## Solver Title

## Generating PDF...

- Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics
- Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
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- Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
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- Conversions Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time
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## Most Used Actions

Number line.

- \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
- \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
- \mathrm{Bob's\:age\:is\:twice\:that\:of\:Barry's.\:Five\:years\:ago,\:Bob\:was\:three\:times\:older\:than\:Barry.\:Find\:the\:age\:of\:both.}
- \mathrm{Two\:men\:who\:are\:traveling\:in\:opposite\:directions\:at\:the\:rate\:of\:18\:and\:22\:mph\:respectively\:started\:at\:the\:same\:time\:at\:the\:same\:place.\:In\:how\:many\:hours\:will\:they\:be\:250\:apart?}
- \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
- How do you solve word problems?
- To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
- How do you identify word problems in math?
- Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
- Is there a calculator that can solve word problems?
- Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
- What is an age problem?
- An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

word-problems-calculator

- Middle School Math Solutions – Equation Calculator Welcome to our new "Getting Started" math solutions series. Over the next few weeks, we'll be showing how Symbolab... Read More

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## Problem Solver Subjects

Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

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Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

## Basic Math Solutions

Below are examples of basic math problems that can be solved.

- Long Arithmetic
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- Operations with Fractions
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## Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

## Pre-Algebra Solutions

Below are examples of Pre-Algebra math problems that can be solved.

- Variables, Expressions, and Integers
- Simplifying and Evaluating Expressions
- Solving Equations
- Multi-Step Equations and Inequalities
- Ratios, Proportions, and Percents
- Linear Equations and Inequalities

## Algebra Solutions

Below are examples of Algebra math problems that can be solved.

- Algebra Concepts and Expressions
- Points, Lines, and Line Segments
- Simplifying Polynomials
- Factoring Polynomials
- Linear Equations
- Absolute Value Expressions and Equations
- Radical Expressions and Equations
- Systems of Equations
- Quadratic Equations
- Inequalities
- Complex Numbers and Vector Analysis
- Logarithmic Expressions and Equations
- Exponential Expressions and Equations
- Conic Sections
- Vector Spaces
- 3d Coordinate System
- Eigenvalues and Eigenvectors
- Linear Transformations
- Number Sets
- Analytic Geometry

## Trigonometry Solutions

Below are examples of Trigonometry math problems that can be solved.

- Algebra Concepts and Expressions Review
- Right Triangle Trigonometry
- Radian Measure and Circular Functions
- Graphing Trigonometric Functions
- Simplifying Trigonometric Expressions
- Verifying Trigonometric Identities
- Solving Trigonometric Equations
- Complex Numbers
- Analytic Geometry in Polar Coordinates
- Exponential and Logarithmic Functions
- Vector Arithmetic

## Precalculus Solutions

Below are examples of Precalculus math problems that can be solved.

- Operations on Functions
- Rational Expressions and Equations
- Polynomial and Rational Functions
- Analytic Trigonometry
- Sequences and Series
- Analytic Geometry in Rectangular Coordinates
- Limits and an Introduction to Calculus

## Calculus Solutions

Below are examples of Calculus math problems that can be solved.

- Evaluating Limits
- Derivatives
- Applications of Differentiation
- Applications of Integration
- Techniques of Integration
- Parametric Equations and Polar Coordinates
- Differential Equations

## Statistics Solutions

Below are examples of Statistics problems that can be solved.

- Algebra Review
- Average Descriptive Statistics
- Dispersion Statistics
- Probability
- Probability Distributions
- Frequency Distribution
- Normal Distributions
- t-Distributions
- Hypothesis Testing
- Estimation and Sample Size
- Correlation and Regression

## Finite Math Solutions

Below are examples of Finite Math problems that can be solved.

- Polynomials and Expressions
- Equations and Inequalities
- Linear Functions and Points
- Systems of Linear Equations
- Mathematics of Finance
- Statistical Distributions

## Linear Algebra Solutions

Below are examples of Linear Algebra math problems that can be solved.

- Introduction to Matrices
- Linear Independence and Combinations

## Chemistry Solutions

Below are examples of Chemistry problems that can be solved.

- Unit Conversion
- Atomic Structure
- Molecules and Compounds
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- Solutions and Concentrations

## Physics Solutions

Below are examples of Physics math problems that can be solved.

- Static Equilibrium
- Dynamic Equilibrium
- Kinematics Equations
- Electricity
- Thermodymanics

## Geometry Graphing Solutions

Below are examples of Geometry and graphing math problems that can be solved.

