT Solutions Class 5 Maths

The NCERT solutions for class 5 maths would encourage kids of class 5 to grasp everything from angles to areas by guiding you with the step by step explanations. These solutions would help you in cultivating problem-solving skills that would help you in tackling real-life scenarios. Further, the following are the most important features of class 5 solutions of NCERT maths.

• Improved Concept Clarity: Our step-by-step and attentively curated solutions would help the kids to grasp the concepts which in turn help them to break complex concepts into simple steps.
• Exam Readiness and Beyond:  These NCERT solutions for class 5 maths not only help in achieving better grades in their school and also help them perform better in the competition exams like olympiads .
• Self-Learning: These solutions help class 5 kids to learn the maths solutions on their own as the solutions are developed with clear explanations and necessary diagrams where required.

☛ Also Check:  NCERT Class 5 Maths Worksheets

FAQs on NCERT Solutions for Class 5 Maths

What are the chapters of ncert class 5 maths.

Class 5 maths of NCERT has 14 chapters. Here is the list of all chapters:

• The Fish Tale
• Shapes and Angles
• How Many Squares?
• Parts and Wholes
• Does It Look the Same?
• Be My Multiple, I'll Be Your Factor
• Can You See the Pattern?
• Mapping Your Way
• Boxes and Sketches
• Tenths and Hundredths
• Area and Its Boundary
• Smart Charts
• Ways to Multiply and Divide
• How Big? How Heavy?

Where to Find NCERT Class 5 Maths Solutions?

You are just 1 click away from getting Cuemath 's  NCERT solutions for class 5 maths . Just scroll up or click here to find PDF solutions with step-by-step solutions.

Do NCERT Solutions for Class 5 Maths Cover Entire Maths Syllabus?

Yes, our solutions cover the entire syllabus of class 5 math (including the solutions of all questions of all 14 chapters).

Are NCERT Solutions for Class 5 Maths Free?

Yes, the solutions of NCERY class 5 maths are completely free. Just scroll up this page, where you will find chapter-wise solutions. Just click on "PDF Solution" of the chapter that you need, download it, and enjoy learning maths in the easiest ways.

How Useful are the Solutions of Class 5 Maths NCERT?

The solutions of class 5 maths present on this page are very interactive provided with diagrams wherever required that help kids to understand the solution on their own.

NCERT Solutions for Class 5 Maths

NCERT Solutions for Class 5 Maths Question Answers of Math-Magic Part 5 in Hindi and English Medium prepared for CBSE 2024-25. Class 5 Maths NCERT solutions offer several features to help students in the 5th grade understand and engage with mathematical concepts. The key features of Class 5 Maths NCERT solutions cover a wide range of mathematical topics including whole numbers, fractions, decimals, measurements, geometry, and more, providing a comprehensive understanding of the subject. Chapter Wise Class 5 Maths NCERT Solutions Chapter 1. The fish Tale Chapter 2. Shapes and Angles Chapter 3. How Many Squares? Chapter 4. Parts and Wholes Chapter 5. Does it Look the Same? Chapter 6. Be My Multiple, I’ll be Your Factor Chapter 7. Can You See the Pattern? Chapter 8. Mapping Your Way Chapter 9. Boxes and Sketches Chapter 10. Tenths and Hundredths Chapter 11. Area and its Boundary Chapter 12. Smart Charts Chapter 13. Ways to Multiply and Divide Chapter 14. How Big? How Heavy? 5th Math Solutions use language suitable for 5th-grade students, making the explanations and instructions easy to understand. For practice exercises, solutions provide step-by-step explanations of problem-solving methods, helping students understand the process.

Class 5 Solutions incorporate visual aids like diagrams, illustrations, and charts to help students visualize mathematical concepts and make them more accessible. Many solutions include interactive elements such as puzzles, activities, and questions that encourage hands-on learning and active engagement. Overall, Class 5 Maths NCERT solutions are designed to make math enjoyable, understandable, and relatable for 5th-grade students. They provide the necessary support for learning, practicing, and mastering mathematical concepts at this stage of education.

Download App for Class 5

Class V Mathematics solutions in Hindi Medium are useful for those who want to study in Hindi language. All the solutions are given here free to download without any registration. Solutions often relate mathematical concepts to real-life scenarios, helping students understand the practical relevance of what they are learning.

Class 5 Maths is easy to understand and solve it. A regular practice is required to be confident. Otherwise, you may face problems like Maths fear or Maths panic or you may dislike this subject as a burden for your whole life. Many of you students are fond of engineering and want to become successful engineers. Solutions guide students through different problem-solving strategies, fostering critical thinking and logical reasoning skills. Without mathematics a learner cannot dream of engineering and many other fields. But now there is no need to fear because we are here to help you. Tiwari Academy provides 5th Class NCERT Book Maths Solutions for all chapters. NCERT Class 5 Maths Solutions are prepared by our most trusted and experienced subject experts.

Grade 5 Maths NCERT Solutions are thoroughly verified and double-checked for your safety and guarantee excellent scores. Students will find it very easy if you learn the basics of formulas very well. You should practice several questions daily and do self-assessment at regular intervals to find out your progress or decline, if any. NCERT Solutions for Class 5 Maths Based on the guidelines followed by CBSE and their recent as well as past year questions. Solutions include a variety of practice exercises that allow students to apply their learning and reinforce their skills. Additional notes or tips may be included to help parents and teachers explain concepts effectively to students. Class 5 Maths NCERT solutions help students transition from elementary to more complex mathematical concepts in higher grades.

After completing Class 5 Maths basics and formulae given in NCERT, children should complete the exercises given with each chapter. This is an important step because when you do it, you can see all the types of questions that can be shown in the exam. Solutions emphasize understanding over rote memorization, ensuring students have a clear grasp of the fundamental concepts. In doing so, you may find it difficult to solve various problems, mostly concept-based questions. Tiwari Academy’s NCERT Class 5 Maths Chapter Solution App PDF file containing solutions of all the questions covered in various chapter exercises. The solutions are solved in very simple steps and it also includes the explanation of each step so that all the steps are grasped with great fluency by all types of students.

Free PDF Download While studying a subject like Mathematics , if you can follow the right learning techniques, Maths will be a very enjoyable and enjoyable subject. Here, we follow all these techniques to make you a pleasant and enjoyable learning experience. Hence, NCERT 5th Class Maths Solutions comprises a total of 14 chapters. The solutions are often presented in an engaging and child-friendly format, maintaining the interest and motivation of young learners. Solutions align with the curriculum and can be used to prepare for assessments, helping students perform well in exams.

You can also download PDF file for each chapter from the link given below. Because of this, they will be able to grasp complex concepts later as they move up to the secondary and higher secondary level. You can download NCERT 5th Class Maths Solutions in PDF format and print them to help child’s study well. Class 5 Maths NCERT solutions provide foundational math skills that are essential for future academic pursuits and real-life applications.

As a parent, you may find this worrying as your child moves from a lower grade to a higher grade. We want to do all we can to help your child and for this you can also look for an academic PDF with study material. However, it is not certain that only this will give your child the support and help that he needs. At this age the focus on personal development is important to prepare for future classes. When a student reaches the fifth grade, his academic curriculum becomes more specialized than that of his previous classes. It is important to have a solid foundation at this stage. Starting with class 5, student’s school’s curriculum of activities will become more specific. Hence, as a parent, you need to help them to follow a specific subject approach for their exam preparation.

These NCERT solutions for class 5 Maths includes all fundamentals like Factors, Large Numbers, HCF and LCM, Fraction, Decimal, Percentage, Average, Divisibility Test, Simple Interest, Time, Profit and Loss, Metric Measurement, Unit Method, Geometry, Temperature and more do cover more. We have provided chapter solutions to the students for a deeper understanding of all the concepts. Students can easily download PDF solutions of all chapters without any login.

The number one study material that helps the students to complete the syllabus by gaining a deep understanding of the concepts should be NCERT books. Through these books, you will have access to comprehensive information that strengthens your fundamentals and helps you build a solid foundation for your senior classes. It is recommended that all CBSE and state board students follow NCERT books for all subjects in their class.