- Step By Step Graphing
- Linear Equations and Functions
- Polar Equations

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## Math Word Problem Worksheets

Read, explore, and solve over 1000 math word problems based on addition, subtraction, multiplication, division, fraction, decimal, ratio and more. These word problems help children hone their reading and analytical skills; understand the real-life application of math operations and other math topics. Print our exclusive colorful theme-based worksheets for a fun-filled teaching experience! Use the answer key provided below each worksheet to assist children in verifying their solutions.

## List of Word Problem Worksheets

Explore the word problem worksheets in detail.

Addition Word Problems

Have 'total' fun by adding up a wide range of addends displayed in these worksheets! Simple real-life scenarios form the basis of these addition word problem worksheets.

Subtraction Word Problems

Learning can be a huge 'take away'! Find the difference between the numbers provided in each subtraction word problem. Large number subtraction up to six-digits can also be found here.

Addition and Subtraction Word Problems

Bring on 'A' game with our addition and subtraction word problems! Read, analyze, and solve real-life scenarios based on adding and subtracting numbers as required.

Multiplication Word Problems

Get 'product'ive with over 100 highly engaging multiplication word problems! Find the product and use the answer key to verify your solution. Free worksheets are also available.

Division Word Problems

"Divide and conquer" this huge collection of division word problems. Exclusive worksheets are available for the division problem leaving no remainder and with the remainder.

Fraction Word Problems

Perform various mathematical operations to solve the umpteen number of word problems based on like and unlike fractions, proper and improper fractions, and mixed numbers.

Decimal Word Problems

Let's get to the 'point'! Add, subtract, multiply, and divide to solve these decimal word problems. A wide selection of printable worksheets is available in this section. Use the answer key to verify your answers.

Ratio Word problems

Double up your success ratio with these sets of word problems, which cover a multitude of topics like express in the ratio, reducing the ratio, part-to-part ratio, part-to-whole ratio and more.

Venn Diagram Word Problems - Two Sets

Help your children improve their data analysis skills with these well-researched Venn diagram word problem worksheets. Find the union, intersection, complement and difference of two sets.

Venn Diagram Word Problems - Three Sets

These Venn diagram word problems provide ample practice in real-life application of Venn diagram involving three sets. The worksheets containing the universal set are also included.

Equation Word Problems

The printable worksheets here feature exercises consisting of one-step, two-step and multi-step equation word problems involving fractions, decimals and integers. MCQs to test the knowledge acquired have also been included.

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## 120 Math Word Problems To Challenge Students Grades 1 to 8

Written by Marcus Guido

## Hey teachers! 👋

Use Prodigy to spark a love for math in your students – including when solving word problems!

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You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

A jolt of creativity would help. But it doesn’t come.

Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

## 120 Math word problems, categorized by skill

Addition word problems.

Best for: 1st grade, 2nd grade

1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?

2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?

3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?

5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?

6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?

8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?

## Subtraction word problems

Best for: 1st grade, second grade

9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?

10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?

11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

## Practice math word problems with Prodigy Math

Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!

12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?

13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?

14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?

15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?

16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?

## Multiplication word problems

Best for: 2nd grade, 3rd grade

17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?

18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?

19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?

21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?

## Division word problems

Best for: 3rd grade, 4th grade, 5th grade

22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?

23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?

24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?

25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?

26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?

## Mixed operations word problems

27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?

28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?

29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?

30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?

## Ordering and number sense word problems

31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?

32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?

33. Composing Numbers: What number is 6 tens and 10 ones?

34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?

35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?

## Fractions word problems

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?

37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?

38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?

39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?

40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?

41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?

42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?

43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?

44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.

45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?

46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.

## Decimals word problems

Best for: 4th grade, 5th grade

47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?

48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?

49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?

50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?

51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?

52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?

## Comparing and sequencing word problems

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?

56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?

57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?

58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?

59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?

## Time word problems

66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?

69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?

70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?

71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?

## Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?

61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?

62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?

63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?

64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?

65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?

67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.

68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?

## Physical measurement word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?

73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?

74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?

75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?

76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?

77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?

78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?

79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?

80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?

81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?

## Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?

84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?

87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

## Probability and data relationships word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade

89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?

90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?

91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.

92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?

93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?

94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?

95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .

## Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

96. Introducing Perimeter: The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?

97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?

98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?

101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?

104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?

105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?

106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?

107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?

108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?

109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?

110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?

111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?

112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?

113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?

## Variables word problems

Best for: 6th grade, 7th grade, 8th grade

115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?

116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.

117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.

118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.

119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?

## How to easily make your own math word problems & word problems worksheets

Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:

- Link to Student Interests: By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
- Make Questions Topical: Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
- Include Student Names: Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
- Be Explicit: Repeating keywords distills the question, helping students focus on the core problem.
- Test Reading Comprehension: Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
- Focus on Similar Interests: Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
- Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.

## Final thoughts about math word problems

You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.

Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.

The result?

A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.

## Math Word Problems

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

- Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
- Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
- Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
- Calculate : Use your strategy to solve the problem.
- Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.

## Most Popular Math Word Problems this Week

## Various Word Problems

Various word problems for students who have mastered basic arithmetic and need a further challenge.

## Addition word problems

## Subtraction word problems

## Multiplication word problems

## Division word problems

## Multi-Step word problems

Copyright © 2005-2023 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.

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## Math Word Problems Worksheets

Word problems worksheets for kindergarten to grade 5.

Our word problems worksheets are best attempted after a student is familiar with the underlying skill. We include many mixed word problems or word problems with irrelevant data so that students must think about the problem carefully rather than just apply a formulaic solution.

## Choose your grade / topic:

Kindergarten:

Addition word problems

Subtraction word problems

Grade 1 word problems

Grade 2 word problems

Grade 3 word problems

Grade 4 word problems

Grade 5 word problems

Topics include:

## Kindergarten addition word problems

- Simple word problems with 1-digit addition

## Kindergarten subtraction word problems

- Simple word problems with 1-digit subtraction

## Grade 1 word problems worksheets

- Single digit addition word problems
- Addition with sums 50 or less
- Adding 3 or more numbers
- Subtracting 1-digit numbers
- Subtracting numbers under 50
- Mixed addition & subtraction
- Time and elapsed time
- Counting money word problems
- Measurement word problems (lengths)
- Writing fractions from a story
- Mixed word problems

## Grade 2 word problems worksheets

- 1,2 and 3-digit addition word problems
- 1,2 and 3-digit subtraction
- Mixed addition and subtraction
- Multiplication within 25
- Lengths - adding / subtracting / comparing (customary and metric)
- Time and elapsed time (1/2 hour intervals)
- Time and elapsed time (5 minute intervals)
- Counting money (coins and bills)
- Writing fractions word problems
- Comparing fractions

## Grade 3 word problems worksheets

- Simple addition word problems (numbers under 100)
- Addition in columns (numbers under 1,000)
- Mental subtraction
- Subtraction in columns (2-3 digits)
- Simple multiplication (1-digit by 1 or 2-digit)
- Multiplying multiples of 10
- Multiplication in columns
- Simple division
- Long division with remainders (numbers 1-100)
- Mixed multiplication and division word problems
- Identifying, comparing and simplifying fractions
- Adding and subtracting fractions (like denominators)
- Length word problems
- Time word problems (nearest 1 minute)
- Mass and weight word problems
- Volume and capacity word problems
- Word problems with variables

## Grade 4 word problems worksheets

- Four operations (addition, subtraction, multiplication, division)
- Estimating and rounding
- Writing and comparing fractions
- Multiplying fractions by whole numbers
- Adding and subtracting decimals (up to 3 terms)
- Length word problems (customary and metric units)
- Time word problems (including am vs pm)
- Money word problems (with decimal notation)
- Shopping word problems

## Grade 5 word problems worksheets

- Mixed 4 operations (addition, subtraction, multiplication, division)
- Estimating and rounding word problems (based on the 4 operations)
- Add and subtract fractions and mixed numbers (like and unlike denominators)
- Multiplying and dividing fractions
- Mixed operations with fractions (add, subtract, multiply, divide)
- Decimals word problems (add, subtract, multiply)
- Mass and weight word problems (oz, lbs / gm, kg)
- Variables and expressions word problems
- Variables and equations word problems
- Volume of rectangular prism
- GCF / LCM word problems

## Related topics

Fractions worksheets

Geometry worksheets

Sample Word Problems Worksheet

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## Praxis Core Math

Course: praxis core math > unit 1.

- Algebraic properties | Lesson
- Algebraic properties | Worked example
- Solution procedures | Lesson
- Solution procedures | Worked example
- Equivalent expressions | Lesson
- Equivalent expressions | Worked example
- Creating expressions and equations | Lesson
- Creating expressions and equations | Worked example

## Algebraic word problems | Lesson

- Algebraic word problems | Worked example
- Linear equations | Lesson
- Linear equations | Worked example
- Quadratic equations | Lesson
- Quadratic equations | Worked example

## What are algebraic word problems?

What skills are needed.