In the primary and upper primary classes, the school curriculum becomes very specific. In Tiwari Academy’s NCERT 5th Class Maths Solutions, you will find specific solutions for various chapters and exercises. Class 5 Maths NCERT solutions are available for all the sums given in the chapters of class 5 NCERT Maths textbook. You can easily download the solutions for a specific chapter and then follow the solutions for the problems given there. For example, there is a chapter on standard units in the Class 5 textbook. This chapter explores the concepts of distance, height, weight, and measure.

Although grade 5 is the most basic level, these concepts are very important for your middle, secondary, and higher secondary level subjects. This is why it is necessary that students fully understand and be able to apply the concepts in Class V. All the chapter exercises are meant to test the knowledge of the student after the chapter is over. However, if you want to grasp a new concept completely, you may need the help of answer keys. Learn here the ways to solve Maths in class 5 in simple steps. It is not uncommon for students to check their answers after solving the problem. In fact, almost all math books come with solutions at the end. But, they only provide the answer and not the explanation of the concept.

Is NCERT Class 5 Maths Easy to solve?

Do you know, what is math? Is it a challenging or easy subject? You may have heard people randomly say that they are good at Maths, but others are not good enough at it. By the way, let us tell you that mathematics is a very complex subject. Yes, because either you will be good at it or you will be average, you may face a lot of problems while going through this. But it is still not too late as you are in class 5 and you can build your foundation for Maths and do it very hard. Otherwise, you may face a lot of serious problems in future due to lack of basic concepts that you know. Practice is the only way to make Mathematics easier.

What is the easier way to solve Class 5 Maths NCERT assignments?

To ensure that the NCERT Book for Class 5 Maths has the right approach to the problems of the students, we have prepared the best NCERT Solutions for Class 5 Maths. Only the best experts in the field are involved in preparing these NCERT 5th Class Maths Solutions who provide the answers to the problems with detailed explanation. These solutions are very effective to strengthen your concepts and clear your doubts. With Tiwari Academy’s NCERT 5th Class Maths Solutions, students will be able to manage their assignments easily and prepare well for their exams.

How to prepare Class 5 Maths all Chapters for Exams?

We, the best free educational academy in India, would suggest that all the students completely concentrate on all the chapters of NCERT Textbook Class 5 Maths, and crack the exam, get good grades. Firstly, students should read all the concepts from their NCERT Class 5 books, learn them, memorize all the given formulas correctly to memorize those concepts quickly, and then apply the formulas. Some questions should be practiced regularly.

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Maths Problems with Answers for Grade 5

Grade 5 maths problems with answers are presented. Also Solutions and explanations are included.

• Three toy cars and 4 toy trains cost $18. Two toy cars and 3 toy trains cost $13. What is the price of one toy car and the price of one toy train if both prices are whole numbers of Dollars? (Hint: Use a table) Solution
• 450 chocolate bars
• 4 hours and 30 minutes
• 11,800 TV sets
• Tom: 22 , Bob: 27
• same time , 12 minutes
• Jim: 5 years , Carla: 10 years , Tomy: 16 years
• 10,080 minutes
• 700 meters squared
• 114 centimeters squared
• one toy car costs $2 and 1 toy train costs $3.

More References and links

Primary Maths (grades 4 and 5) with Free Questions and Problems With Answers Middle School Maths (grades 6,7,8 and 9) with Free Questions and Problems With Answers High School Maths (Grades 10, 11 and 12) - Free Questions and Problems With Answers

• NCERT Solutions
• NCERT Class 5
• NCERT 5 Maths
• Chapter 13: Ways To Multiply And Divide

NCERT Solutions Class 5 Maths Chapter - 13 Ways to Multiply and Divide

NCERT Solutions Class 5 Maths Chapter-13 Ways to Multiply and Divide, are provided here with solved questions for students so that students can refer to them while preparing for the exam. The NCERT Solutions are prepared by experts in the Maths subject, with respect to the CBSE syllabus (2023-2024) for Class 5.

Maths has always been one of the core subjects in almost every field. Therefore, it is vital to know and learn mathematics. Furthermore, this grade is a crucial phase in a child’s academics, where the elementary concepts are made clear to the students. Students in 5th grade can get the learning materials from here such as notes, textbooks , solutions, etc.

NCERT Solutions Class 5 Maths Chapter – 13 Ways to Multiply and Divide

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Access NCERT Solutions to Class 5 Maths Chapter 13 Ways to Multiply and Divide

Page No: 170

Manirathinam – The Cashier

1. Maniratnam is the cashier of king Jayan. His job is to find out the salary of all the people who work for the king. This chart shows how much salary each person gets in a day.

Maniratnam wanted to calculate the salary of the cook for the month of January. He wrote —

Rupees 1800 + 150 + 60 + 5 = Rs ________

Rupees 1800 + 150 + 60 + 5 = Rs (1950 + 65) = Rs 2015

2. Maniratnams daughter Bela has learnt another method to multiply. She wrote like this and showed it to Bhanu, her brother.

3. Now Bhanu tried to find the salary of a minister for the month of January. He wanted to multiply 195 × 31.

Practical time

1. Use Bela’s method to multiply these numbers.

a) 32 × 46 b) 67 × 18

a) 32 × 46 = 1472 b) 67 × 18 = 1206

2) Do these in your notebook using Bela’s method.

a) 47 × 19 b) 188 × 91

c) 63 × 57 d) 225 × 22

e) 360 × 12 f) 163 × 42

Shantaram a Special Cook

1. Shantaram is a special cook who comes only on party days. Last year he was called for only 28 days. For each day he has to be paid Rs 165. Find out how much money he will get in all.

Salary paid to Shantaram for 1 day = Rs 165

So, the salary paid to Shantaram for 28 days = Rs 165 × 28

Hence, the money Shantaram gets in all is Rs 4620.

2. If he is called for all days of the year, how much salary will he get?

Thus, the cook will get a salary of Rs 60,225

3. Now find the salaries of the minister and horse rider for 1 year.

The salary paid to the minister for 1 day = Rs 195

So, the salary paid to the minister for 365 days = Rs 195 × 365

Hence, the salary of the minister for 1 year is Rs 71,175

The salary paid to the horse rider for 1 day = Rs 95

So, the salary paid to the horse rider for 365 days = 365 × Rs 95

Hence, the salary of the minister for 1 year is Rs 34,675

Years and Years

(a) Sohan drinks 8 glasses of water every day.

• How many glasses will he drink in one month? __________

• How many glasses will he drink in one year?

• If 125 people living in a colony drink 8 glasses of water in a day, how much water will they drink in a year?

The number of glasses of water Sohan drinks everyday = 8

We know that, 1 months – 30 days

So, the number of glasses of water consumed by Sohan = 8 x 30

Hence, Sohan will drink 240 glasses of water in one month.

Now, we know 1 year = 365 days

So, the number of glasses of water consumed by Sohan in 365 days = 365 x 8

Hence, Sohan will drink 2,920 glasses of water in one year.

We have, the number of glasses of water consumed by 1 person for a year = 2,920

So, the number glasses of water consumed by 125 people of the colony for one year = 2920 x 125

Therefore, 125 people of the colony will drink 3, 65,000 glasses of water in one year.

(b) If Soha’s heart beats 72 times in one minute, how many times does it beat in one hour?

• Now find out how many times it beats in one day.

• Count your own heart beats to find out how many times your heart beats in one week.

The number of times Soha’s heart beats in one minute = 72

We know, 1 hour = 60 minutes

So, the number of times Soha’s heart beats in one hour = 72 x 60

Hence, Soha’s heart beats 4,320 times in one hour.

Now, we know one day has 24 hours.

So, the number of times Soha’s heart beats in a day = 4320 x 24

Hence, the number of times Soha’s heart beat in a day is 1, 03,680.

My heart beats 72 times in a minute. We know, 1 week has 7 days.

So, the number of times my heart beats in one week = 1, 03,680 x 7

Hence, the number times my heart beats in a week is 7, 25,760.

(c) A baby elephant drinks around 12 L of milk every day. How much milk will it drink in two years?

The number of litres of milk the baby elephant drinks in a day = 12 L

We know, number of days in a year = 365

And the number of days in two years = 365 x 2 = 730

So, the number of litres of milk the baby elephant drinks in two years = 12 x 730

Hence, the number of litres of milk the baby elephant will consume in two years is 8,760.

(d) A baby blue whale drinks around 200 L of milk in one day. Just imagine how much milk that is! Find out in how many days your family would use 200 L milk. How much milk would the baby blue whale drink in eight months?

Number of litres of milk a baby blue whale drinks in one day = 200

Number of litres of milk used in my family in one day = 2

So, the number of days for consuming 200 L of milk by my family = 200/2 = 100 days

We know 1 month = 30 days then, 8 months = 30 x 8 = 240 days

So, the number of litres of milk the baby blue whale will drink in eight months = 200 x 240

Hence, the baby blue whale will consume 48,000 L of milk in eight months.

Karunya – The landlord

Karunya bought three fields.

1. Find the area of all the three

Field (A) ____________ square metre.

Field (B) ____________ square metre.

Field (C) ____________ square metre.

Dimensions of field (A): Length = 27 m and breadth = 28 m

Area (A) = 27 x 28

Field (A) 756 square metre.

Dimensions of field (B): Length = 36 m and breadth = 12 m

Area (B) = 36 x 12

Field (B) 432 square metre.

Dimensions of field (C): Length = 27 m and breadth = 19 m

Area (C) = 27 x 19

Field (C) 513 square metre.

2. He bought field (A) at the rate of Rs 95 for a square metre, field

(B) at Rs 110 for a square metre and field (C) at Rs 120 for a square metre.

Find the cost of all three fields.

Cost of 1 square metre of field A = Rs 95

So, the cost of 756 square metre of field A = Rs (756 x 95)

Thus, the cost of field A is Rs 71,820

Cost of 1 square metre of field B = Rs 110

So, the cost of 432 square metre of field B = Rs (432 x 110)

Thus, the cost of field B is Rs 47,520

Cost of 1 square metre of field C = Rs 120

So, the cost of 513 square metre of field C = Rs (756 x 95)

Thus, the cost of field C is Rs 61,560

The total cost of all the fields = Rs 71,820 + Rs 47,520 + Rs 61,560 = Rs 1, 80,900

Thulasi and her husband work on Karunya’s farm. The Government has said that farm workers should be paid at least Rs 71 for one day’s work. But he pays Rs 55 to Thulasi and Rs 58 to her husband.

If Thulasi works for 49 days, how much money does she get? _______

If her husband works for 42 days, how much money does he get? ___________

Find the money they earn together ___________

Thulasi is paid Rs 55 for one day’s work.

So, if she works for 49 days, she will get = Rs 55 x 49

Thus, Thulasi will get Rs 2,695 for working 49 days in the farm.

Thulasi’s husband is paid Rs 58 for a day’s work.

So, if he works for 42 days, he will get = Rs 58 x 42

Thus, Thulasi’s husband will get Rs 2,436 for working 42 days in the farm.

Total money earned by both of them = Rs 2,695 + Rs 2,436 = Rs 5,131

The table shows the amounts fixed by four states.

a) For farm work which state has fixed the highest amount? Which state has fixed the lowest?

b) Bhairon Singh is a worker in Rajasthan. If he works for 8 weeks on the farm, how much will he earn?

c) Neelam is a worker in Haryana. If she works for 2½ months on the farm, how much will she earn?

d) How much more will a farm worker in Madhya Pradesh get than a worker in Orissa after working for 9 weeks?

(a) For farm work, Haryana has fixed the highest amount of Rs 135 for one day. The lowest is for Rajasthan paying Rs 73 for one day.

(b) Bhairon Singh works in Rajasthan, so he will be paid Rs 73 for one day.

We know, 1 week = 7 days

Then, 8 weeks = 7 x 8 = 56 days

So, Bhairon Singh’s earnings for working in the farm for 56 days = Rs 73 x 56

Thus, Bhairon Singh will earn Rs 4,088 in 8 weeks.

(c) Neelam working in Haryana will be paid Rs 135 for one day.

We know, 1 month = 30 days and ½ month = 30/2 = 15 days

Then, 2 ½ months = (2 x 30) + 15 = 75 days

So, the earnings of Neelam for working in the farm for 2 ½ months = Rs 135 x 75

Hence, Neelam will earn Rs 10,125 in 2 ½ months.

(d) The salary of a farm workers for one day in Madhya Pradesh = Rs 97

We know, one week = 7 days

Then, 9 weeks = 9 x 7 = 63 days

So, the earning of a farm worker working for 63 days = Rs 97 x 63

Hence, a farm worker will get Rs 6,111 in 9 weeks working in Madhya Pradesh.

The salary of a farm workers for one day in Orissa = Rs 75

So, the earning of a farm worker working for 63 days = Rs 75 x 63

Hence, a farm worker will get Rs 4,725 in 9 weeks working in Madhya Pradesh.

Difference between the earning of the farm workers = Rs 6,111 – Rs 4,725 = Rs 1,386

Therefore, a farm worker in Madhya Pradesh will get Rs 1,386 more than a farm worker in Orissa after working for 9 weeks.

Satish’s story

Satish is a 13 year old boy. His father had taken a loan for farming. But the crops failed. Now Satish’s mother has to pay Rs 5000 every month for the loan.

Satish started working — he looked after 17 goats of the village.

He earns Rupee 1 every day for one goat.

• How much will he earn in one month? • Does he earn enough to help pay the loan every month?

• How much will he earn in one year?

Satish earns Rs 1 for one goat every day. He looked after 17 goats of his village.

So, Satish will earn = Rs 1 x 17 = Rs 17 for a day

For a month Satish will earn = Rs 17 x 30

Thus, Satish will earn Rs 510 in one month.

Satish’s mother has to pay Rs 5,000 every month for the loan. But, the earnings of Satish will not help pay the loan every month.

We know, 1 year = 12 months

Satish’s earning in one year = Rs 510 x 12

Therefore, Satish will earn Rs 6,120 in one year for looking after 17 goats.

Kamla Bai’s story

To help farmers the State Government gave cows. Kamla Bai Gudhe also got a cow. The cost of the cow was Rs 17,500. She had to pay Rs 5,500 and the government spent the rest of the money.

• How much did the government spend on the cow?

• If 9 people from her village got cows, how much did the government spend in all?

But Kamla Bai was not happy, She had to spend Rs 85 everyday on the cow. She made some money by selling the milk. But still she wanted to sell the cow.

• If Kamla Bai spends Rs 85 a day, find out how much she will spend in one month.

• The cow gives 8 litre of milk every day. How much will it give in one month?

• If the milk is sold at Rs 9 per litre, how much money will Kamla Bai make in one month? ___________

So the money spent on keeping the cow was Rs ___________

Money earned by selling the milk Rs ___________

Which is more — money spent on the cow or money earned form it? How much?

• Explain why she wanted to sell the cow.

• Kamla Bai paid Rs 5,500 for getting the cow.

The cost of the cow is Rs 17,500.

So, the amount government spent on the cow = Rs (17,500 – 5,500)

Hence, the government spent Rs 12,000 on one cow.

• Now, we know the money spent by the government for one cow is Rs 12,000

So, for 9 cows the money spent by the government would be = Rs 12,000 x 9

Hence, the government spent Rs 1, 08,000 on nine cows for nine people.

• Kamla Bai spends Rs 85 a day.

I month = 30 days

So, the money spent by Kamla Bai in one month = Rs 85 x 30

Hence, Kamla Bai will spend Rs 2,550 on the cow in one month.

• The cow gives 8 litres a day.

1 month = 30 days

So, the amount of milk the cow will give in one month = 8 L x 30

Hence, the cow will give 240 litres of milk in one month.

• The milk is sold at Rs 9 per litre.

Then, the selling price for 240 litres of milk = Rs 9 x 240

Hence, Kamla Bai will earn Rs 2,160 by selling 240 litres of milk in one month.

So, the money spent for keeping the cow was Rs 2,550

Money earned by selling the milk Rs 2,160

The money spent on the cow is more as compared to the money earned by the cow.

= Money spent for the cow – Money earned by selling milk

= Rs 2,550 – Rs 2,160

Hence, the money spent on keeping the cow is Rs 390 more than the money earned by selling the milk.

• She wanted to sell the cow because she had to spend more money on the cow compared to her earnings by selling the milk of the cow.

Practice time

(a) Sukhi works on a farm. He is paid Rs 98 for one day. If he works for 52 days, how much will he earn?

(b) Hariya took a loan to build his house. He has to pay back Rs 2,750 every month for two years. How much will he pay back in 2 years?