- Translating sentences to equations
- Solving linear equations with one variable
- Evaluating algebraic expressions
- Solving problems using Venn diagrams

## How do we solve algebraic word problems?

- Define a variable.
- Write an equation using the variable.
- Solve the equation.
- If the variable is not the answer to the word problem, use the variable to calculate the answer.

## What's a Venn diagram?

- Your answer should be
- an integer, like 6
- a simplified proper fraction, like 3 / 5
- a simplified improper fraction, like 7 / 4
- a mixed number, like 1 3 / 4
- an exact decimal, like 0.75
- a multiple of pi, like 12 pi or 2 / 3 pi
- (Choice A) $ 4 A $ 4
- (Choice B) $ 5 B $ 5
- (Choice C) $ 9 C $ 9
- (Choice D) $ 14 D $ 14
- (Choice E) $ 20 E $ 20
- (Choice A) 10 A 10
- (Choice B) 12 B 12
- (Choice C) 24 C 24
- (Choice D) 30 D 30
- (Choice E) 32 E 32
- (Choice A) 4 A 4
- (Choice B) 10 B 10
- (Choice C) 14 C 14
- (Choice D) 18 D 18
- (Choice E) 22 E 22

## Things to remember

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## Free Math Word Problems Collection for Grades 1-5

The LogicLike team has collected over 500+ math problems on various topics! We provide word problems and math puzzles designed by experienced teachers. LogicLike helps children improve their math skills in a playfull way!

Educational platform LogicLike.com helps children to build critical thinking, math & logic skills. Adults improve mental abilities and develop ingenuity.

## Choose Word Problems by Grade

Our team has created word math problems for grades 1-5! Choose your grade, learn math and have fun with LogicLike!

## 1st Grade Math Word Problems

In first grade, an important task for students is to learn addition and subtraction. Word problems will help them do it! Go to Math Word Problems for 1st Grade .

## 2nd Grade Math Word Problems

In second grade children learn to add and subtract more complex numbers. We offer our own collection of word math problems for 2nd grade students to practice! Go to Math Word Problems for 2nd Grade .

## 3rd Grade Math Word Problems

In grade 3 children begin to master multiplication and division, two-step word problems, solve time and measurement problems! Go to Math Word Problems for 3rd Grade .

## 4th Grade Math Word Problems

In 4th grade, it is very important to consolidate all your knowledge from previous years and learn how to apply it to more difficult word problems! Go to Math Word Problems for 4th Grade .

## 5th Grade Math Word Problems

In fifth grade, children begin to learn fractions, variable equations and mixed numbers. LogicLike will help them do just that! Go to Math Word Problems for 5th Grade .

## Choose Word Problems by Topic

LogicLike has made over 13 themed picks for learning important topics in math! You can solve the best word problems for addition and subtraction, multiplication and division, fractions and mixed numbers, and more!

## Money Word Problems

Tom has 50 cents, and his mother gives him 4 quarters. How much money does Tom have?

Sara wants to buy 14 ChocoPies. The ChocoPies cost 35 cents each. How much money will 14 ChocoPies cost?

490 cents / $4.90.

Michael had $9,896.00 in his checking account. Then, he spent $3,458.00 on the account. How much money is left in Michael's checking account?

## Mixed Addition and Subtraction Word Problems

Sam caught 4 fish in the morning. Later, he caught 1 more fish. How many fish did Sam catch in all?

4 + 1 = 5 fish.

At the birthday party, there were 12 cups but 4 cups were broken. Mom goes out and buys 10 cups. How many cups are there after she returns?

12 - 4 + 10 = 18 cups.

The pirate has a chest with coins. Inside there are 328 gold, 264 silver and 136 copper coins. How many coins are in the chest in total?

328 + 264 + 136 = 728 coins.

solve 10-20 puzzles a day. Can you do more?

## Multi-Step (Multiple Step) Word Problems

There were 6 yellow apples and 4 red apples on the plate. We ate 7 apples. How many apples are left on the plate?

6 + 4 = 10 10 - 7 = 3 apples.

The clown had balloons of 3 colors, 6 pieces of each color. He gave the kids 4 balls of 2 colors. How many balloons does the clown have left?

3 * 6 = 18 4 * 2 = 8 18 - 8 = 10 balloons.

Mary bought 15 pounds of strawberries at $1.68 per pound. Marion bought 14 pounds of strawberries at $1.80 per pound. Who paid more?

$1.68 * 15 = $25.2 $1.80 * 14 = $23.2 $25.2 - $23.2 = $2.