(c) Ratiram is milk seller in the city. He sells 13 litres of milk everyday at Rs 23 per litre. How much does he earn?

(d) A farmer sells 1 litre of milk for Rs 11. In one month he sells 210 litres of milk. How much does he earn in a month?

(e) A company sells 1 litre of packed water for Rs 12. A shopkeeper buys 240 litres of packed water. How much does he pay?

(a) Sukhi is paid Rs 98 for working one day on a farm.

So, his earning if we works 52 days will be = Rs 98 x 52

Hence, Sukhi will earn Rs 5,096 by working in the farm for 52 days.

(b) Hariya pays back Rs 2,750 every month.

She has to pay the amount for a period of 2 years.

2 years = 2 x 12 months = 24 months

So, the money to be paid by Hariya in 24 months = Rs 2,750 x 24

Hence, Hariya will pay back Rs 66,000 in 2 years for the loan.

(c) The earnings of Ratiram by selling 1 litre of milk = Rs 23.

Then, the earnings of Ratiram by selling 13 litres of milk = Rs 23 x 13

Hence, Ratiram earns Rs 299 after selling 13 litre of milk every day.

(d) The farmer sells 1 litre of milk at Rs 11.

So, the earning of selling 210 litres of milk in one month = Rs 11 x 210

Hence, the farmer earns Rs 2,310 in a month by selling milk.

(e) Selling price of 1 litre of packed water = Rs 12

Then, the amount the shopkeeper has to pay for buying 240 litres of packed water = Rs 12 x 240

Hence, the shopkeeper has to pay Rs 2,880 for 240 litres of packed water.

Fun with multiplication

A) Look for the pattern and take this forward.

B) Each letter a, b, c stands for a number.

Take a = 1, then find what the numbers b and c will be.

Therefore, we have b = 2 and c = 3.

C) Tricks with your age.

Write your age __________

Multiply it by 7 __________

Again multiply the answer by 13 _________

Multiply again that answer by 11 _________

Now look at your last answer. Can you find your age in that answer? How many times does your age show in the answer?

Now try this trick with other people.

Write your age: 10

Multiply it by 7: 10 x 7 = 70

Again multiply the answer by 13: 70 x 13 = 910

Multiply again that answer by 11: 910 x 11 = 10010

Yes, I can find my age in the final answer. My age appears two times in the answer.

D) Going round and round!

Do you find a pattern in all these answers? Discuss this with your friends.

No, we didn’t find any pattern in the answer.

Dolma took a loan from a friend to buy a moped for Rs 9,588. She has to pay it back in equal amounts every month for six months.

• How much will she have to pay every month? She asked her children to calculate .

• Will both of them get the same answer? Discuss.

The answer calculated by her daughter = 500 + 500 + 90 + 8 = 1598

The answer calculated by her son = 1000 + 500 + 90 + 8 = 1598.

So, both the children get the same answer.

Therefore, Dolma has to pay a sum of Rs 1,598 every month for 6 months to her friend.

Try to solve these using as few steps as you can.

a) 4228 ÷ 4 b) 770 ÷ 22 c) 9872 ÷ 8

d) 672 ÷ 21 e) 772 ÷ 7 f) 639 ÷ 13

How Much Petrol?

Isha has Rs 1000 with her. She wants to buy petrol. One litre of petrol costs Rs 47. How many litres can she buy?

Money with Isha = Rs 1000

Cost of 1 litre = Rs 47

Litres of petrol she can buy = Rs 1000 ÷ Rs 47 =?

Isha can buy ________ litres of petrol. 

Dividing Rs 1000 ÷ Rs 47 we have,

Remainder = 13

Hence, Isha can only buy 21 litres of petrol with Rs 1,000.

If Isha comes to your city, how much petrol can she buy with the same money?

The cost of petrol in my city = Rs 50

So, the number of litres of petrol Isha can buy with Rs 1000 = 1000 ÷ 50

Thus, Isha can buy 20 litres of petrol in my city.

Children’s Day

Children are happy today. They are celebrating Children s Day. Each child will be given 4 coloured pencils from school. The school has got 969 pencils. To find out how many children can get pencils the teacher asks them to divide.

Complete Iru’s and Sreeni’s way of division. What is the answer you get?

In both the ways we got the same answer which is 242.

Hence, 242 students can get the colour pencils.

Practice Time

1. 576 books are to be packed in boxes. If one box has 24 books, how many boxes are needed?

Total number of books to be packed in boxes = 576

Number of books one box = 24

The number of boxes required to put 576 books = 576 ÷ 24

Hence, 24 boxes are required to pack 576 books.

2. 836 people are watching a movie in a hall. If the hall has 44 rows, how many people can sit in 1 row?

Total number of people watching movie in the hall = 836

Number of rows in the hall = 44

The number of people sitting in one row = 836 ÷ 44

Hence, 19 people are sitting in 1 row of hall.

3. A gardener bought 458 apple trees. He wants to plant 15 trees in each row. How many rows can he plant?

How many trees would be left over?

Total number of trees bought by gardener = 458

Number of trees planted in one row = 15

So, the number of rows he can plant = 458 ÷ 15

Thus, the gardener can plant 30 rows of apple trees and he’ll be left with 8 trees.

Brain Teaser

1. Shyamli bought a battery. She read on it ‘Life: 2000 hours’. She uses it throughout the day and the night. How many days will the battery run?

The life of the battery = 200 hours

She uses it all day and night, i.e. for 24 hours

So, the number of days the battery will run = 2000 ÷ 24

Thus, the battery will run for 83 days.

More with Multiplication and Division

1. A tank is full of 300 L of water. How much water will be filled in 25 tanks? If 15 buckets can be filled with one tank of water, how many buckets in all can be filled with the water in 25 tanks?

Amount of water in 1 tank = 300 L

Then, the amount of water in 25 tanks = 25 x 300 L = 7500 L

The number of buckets that can be filled with one tank of water = 15

So, the number of buckets that can be filled with 25 tanks of water = 25 x 15

Hence, 375 buckets can be filled with 25 tanks of water.

2. There are 28  laddoos  in 1 kg. How many  laddoos  will be there in 12 kg? If 16  laddoos  can be packed in 1 box, how many boxes are needed to pack all these  laddoos ?

Number of laddoos in 1 kg = 28

Then, the number of laddoos in 12 kg = 28 x 12

Hence, there will be 336 laddoos in 12 kg,

Number of laddoos that can be packed in one box = 16

So, the number of boxes required to pack 336 laddoos = 336 ÷ 16

Hence, 21 boxes are needed to pack all the laddoos.

3. There are 26 rooms in a school. Each room has 4 plants. If each plant needs 2 cups of water, how much water do we need for all the plants?

Number of rooms in the school = 26

Number of plants in each room = 4

So, the total number of plants = 26 x 4 = 104

Number of cups needed for each plant = 2 cups

Then, the total number of cups required for 104 plants = 104 x 2 = 208

Hence, we need 208 cups of water for all the plants.

Make the Best Story Problem

Each line gives a story. You have to choose the question which makes the best story problem.

(1) A shopkeeper has 50 boxes. There are 48 fruits in one box.

Explain why (a) and (c) are not good choices.

Option (a) is not a good choice because price is not given in the story

Option (c) is not a good choice because total number of boxes is given in the story.

(2) 352 children from a school went on a camping trip. Each tent had a group of 4 children.

(3) A shopkeeper has 204 eggs. He puts them in egg trays. Each tray has 12 eggs.

(4) The cost of one book is Rs 47. Sonu buys 23 books.

Do these divisions. Check your results by multiplication.

(a) 438 ÷ 9 (b) 3480 ÷ 12 (c) 450 ÷ 7

(d) 900 ÷ 10 (e) 678 ÷ 6 (f) 2475 ÷ 11

Quotient = 48, Remainder = 6 and Divisor = 9.

Divisor x Quotient + Remainder = 9 x 48 + 6 = 438 = Dividend

Quotient = 290, Remainder = 0 and Divisor = 12.

Divisor x Quotient + Remainder = 12 x 290 + 0 = 3480 = Dividend

Quotient = 64, Remainder = 2 and Divisor = 7.

Divisor x Quotient + Remainder = 7 x 64 + 2 = 450 = Dividend

Quotient = 90, Remainder = 0 and Divisor = 10.