## Multiplication Word Problems

Jessica saw 4 dozen doves in the park. How many doves did Jessica see?

4 × 12 = 48.

The chef of the restaurant prepares an omelet from 3 eggs. If the chef has 72 omelets to make, how many eggs will he need?

3 × 72 = 216.

Brenda's kitten weighs 3 3/5 pounds. Oliver's dog weighs 4 times more. How much does Oliver's dog weigh?

3 3/5 × 4 = 18/ 5 × 5/1 = 18 pounds.

## Mixed Multiplication and Division Word Problems

Each crayon costs $3.00. How much do 18 crayons cost?

3 × 18 = $54

A concert hall contains 6 sections of seats with the same number of seats in each section. If there are 768 seats, how many seats are in each section?

768 ÷ 6 = 128

The online store has $ 21,000 to buy online ads. If each ad costs $ 6, how many ads can an online store purchase in a month? Is this enough to get 300 ads per month for a year?

21,000 ÷ 6 = 3,500 3500 ÷ 12 = 291.7 It’s not enough.

## Division Word Problems

There are 3 students in the class and 21 pens. If the pens are divided equally among the students, how many does each student get?

Monika earned $216 babysitting in 9 months. She earned the same amount each month. How much did Tina earn babysitting each month?

216 ÷ 9 = $24

The toy company makes Teddy bears in two sizes - big and small. The company produced 1,620 Teddy Bears last week. They made 11 times more small Teddies than large ones. How many big size toys did they make?

11 + 1 = 12 1620 ÷ 12 = 135

## Fraction Word Problems

Sarah made nine chocolate bars. She put powdered sugar on three chocolate bars. Which part of the bars now have powdered sugar?

Jessica had $200, 1/4 of this money she spent on cosmetics. How much money did Jessica spend?

200 × 1/4 = 200 ÷ 4 = $50

The perimeter of the triangle is 40 inches. The first side is 3/10 of the perimeter, the other is 3/2 of the first side. What is the third side of the triangle?

40 ÷ 10 × 3 = 12 inches — the first side. 12 ÷ 2 × 3 = 18 inches — the second side. 40 − (18 + 12) = 10 inches — the third side.

## Proportion Word Problems and Worksheets

The cinema has 400 seats, 260 of which are occupied by spectators. Express the attendance at a percent of capacity.

260 / 400 = x / 100 x = 260 × 100 ÷ 400 x = 65%

Molly has 45 markers. 20% of the markers write poorly. How many markers are bad at writing?

x / 45 = 20 / 100 x = 45 × 20 ÷ 100 x = 9

In an exam, Shawna secured 340 marks. If she secured 85% makes, find the maximum marks.

340 / x = 85 / 100 x = 340 × 100 ÷ 85 x = 400

## Ratio Word Problems

The ratio of green and red apples in a bag is 2 : 5. If there are only green and red apples in a bag, what is the smallest total number of apples possible?

65 children are swimming in the pool. There are 15 more boys than girls. What is the ratio of boys to girls?

(15 + x) + x = 65 2x = 65 − 15 2x = 50 x = 25 girls 15 + 25 = 40 boys 40 : 25 = 8 : 5

James gives Kathy a box of building blocks and tells her that the ratio of red blocks to total is 3 to 19. He also tells her there are 3 times as many yellow blocks as red, and that there are 2 more green than red. What is the ratio of yellow blocks to green?

x + 3x + (x + 2) = (19 / 3) x x = 1.5 4.5 yellow blocks, 3.5 greens blocks 1.5 + 4.5 + 3.5 = 9.5 4.5 : 3.5

## Dividing Decimals Word Problems

Jack paid $99 for 6 pizzas. How much did he pay per pizza?

Mark has run a total of 84.24 miles in 32.4 days of running training. How many miles did he run on average per day?

2.6 miles per day.

An Olive Oil Factory made 809.9 pounds of olive oil in 6.5 minutes. How much oil, on average, did the factory make each minute?

124.6 pounds of oil.

## Volume Word Problems

Ship container has a length of 40 feet, width 8 feet, and 9.6 feet in height. Find the volume of the container in cubic feet.

40 × 8 × 9.6 = 3,072 cubic feet.

The volume of a cylinder is 441 cubic inches. The height of the cylinder is 9 in. Find the radius of the cylinder to the nearest tenth of an inch.

441 ≈ 3.14 × r² × 9 441 ≈ 28.26 × r² r² ≈ 441 ÷ 28.26 r² ≈ 15.6 inches.