Divisor x Quotient + Remainder = 10 x 90 + 0 = 900 = Dividend

Quotient = 113, Remainder = 0 and Divisor = 6.

Divisor x Quotient + Remainder = 6 x 113 + 0 = 678 = Dividend

Quotient = 225, Remainder = 0 and Divisor = 11.

Divisor x Quotient + Remainder = 11 x 225 + 0 = 2475 = Dividend

2) Solve the given sums and colour the answers in the grid given below See what you find.

These solutions are designed in such a way that the student finds it very easy to understand the concepts. Furthermore, questions are provided that depict real-life scenarios where these concepts are being used. Students can practise Class 5 NCERT Solutions for Maths  for all chapters and excel in them.

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5th Grade Math Problems

In 5th grade math problems you will get all types of examples on different topics along with the solutions.

Keeping in mind the mental level of child in Grade 5, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts.

If student follow math-only-math they can improve their knowledge by practicing the solutions step by step which will help you to score in your exam. In 5th grade we will mainly follow on the four basic operations, fractions, decimals, etc…..

●  Roman Numerals

• Roman Numeration
• Conversion of Roman Numeration
• Operations on Roman Numerals

●  Roman Numerals - Worksheets

• Worksheet on Roman Numeration
• Worksheet on Comparison of Roman Numerals
• Worksheet on Operations on Roman Numerals

5th Grade Numbers.

●  Various Types of Numbers

• Prime and Composite Numbers

●  Operations On Whole Numbers

• Addition Of Whole Numbers.
• Word Problems on Addition and Subtraction of Whole Numbers
• Subtraction Of Whole Numbers.
• Multiplication Of Whole Numbers.
• Properties Of Multiplication.
• Multiplication by Ten, Hundred and Thousand
• Division Of Whole Numbers.
• Properties Of Division.
• Word Problems on Multiplication and Division of Whole Numbers
• Estimation in Operations on Numbers
• Worksheet on Addition and Subtraction of Large Numbers
• Worksheet on Word Problems on Multiplication of Whole Numbers
• Worksheet on Multiplication and Division of Large Numbers
• Worksheet on Operations On Whole Numbers

●  Integers

• Representation of Integers on a Number Line.
• Addition of Integers on a Number Line.
• Addition of Integers
• Rules to Add Integers.
• Subtraction of Integers
• Rules to Subtract Integers.

●   Multiplication is Repeated Addition.

• Multiplication of a Whole Number by a Fraction
• Multiplication of Fractional Number by a Whole Number.
• Multiplication of a Fraction by Fraction.
• Properties of Multiplication of Fractional Numbers.
• Multiplicative Inverse.
• Problems on Multiplication of Fractional Numbers 
• Worksheet on Multiplication on Fraction.
• Division of a Fraction by a Whole Number.
• Division of a Fractional Number.
• Division of a Whole Number by a Fraction.
• Properties of Fractional Division.
• Problems on Division of Fractional Numbers
• Worksheet on Division of Fractions.
• Simplification of Fractions.
• Worksheet on Simplification of Fractions.
• Word Problems on Fraction.
• Worksheet on Word Problems on Fractions.

●  Decimal.

• Tenth Place in Decimals
• Hundredths Place in Decimals
• Thousandths Place in Decimals
• Whole Numbers and Decimals
• Decimal Place Value Chart.
• Expanded form of Decimal Fractions
• Like Decimal Fractions.
• Unlike Decimal Fraction.
• Equivalent Decimal Fractions.
• Changing Unlike to Like Decimal Fractions.
• Ordering Decimals
• Comparison of Decimal Fractions.
• Conversion of a Decimal Fraction into a Fractional Number.
• Conversion of Fractions to Decimals Numbers.
• Addition of Decimal Fractions.
• Problems on Addition of Decimal Fractions
• Subtraction of Decimal Fractions.
• Problems on Subtraction of Decimal Fractions
• Multiplication of a Decimal Numbers.
• Multiplication of a Decimal by 10, 100, 1000
• Multiplication of a Decimal by a Decimal.
• Properties of Multiplication of Decimal Numbers.
• Problems on Multiplication of Decimal Fractions
• Division of a Decimal by a Whole Number.
• Division of Decimal Fractions
• Division of Decimal Fractions by Multiples.
• Division of a Decimal by a Decimal.
• Division of a whole number by a Decimal.
• Properties of Division of Decimal Numbers
• Problems on Division of Decimal Fractions
• Conversion of fraction to Decimal Fraction.
• Simplification in Decimals.
• Word Problems on Decimal.

● Simplification of Numerical Expressions

• Numerical Expressions Involving Whole Numbers
• Numerical Expressions Involving Fractional Numbers
• Numerical Expressions Involving Decimal Numbers

●  Rounding Numbers.

• Round off to Nearest 10.
• Round off to Nearest 100.
• Round off to Nearest 1000.
• Rounding Large Numbers
• Rounding off Decimal Fractions.
• Correct to One Decimal Place.
• Correct to Two Decimal Place.
• Worksheet on Rounding off number.

●  Factors.

• Common Factors.
• Prime Factors.
• Repeated Prime Factors.
• Highest Common Factor (H.C.F).
• Examples on Highest Common Factor (H.C.F).
• Greatest Common Factor (G.C.F).
• Examples of Greatest Common Factor (G.C.F).
• Prime Factorisation.
• To find Highest Common Factor by using Prime Factorization Method.
• Examples to find Highest Common Factor by using Prime Factorization Method.
• To find Highest Common Factor by using Division Method.
• Examples to find Highest Common Factor of two numbers by using Division Method.
• To find the Highest Common Factor of three numbers by using Division Method.

● Multiples.

• Common Multiples.
• Least Common Multiple (L.C.M).
• To find Least Common Multiple by using Prime Factorization Method.
• Examples to find Least Common Multiple by using Prime Factorization Method.
• To Find Lowest Common Multiple by using Division Method
• Examples to find Least Common Multiple of two numbers by using Division Method.
• Examples to find Least Common Multiple of three numbers by using Division Method.
• Relationship between H.C.F. and L.C.M.
• Worksheet on H.C.F. and L.C.M.
• Word problems on H.C.F. and L.C.M.
• Worksheet on word problems on H.C.F. and L.C.M.

●  Multiples and Factors.

• Worksheet on Multiples and Factors

●  Divisibility Rules.

• Properties of Divisibility.
• Divisible by 2.
• Divisible by 3.
• Divisible by 4.
• Divisible by 5.
• Divisible by 6.
• Divisible by 7.
• Divisible by 8.
• Divisible by 9.
• Divisible by 10.
• Problems on Divisibility Rules
• Worksheet on Divisibility Rules

●  Percentage.

• To Convert a Percentage into a Fraction
• To Convert a Fraction into a Percentage
• To find the percent of a given number
• To find what Per cent is one Number of another Number
• To Calculate a Number when its Percentage is Known
• Metric measures as Percentages
• Problems Involving Percentage
• Worksheet on Problems Involving Percentage
• 5th Grade Percentage Worksheet

● Profit and Loss.

• Formulas of Profit and Loss.
• Finding Profit or Loss
• Calculating Cost Price
• Calculating Selling Price
• To find Cost Price or Selling Price when Profit or Loss is given.
• Worksheet on Profit and Loss.
• Worksheet on Calculating Selling Price and Cost Price
• Worksheet on Finding Profit or Loss

● Simple Interest.

• Word Problems on Simple Interest.
• Factors Affecting Interest
• In Simple Interest when the Time is given in Months and Days.
• To find Principal when Time Interest and Rate are given.
• To find Rate when Principal Interest and Time are given .
• To find Time when Principal Interest and Rate are given.
• Worksheet on Simple Interest.
• Worksheet on Factors affecting Interest

● Temperature.

• Converting the Temperature from Celsius to Fahrenheit.
• Converting the Temperature from Fahrenheit to Celsius.
• Conversion of Temperature
• Clinical Thermometer.
• Worksheet on Conversion of Temperature
• Worksheet on Temperature.
• Word Problems on Average
• Worksheet on Average.
• Worksheet on word Problems on Average

●  Speed Distance and Time.