A cylindrical hole with a diameter of 8 inches is bored through a cub 10 inches on a side. Find the surface area and volume of this solid casting.

V ≈ 3.14 × 4² × 10 ≈ 502.4 V = 10³ = 1,000 1,000 − 502.4 = 497.6 cubic inches.

## Measurement Word Problems

Jack was 5 feet 9 inches tall last year. He grew 7 inches in the past year. How tall is he now?

5 ft 9 in. + 7 in. = 5 ft 16 in. = 6 ft 4 in.

The turkey is 18 lb 11 oz and the stuffing inside the turkey is 5 oz. What is the total weight of the roasted turkey?

18 lb 11 oz + 5 oz = 18 lb 16 oz = 19 lb

From 10g of instant coffee, 120 ml of coffee can be brewed. In a can of instant coffee is 200 g. How much coffee (in liters) can you make from a can?

200 ÷ 10 = 20 20 × 120 = 2,400 = 2 L 400 ml

## Age Word Problems

Mila is 5 years older than her brother, but 3 times younger than her mother. How old is Mila and how old is her mother, if Mila's brother is 6 years old?

6 + 5 = 11 Mila's age. 11 × 3 = 33 mother's age.

In 8 years, Mary will be 3 times as old as she is today. How old is Mary today?

x + 8 = 3x 8 = 3x − x 8 = 2x x = 4 Mary is 2 years old today.

Felix is twice as old as his friend Greg. Greg is 5 years older than Rachel. In 5 years, Felix will be three times as old as Rachel. How old is Greg now?

In 5 years, Felix will be three times as old as Rachel. 2x + 5 = 3 × (x − 5 + 5) 2x + 5 = 3x x = 5 Greg is now 5 years old.

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## 3rd Grade Math Word Problems: Free Worksheets with Answers

May 6, 2020 by Anthony Persico

## Free 3th Grade Math Word Problems Worksheets!

Are you looking for engaging 3rd grade math word problems with answers to add to your upcoming lesson plans? The following collection of free 3th grade maths word problems worksheets cover topics including addition, subtraction, multiplication, division, and measurement.

These free 3rd 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 3rd grade math worksheets, check out this free library!

## Addition 3rd Grade Math Word Problems (PDF Download)

Click the link below to download your free 3rd grade math word problems worksheet and answer key.

Looking for more free 3rd grade math worksheets? Click here to access our full PDF library.

And click here to access our free library of 3rd Grade Math Videos!

## Subtraction 3rd Grade Math Word Problems (PDF Download)

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## Multiplication 3rd Grade Math Word Problems (PDF Download)

## Division 3rd Grade Math Word Problems (PDF Download)

## Measurement 3rd Grade Math Word Problems (PDF Download)

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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)

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## Math word problems for kids - Easy math word problems for kids with answers

Math problem solving examples for elementary.

Discover the best way to enhance your kid’s mental math skills with our math word problems for kids . As a matter of fact, these easy math word problems for kids with answers will provide you with a daily practice of fun captivating word problems in all areas of math.

As we know, sometimes in real life, your kids will need to solve math problems like determining the price of an item on sale, calculating how many miles are left to arrive at a destination, etc.

As such, our aim to build remarkable problem solving skills in your kids have motivated us to design a whole lot of math problem solving examples for elementary classes from pre-k up to grade 6. These skills demand proper attention from the earliest grades, and throughout their lives.

Most importantly, you’ll find here very simple and short math problem solving steps and strategies in every concept. Hence, as they go through these strategies, they will become proficient in quick solving both real life and classroom math problems.

## How to make math word problems for kids easy, fun and enjoyable

Our endeavor in this amazing resource has been focused on how to make math word problems for kids easy, fun and enjoyable.

In the first place, we have used very simple and familiar language in formulating these real life problems. Thus we expect your kids to easily read and quickly tell what the problem is asking them to do.

Secondly, our key words are clear and simple enough to attract kid’s attention. As these key words are helpful to indicate math operations, we require kids to always underline them when reading the problem.

Most importantly, you’ll be provided with just the best of all solving strategies in every concept of all grades.

## WHAT’S THIS ALL ABOUT?

This is math-wordproblems.com a premium math quality website with original Math activities and other contents for math practice. We provide 100% free Math ressources for kids from Grade 2 to Grade 6 to improve children skills.

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- Solving word problems

## Grade 6 Math Word Problems: Tips, Tricks, and Answers

Do you want to stimulate your 6 th grader’s creative thinking skills? Then, enjoy this brilliant math article. In this comprehensive guide, we will provide you with a treasure trove of fun solving strategies, tips, tricks, and answers to tackle those tricky grade 6 math word problems that have been confusing your students for some time now.

In this page, you will discover why math word problems are important for 6th-graders and simple methods of breaking down complex word problems into manageable steps.

Nevertheless, we will introduce you to Mathskills4kids.com , an outstanding website with thousands of common types of grade 6 math word problems and a step-by-step approach to solving them. Interestingly, we will illustrate how to use diagrams and models to solve math word problems efficiently.

## Learn to love Grade 6 Math word problems with these worksheets and answers

Hello and welcome to Grade 6 Math word problems worksheets and answers , where your 6 th Grade students will learn to love and solve math problems and activities at all times.

We understand that word problems can often frustrate students, as they require a solid understanding of mathematical concepts and the ability to interpret and apply them to real-life situations. That's why we have compiled a collection of proven strategies and techniques to empower your students to approach word problems confidently and accurately.

From understanding problem-solving strategies to breaking down complex questions into manageable steps, this guide will equip you with the knowledge and resources to make math word problems a breeze. So, let's dive in and unlock the secrets to conquering grade 6 math word problems together!

## BROWSE THE WEBSITE

Download free worksheets, grade 6 math topics.

- Whole numbers

Multiplication

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- Add & subtract decimals
- Multiply & divide decimals
- Fractions & mixed numbers
- Add & subtract fractions
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## Start practice on Sixth Grade here

Why are math word problems important for 6th-graders.

Math word problems are about more than just doing calculations. They are also about applying your math knowledge to real-world situations. Math word problems are important for 6 th graders because they help them to:

- Learn how to use different math concepts and skills in various contexts
- Develop their logical thinking and reasoning abilities
- Enhance their communication and literacy skills
- Prepare them for standardized tests and future math courses

Math word problems also make math more exciting and relevant. They show us how math can solve everyday problems and challenges. They also expose us to different topics and scenarios we may not encounter in our regular math lessons.

## Strategies for solving Grade 6 math word problems

Solving Grade 6 math word problems can be intimidating, especially involving multiple steps or operations. But don't worry. Some general strategies will help your students confidently approach any word problem. Here are some of them:

- Please encourage them to read the problem carefully and identify the given information, the unknowns, and the question.
- They should rewrite the problem in their own words or summarize it in a sentence.
- Let them choose a suitable method or strategy to solve the problem. Some standard methods are guessing and checking, making a table or chart, drawing a picture or diagram, using a formula or equation, working backward, or using logical reasoning.
- They must show their work and explain each step clearly. Use appropriate units, labels, symbols, and terms.
- Lastly, tell them to check their answer by plugging it back into the problem or using a different method. Ensure their answer makes sense and answers the question.

## Breaking down complex word problems into manageable steps

Some word problems may seem too complex or confusing at first glance. They may have too much information, too many steps, or too many operations. In such cases, breaking down the problem into smaller and simpler parts is helpful. Here are some tips on how to do that:

Words like "difference," "subtract," "take away," or "minus" indicate s ubtraction .

Words like "product," "multiply," "times," or "of" indicate multiplication .

Words like "quotient," "divide," "per," or "out of" indicate division .

Words like "ratio," "fraction," "percent," or "part" indicate fractions or decimals .

Words like "equal," "same as," or "is" indicate equations .

Words like "more than,” “less than," "greater than," or "smaller than" indicate inequalities .

Words like "average," "mean," or "median" indicate statistics .

Words like "area," "perimeter," "volume," or "surface area" indicate geometry , etc.

- Use parentheses, brackets, or other symbols to group the parts of the problem that belong together . For example, if the problem says:

You can rewrite it as:

- (John has 12 apples) + (Mary has 8 apples) = (total number of apples) / (4 people) = (number of apples per person)

This way, you can see the structure of the problem more clearly and focus on one part at a time.

- Solve each part of the problem separately and write down the intermediate results . For example, using the previous problem:
- (John has 12 apples) + (Mary has 8 apples) = (total number of apples)
- 12 + 8 = 20
- (total number of apples) / (4 people) = (number of apples per person)

This way, you can keep track of your work and avoid making mistakes.

- Combine the intermediate results to get the final answer. For example, using the previous problem :

This way, you can answer the question and check your answer.