• Relation of Speed Distance and Time
• Express Speed in Different Units
• To find Speed when Distance and Time are given.
• To find the Distance when Speed and Time are given.
• To find Time when Distance and Speed are given.
• Worksheet on Expressing Speed in Different Units
• Worksheet on Calculating Distance and Time
• Worksheet on Speed, Distance and Time.
• Preparing a Bill
• Worksheet on Bills

● Measurement.

• Units of Measurement
• Addition and Subtraction of Units of Measurement
• Multiplication and Division of Units of Measurement
• Worksheet on Addition and Subtraction of Units of Measurement
• Multiplication of Units of Mass
• Division of Units of Mass
• Adding and Subtracting Time
• Multiplication and Division of Time
• Elapsed Time
• Worksheet on Word Problems on Measurement
• Worksheet on Measurement.
• 5th Grade Measurement Worksheet
• 5th Grade Time Worksheet

● Unitary Method.

• Worksheet on Unitary Method

5th Grade Geometry

• Interior and Exterior of an Angle.
• Measuring an Angle by a Protractor.
• Construction of an Angle using a Protractor
• Types of Angles.
• Pairs of Angles.
• Bisecting an angle.
• Construction of Angles by using Compass.
• Worksheet on Angles.
• Geometry Practice Test on angles.

●  Triangle.

• Classification of Triangle.
• Properties of Triangle.
• Examples of Properties of Triangle
• Worksheet on Properties of Triangle
• Worksheet on Triangle.
• To Construct a Triangle whose Three Sides are given.
• To Construct a Triangle when Two of its Sides and the included Angles are given.
• To Construct a Triangle when Two of its Angles and the included Side are given.
• To Construct a Right Triangle when its Hypotenuse and One Side are given.
• Worksheet on Construction of Triangles.

●  Circle

• Relation between Diameter Radius and Circumference.
• Worksheet on Circle.
• Practice Test on Circle.

● Quadrilaterals.

• Elements of a Quadrilateral.
• Types of Quadrilaterals.
• Parallel Lines.
• Drawing Parallel Lines with Set-Squares
• Intersecting Lines
• Perpendicular Lines.
• Construction of Perpendicular Lines by using a Protractor.
• Sum of Angles of a Quadrilateral.
• Worksheet on Quadrilateral.
• Practice Test on Quadrilaterals.
• Area of a Rectangle.
• Area of a Square.
• To find Area of a Rectangle when Length and Breadth are of Different Units.
• To find Length or Breadth when Area of a Rectangle is given.
• Areas of Irregular Figures.
• To find Cost of Painting or Tilling when Area and Cost per Unit is given.
• To find the Number of Bricks or Tiles when Area of Path and Brick is given.
• Worksheet on Area.
• Word Problems on Area of a Rectangle
• Word Problems on Area of a Square
• Worksheet on Area of a Square and Rectangle
• Worksheet on Area of Regular Figures
• Practice Test on Area.
• Mental Math on Perimeter and Area
• Units of Volume
• Practice Test on Volume.
• Worksheet on Volume of a Cube and Cuboid
• Worksheet on Volume.

● Representation of Tabular Data

• Advantages of Tabular Data
• Worksheet on Representation of Tabular Data

● Dada Handling

• Reading Pictographs
• Bar Graph on Graph Paper
• Construct bar Graph on Graph Paper
• Worksheet on Pictograph and Bar Graph
• Double Bar Graph
• 5th Grade Data Handling Worksheet

5th Grade Math Worksheets From 5th Grade Math Problems to HOME PAGE

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Unit 9: Shapes and angles

Angle introduction.

• Angles: introduction (Opens a modal)
• Naming angles (Opens a modal)
• Angle basics Get 3 of 4 questions to level up!
• Name angles Get 3 of 4 questions to level up!

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Stormy Daniels Takes the Stand

The porn star testified for eight hours at donald trump’s hush-money trial. this is how it went..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

It’s 6:41 AM. I’m feeling a little stressed because I’m running late. It’s the fourth week of Donald J. Trump’s criminal trial. It’s a white collar trial. Most of the witnesses we’ve heard from have been, I think, typical white collar witnesses in terms of their professions.

We’ve got a former publisher, a lawyer, accountants. The witness today, a little less typical, Stormy Daniels, porn star in a New York criminal courtroom in front of a jury more accustomed to the types of witnesses they’ve already seen. There’s a lot that could go wrong.

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.”

Today, what happened when Stormy Daniels took the stand for eight hours in the first criminal trial of Donald J. Trump. As before, my colleague Jonah Bromwich was inside the courtroom.

[MUSIC PLAYING]

It’s Friday, May 10th.

So it’s now day 14 of this trial. And I think it’s worth having you briefly, and in broad strokes, catch listeners up on the biggest developments that have occurred since you were last on, which was the day that opening arguments were made by both the defense and the prosecution. So just give us that brief recap.

Sure. It’s all been the prosecution’s case so far. And prosecutors have a saying, which is that the evidence is coming in great. And I think for this prosecution, which is trying to show that Trump falsified business records to cover up a sex scandal, to ease his way into the White House in 2016, the evidence has been coming in pretty well. It’s come in well through David Pecker, former publisher of The National Enquirer, who testified that he entered into a secret plot with Trump and Michael Cohen, his fixer at the time, to suppress negative stories about Trump, the candidate.

It came in pretty well through Keith Davidson, who was a lawyer to Stormy Daniels in 2016 and negotiated the hush money payment. And we’ve seen all these little bits and pieces of evidence that tell the story that prosecutors want to tell. And the case makes sense so far. We can’t tell what the jury is thinking, as we always say.

But we can tell that there’s a narrative that’s coherent and that matches up with the prosecution’s opening statement. Then we come to Tuesday. And that day really marks the first time that the prosecution’s strategy seems a little bit risky because that’s the day that Stormy Daniels gets called to the witness stand.

OK, well, just explain why the prosecution putting Stormy Daniels on the stand would be so risky. And I guess it makes sense to answer that in the context of why the prosecution is calling her as a witness at all.

Well, you can see why it makes sense to have her. The hush money payment was to her. The cover-up of the hush money payment, in some ways, concerns her. And so she’s this character who’s very much at the center of this story. But according to prosecutors, she’s not at the center of the crime. The prosecution is telling a story, and they hope a compelling one. And arguably, that story starts with Stormy Daniels. It starts in 2006, when Stormy Daniels says that she and Trump had sex, which is something that Trump has always denied.

So if prosecutors were to not call Stormy Daniels to the stand, you would have this big hole in the case. It would be like, effect, effect, effect. But where is the cause? Where is the person who set off this chain reaction? But Stormy Daniels is a porn star. She’s there to testify about sex. Sex and pornography are things that the jurors were not asked about during jury selection. And those are subjects that bring up all kinds of different complex reactions in people.

And so, when the prosecutors bring Stormy Daniels to the courtroom, it’s very difficult to know how the jurors will take it, particularly given that she’s about to describe a sexual episode that she says she had with the former president. Will the jurors think that makes sense, as they sit here and try to decide a falsifying business records case, or will they ask themselves, why are we hearing this?

So the reason why this is the first time that the prosecution’s strategy is, for journalists like you, a little bit confusing, is because it’s the first time that the prosecution seems to be taking a genuine risk in what they’re putting before these jurors. Everything else has been kind of cut and dry and a little bit more mechanical. This is just a wild card.

This is like live ammunition, to some extent. Everything else is settled and controlled. And they know what’s going to happen. With Stormy Daniels, that’s not the case.

OK, so walk us through the testimony. When the prosecution brings her to the stand, what actually happens?

It starts, as every witness does, with what’s called direct examination, which is a fancy word for saying prosecutors question Stormy Daniels. And they have her tell her story. First, they have her tell the jury about her education and where she grew up and her professional experience. And because of Stormy Daniels’s biography, that quickly goes into stripping, and then goes into making adult films.

And I thought the prosecutor who questioned her, Susan Hoffinger, had this nice touch in talking about that, because not only did she ask Daniels about acting in adult films. But she asked her about writing and directing them, too, emphasizing the more professional aspects of that work and giving a little more credit to the witness, as if to say, well, you may think this or you may think that. But this is a person with dignity who took what she did seriously. Got it.

What’s your first impression of Daniels as a witness?

It’s very clear that she’s nervous. She’s speaking fast. She’s laughing to herself and making small jokes. But the tension in the room is so serious from the beginning, from the moment she enters, that those jokes aren’t landing. So it just feels, like, really heavy and still and almost oppressive in there. So Daniels talking quickly, seeming nervous, giving more answers than are being asked of her by the prosecution, even before we get to the sexual encounter that she’s about to describe, all of that presents a really discomfiting impression, I would say.

And how does this move towards the encounter that Daniels ultimately has?

It starts at a golf tournament in 2006, in Lake Tahoe, Nevada. Daniels meets Trump there. There are other celebrities there, too. They chatted very briefly. And then she received a dinner invitation from him. She thought it over, she says. And she goes to have dinner with Trump, not at a restaurant, by the way. But she’s invited to join him in the hotel suite.

So she gets to the hotel suite. And his bodyguard is there. And the hotel door is cracked open. And the bodyguard greets her and says she looks nice, this and that. And she goes in. And there’s Donald Trump, just as expected. But what’s not expected, she says, is that he’s not wearing what you would wear to a dinner with a stranger, but instead, she says, silk or satin pajamas. She asked him to change, she says. And he obliges.

He goes, and he puts on a dress shirt and dress pants. And they sit down at the hotel suite’s dining room table. And they have a kind of bizarre dinner. Trump is asking her very personal questions about pornography and safe sex. And she testifies that she teased him about vain and pompous he is. And then at some point, she goes to the bathroom. And she sees that he has got his toiletries in there, his Old Spice, his gold tweezers.

Very specific details.

Yeah, we’re getting a ton of detail in this scene. And the reason we’re getting those is because prosecutors are trying to elicit those details to establish that this is a credible person, that this thing did happen, despite what Donald Trump and his lawyers say. And the reason you can know it happened, prosecutors seem to be saying, is because, look at all these details she can still summon up.

She comes out of the bathroom. And she says that Donald Trump is on the hotel bed. And what stands out to me there is what she describes as a very intense physical reaction. She says that she blacked out. And she quickly clarifies, she doesn’t mean from drugs or alcohol. She means that, she says, that the intensity of this experience was such that, suddenly, she can’t remember every detail. The prosecution asks a question that cuts directly to the sex. Essentially, did you start having sex with him? And Daniels says that she did. And she continues to provide more details than even, I think, the prosecution wanted.

And I think we don’t want to go chapter and verse through this claimed sexual encounter. But I wonder what details stand out and which details feel important, given the prosecution’s strategy here.

All the details stand out because it’s a story about having had sex with a former president. And the more salacious and more private the details feel, the more you’re going to remember them. So we’ll remember that Stormy Daniels said what position they had sex in. We’ll remember that she said he didn’t use a condom. Whether that’s important to the prosecution’s case, now, that’s a much harder question to answer, as we’ve been saying.

But what I can tell you is, as she’s describing having had sex with Donald Trump, and Donald Trump is sitting right there, and Eric Trump, his son, is sitting behind him, seeming to turn a different color as he hears this embarrassment of his father being described to a courtroom full of reporters at this trial, it’s hard to even describe the energy in that room. It was like nothing I had ever experienced. And it was just Daniels’s testimony and, seemingly, the former President’s emotions. And you almost felt like you were trapped in there with both of them as this description was happening.

Well, I think it’s important to try to understand why the prosecution is getting these details, these salacious, carnal, pick your word, graphic details about sex with Donald Trump. What is the value, if other details are clearly making the point that she’s recollecting something?

Well, I think, at this point, we can only speculate. But one thing we can say is, this was uncomfortable. This felt bad. And remember, prosecutor’s story is not about the sex. It’s about trying to hide the sex. So if you’re trying to show a jury why it might be worthwhile to hide a story, it might be worth —

Providing lots of salacious details that a person would want to hide.

— exposing them to how bad that story feels and reminding them that if they had been voters and they had heard that story, and, in fact, they asked Daniels this very question, if you hadn’t accepted hush money, if you hadn’t signed that NDA, is this the story you would have told? And she said, yes. And so where I think they’re going with this, but we can’t really be sure yet, is that they’re going to tell the jurors, hey, that story, you can see why he wanted to cover that up, can’t you?

You mentioned the hush money payments. What testimony does Daniels offer about that? And how does it advance the prosecution’s case of business fraud related to the hush money payments?

So little evidence that it’s almost laughable. She says that she received the hush money. But we actually already heard another witness, her lawyer at the time, Keith Davidson, testify that he had received the hush money payment on her behalf. And she testified about feeling as if she had to sell this story because the election was fast approaching, almost as if her leverage was slipping away because she knew this would be bad for Trump.

That feels important. But just help me understand why it’s important.

Well, what the prosecution has been arguing is that Trump covered up this hush money payment in order to conceal a different crime. And that crime, they say, was to promote his election to the presidency by illegal means.

Right, we’ve talked about this in the past.

So when Daniels ties her side of the payment into the election, it just reminds the jurors maybe, oh, right, this is what they’re arguing.

So how does the prosecution end this very dramatic, and from everything you’re saying, very tense questioning of Stormy Daniels about this encounter?

Well, before they can even end, the defense lawyers go and they consult among themselves. And then, with the jury out of the room, one of them stands up. And he says that the defense is moving for a mistrial.

On what terms?

He says that the testimony offered by Daniels that morning is so prejudicial, so damning to Trump in the eyes of the jury, that the trial can no longer be fair. Like, how could these jurors have heard these details and still be fair when they render their verdict? And he says a memorable expression. He says, you can’t un-ring that bell, meaning they heard it. They can’t un-hear it. It’s over. Throw out this trial. It should be done.

Wow. And what is the response from the judge?

So the judge, Juan Merchan, he hears them out. And he really hears them out. But at the end of their arguments, he says, I do think she went a little too far. He says that. He said, there were things that were better left unsaid.

By Stormy Daniels?

By Stormy Daniels. And he acknowledges that she is a difficult witness. But, he says, the remedy for that is not a mistrial, is not stopping the whole thing right now. The remedy for that is cross-examination. If the defense feels that there are issues with her story, issues with her credibility, they can ask her whatever they want. They can try to win the jury back over. If they think this jury has been poisoned by this witness, well, this is their time to provide the antidote. The antidote is cross-examination. And soon enough, cross-examination starts. And it is exactly as intense and combative as we expected.

We’ll be right back.

So, Jonah, how would you characterize the defense’s overall strategy in this intense cross-examination of Stormy Daniels?

People know the word impeach from presidential impeachments. But it has a meaning in law, too. You impeach a witness, and, specifically, their credibility. And that’s what the defense is going for here. They are going to try to make Stormy Daniels look like a liar, a fraud, an extortionist, a money-grubbing opportunist who wanted to take advantage of Trump and sought to do so by any means necessary.

And what did that impeachment strategy look like in the courtroom?

The defense lawyer who questions Stormy Daniels is a woman named Susan Necheles. She’s defended Trump before. And she’s a bit of a cross-examination specialist. We even saw her during jury selection bring up these past details to confront jurors who had said nasty things about Trump on social media with. And she wants to do the same thing with Daniels. She wants to bring up old interviews and old tweets and things that Daniels has said in the past that don’t match what Daniels is saying from the stand.

What’s a specific example? And do they land?

Some of them land. And some of them don’t. One specific example is that Necheles confronts Daniels with this old tweet, where Daniels says that she’s going to dance down the street if Trump goes to jail. And what she’s trying to show there is that Daniels is out for revenge, that she hates Trump, and that she wants to see him go to jail. And that’s why she’s testifying against him.

And Daniels is very interesting during the cross-examination. It’s almost as if she’s a different person. She kind of squares her shoulders. And she sits up a little straighter. And she leans forward. Daniels is ready to fight. But it doesn’t quite land. The tweet actually says, I’ll dance down the street when he’s selected to go to jail.

And Daniels goes off on this digression about how she knows that people don’t get selected to go to jail. That’s not how it works. But she can’t really unseat this argument, that she’s a political enemy of Donald Trump. So that one kind of sticks, I would say. But there are other moves that Necheles tries to pull that don’t stick.

So unlike the prosecution, which typically used words like adult, adult film, Necheles seems to be taking every chance she can get to say porn, or pornography, or porn star, to make it sound base or dirty. And so when she starts to ask Daniels about actually being in pornography, writing, acting, and directing sex films, she tries to land a punch line, Necheles does. She says, so you have a lot of experience making phony stories about sex appear to be real, right?

As if to say, perhaps this story you have told about entering Trump’s suite in Lake Tahoe and having sex with him was made up.

Just another one of your fictional stories about sex. But Daniels comes back and says, the sex in the films, it’s very much real, just like what happened to me in that room. And so, when you have this kind of combat of a lawyer cross-examining very aggressively and the witness fighting back, you can feel the energy in the room shift as one lands a blow or the other does. But here, Daniels lands one back. And the other issue that I think Susan Necheles runs into is, she tries to draw out disparities from interviews that Daniels gave, particularly to N-TOUCH, very early on once the story was out.

It’s kind of like a tabloid magazine?

But some of the disparities don’t seem to be landing quite like Necheles would want. So she tries to do this complicated thing about where the bodyguard was in the room when Daniels walked into the room, as described in an interview in a magazine. But in that magazine interview, as it turns out, Daniels mentioned that Trump was wearing pajamas. And so, if I’m a juror, I don’t care where the bodyguard is. I’m thinking about, oh, yeah, I remember that Stormy Daniels said now in 2024 that Trump was wearing pajamas.

I’m curious if, as somebody in the room, you felt that the defense was effective in undermining Stormy Daniels’s credibility? Because what I took from the earlier part of our conversation was that Stormy Daniels is in this courtroom on behalf of the prosecution to tell a story that’s uncomfortable and has the kind of details that Donald Trump would be motivated to try to hide. And therefore, this defense strategy is to say, those details about what Trump might want to hide, you can’t trust them. So does this back and forth effectively hurt Stormy Daniels’s credibility, in your estimation?

I don’t think that Stormy Daniels came off as perfectly credible about everything she testified about. There are incidents that were unclear or confusing. There were things she talked about that I found hard to believe, when she, for instance, denied that she had attacked Trump in a tweet or talked about her motivations. But about what prosecutors need, that central story, the story of having had sex with him, we can’t know whether it happened.

But there weren’t that many disparities in these accounts over the years. In terms of things that would make me doubt the story that Daniels was telling, details that don’t add up, those weren’t present. And you don’t have to take my word for that, nor should you. But the judge is in the room. And he says something very, very similar.

What does he say? And why does he say it?

Well, he does it when the defense, again, at the end of the day on Thursday, calls for a mistrial.

With a similar argument as before?

Not only with a similar argument as before, but, like, almost the exact same argument. And I would say that I was astonished to see them do this. But I wasn’t because I’ve covered other trials where Trump is the client. And in those trials, the lawyers, again and again, called for a mistrial.

And what does Judge Marchan say in response to this second effort to seek a mistrial?

Let me say, to this one, he seems a little less patient. He says that after the first mistrial ruling, two days before, he went into his chambers. And he read every decision he had made about the case. He took this moment to reflect on the first decision. And he found that he had, in his own estimation, which is all he has, been fair and not allowed evidence that was prejudicial to Trump into this trial. It could continue. And so he said that again. And then he really almost turned on the defense. And he said that the things that the defense was objecting to were things that the defense had made happen.

He says that in their opening statement, the defense could have taken issue with many elements of the case, about whether there were falsified business records, about any of the other things that prosecutors are saying happened. But instead, he says, they focused their energy on denying that Trump ever had sex with Daniels.

And so that was essentially an invitation to the prosecution to call Stormy Daniels as a witness and have her say from the stand, yes, I had this sexual encounter. The upshot of it is that the judge not only takes the defense to task. But he also just says that he finds Stormy Daniels’s narrative credible. He doesn’t see it as having changed so much from year to year.

Interesting. So in thinking back to our original question here, Jonah, about the idea that putting Stormy Daniels on the stand was risky, I wonder if, by the end of this entire journey, you’re reevaluating that idea because it doesn’t sound like it ended up being super risky. It sounded like it ended up working reasonably well for the prosecution.

Well, let me just assert that it doesn’t really matter what I think. The jury is going to decide this. There’s 12 people. And we can’t know what they’re thinking. But my impression was that, while she was being questioned by the prosecution for the prosecution’s case, Stormy Daniels was a real liability. She was a difficult witness for them.

And the judge said as much. But when the defense cross-examined her, Stormy Daniels became a better witness, in part because their struggles to discredit her may have actually ended up making her story look more credible and stronger. And the reason that matters is because, remember, we said that prosecutors are trying to fill this hole in their case. Well, now, they have. The jury has met Stormy Daniels. They’ve heard her account. They’ve made of it what they will. And now, the sequence of events that prosecutors are trying to line up as they seek prison time for the former President really makes a lot of sense.

It starts with what Stormy Daniels says with sex in a hotel suite in 2006. It picks up years later, as Donald Trump is trying to win an election and, prosecutors say, suppressing negative stories, including Stormy Daniels’s very negative story. And the story that prosecutors are telling ends with Donald Trump orchestrating the falsification of business records to keep that story concealed.

Well, Jonah, thank you very much. We appreciate it.

Of course, thanks for having me.

The prosecution’s next major witness will be Michael Cohen, the former Trump fixer who arranged for the hush money payment to Stormy Daniels. Cohen is expected to take the stand on Monday.

Here’s what else you need to know today. On Thursday, Israeli Prime Minister Benjamin Netanyahu issued a defiant response to warnings from the United States that it would stop supplying weapons to Israel if Israel invades the Southern Gaza City of Rafah. So far, Israel has carried out a limited incursion into the city where a million civilians are sheltering, but has threatened a full invasion. In a statement, Netanyahu said, quote, “if we need to stand alone, we will stand alone.”

Meanwhile, high level ceasefire negotiations between Israel and Hamas have been put on hold in part because of anger over Israel’s incursion into Rafah.

A reminder, tomorrow, we’ll be sharing the latest episode of our colleague’s new show, “The Interview” This week on “The Interview,” Lulu Garcia-Navarro talks with radio host Charlamagne Tha God about his frustrations with how Americans talk about politics.

If me as a Black man, if I criticize Democrats, then I’m supporting MAGA. But if I criticize, you know, Donald Trump and Republicans, then I’m a Democratic shill. Why can’t I just be a person who deals in nuance?

Today’s episode was produced by Olivia Natt and Michael Simon Johnson. It was edited by Lexie Diao, with help from Paige Cowett, contains original music by Will Reid and Marion Lozano, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Michael Barbaro. See you on Monday.

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• May 13, 2024   •   27:46 How Biden Adopted Trump’s Trade War With China
• May 10, 2024   •   27:42 Stormy Daniels Takes the Stand
• May 9, 2024   •   34:42 One Strongman, One Billion Voters, and the Future of India
• May 8, 2024   •   28:28 A Plan to Remake the Middle East
• May 7, 2024   •   27:43 How Changing Ocean Temperatures Could Upend Life on Earth
• May 6, 2024   •   29:23 R.F.K. Jr.’s Battle to Get on the Ballot
• May 3, 2024   •   25:33 The Protesters and the President
• May 2, 2024   •   29:13 Biden Loosens Up on Weed
• May 1, 2024   •   35:16 The New Abortion Fight Before the Supreme Court
• April 30, 2024   •   27:40 The Secret Push That Could Ban TikTok

Hosted by Michael Barbaro

Featuring Jonah E. Bromwich

Produced by Olivia Natt and Michael Simon Johnson

Edited by Lexie Diao

With Paige Cowett

Original music by Will Reid and Marion Lozano

Engineered by Alyssa Moxley

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music | YouTube

This episode contains descriptions of an alleged sexual liaison.

What happened when Stormy Daniels took the stand for eight hours in the first criminal trial of former President Donald J. Trump?

Jonah Bromwich, one of the lead reporters covering the trial for The Times, was in the room.

On today’s episode

Jonah E. Bromwich , who covers criminal justice in New York for The New York Times.

Background reading

In a second day of cross-examination, Stormy Daniels resisted the implication she had tried to shake down Donald J. Trump by selling her story of a sexual liaison.

Here are six takeaways from Ms. Daniels’s earlier testimony.

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The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Jonah E. Bromwich covers criminal justice in New York, with a focus on the Manhattan district attorney’s office and state criminal courts in Manhattan. More about Jonah E. Bromwich

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