## Common types of grade 6 math word problems

There are many types of word problems that you may encounter in grade 6 math . Some of the most common ones found on Mathskills4kids.com are:

- Ratio and proportion problems : These problems involve finding the relationship between two quantities with the same unit or measure. For example, if 12 pencils cost $3, how much do 20 pencils cost?
- Percent problems : These problems involve finding the part, whole, or percent of a quantity. For example, if 30% of a class is boys, and there are 24 students, how many boys are there?
- Fraction problems : These problems involve adding, subtracting, multiplying, or dividing fractions. For example, how much pizza do you have left if you have 2/3 of a pizza and eat 1/4?
- Decimal problems : These problems involve adding, subtracting, multiplying, or dividing decimals. For example, if you buy a shirt for $12.50 and a pair of jeans for $24.75, how much change do you get from $50?
- Measurement problems : These problems involve converting between different units of measurement or finding the perimeter, area, or volume of shapes. For example, if a rectangle has a length of 15 cm and a width of 10 cm, what is its area in square meters?
- Algebra problems : These problems involve finding the value of an unknown variable or expression. For example, if x + 5 = 13, what is the value of x?

## A step-by-step approach to solving different types of word problems

No matter what type of word problem your 6 th graders are faced with, they can use the following steps to solve it:

- They should read the problem carefully and identify the given information and the question.
- They must choose a variable to represent the unknown quantity and write an equation or expression that relates the given information and the question.
- They can now solve the equation or expression and find the variable's value.
- They can check their answer by plugging it back into the equation or expression to see if it makes sense.
- They can now write their answer in complete sentences and include the appropriate units.

## Using diagrams and models to solve math word problems

Sometimes, it can be helpful to use diagrams and models to visualize the problem and make it easier to solve. Some examples of diagrams and models for solving math word problems are:

- Tape diagrams : These are horizontal or vertical bars showing the relationship between two quantities. For example, you can use a tape diagram to show how much money each person gets when $60 is shared equally among 4 people.
- Number lines : These horizontal lines show numbers and their relative positions. For example, you can use a number line to show how to add or subtract fractions with different denominators.
- Tables : These are grids that show data in rows and columns. For example, you can use a table to show how to find equivalent ratios or fractions.
- Charts : These are graphical representations of data using bars, circles, lines, or other shapes. For example, you can use a chart to show how to find the percent of a quantity or compare different quantities.
- Drawings : These are sketches or illustrations that show shapes or objects. For example, you can use a drawing to show how to find a shape's perimeter, area, or volume.

## Providing answers and explanations to sample Mathskills4kids’ Grade 6 math word problems

Here are some sample Grade 6 math word problems with answers and explanations available at Mathskills4kids.com :

Answer : 6 cups of flour

Explanation : This is a ratio problem. We can use a tape diagram to show the relationship between flour and sugar.

Flour →|<---2 cups--->|<---2 cups--->|<---2 cups---> = 6

Sugar→|<---3 cups--->|<---3 cups--->|<---3 cups---> = 9

We can see that for every 3 cups of sugar, we need 2 cups of flour. So, for 9 cups of sugar, we need 6 cups of flour.

Answer : $15

Explanation : This is a percent problem. We can use a formula to find the sale price of the shirt.

Sale price = Original price - Discount

Discount = Percent off x Original price

We know the percent off is 40%, and the original price is $25. So, we can plug these values into the formula and solve for the sale price.

Discount = 40% x $25

Discount = 0.4 x $25

Discount = $10

Sale price = $25 - $10

Sale price = $15

## Tips for improving problem-solving skills in Grade 6 math

Here are some tips that can help students improve their problem-solving skills in grade 6 math :

- Please encourage them to practice regularly and try different types of word problems.
- They should review the concepts and skills they have learned and apply them to new situations.
- They can use different strategies and methods to solve word problems and compare their results.
- Let them ask for help from the teacher, parents, or peers if they get stuck or confused.
- They should learn from their mistakes and try to avoid them in the future.

## Bonus: additional resources to reinforce Grade 6 math problem skills

If you want to enhance your student's Grade 6 math word problem skills , or if you need some extra help, here are some additional and useful web links that you can check out:

- Math Playground : This website has a lot of fun and interactive games that let 6 th graders practice different types of math word problems, such as fractions, decimals, ratios, proportions, and more. They can also watch videos explaining how to solve some problems. https://www.mathplayground.com/wordproblems.html .
- Khan Academy : This website has many videos and exercises covering various topics in Grade 6 math, including word problems. Students can learn at their own pace and track their progress. https://www.khanacademy.org/math/cc-sixth-grade-math .
- IXL : This website has many practice questions aligned with the Common Core standards for Grade 6 math. Students can choose from different categories of word problems, such as expressions and equations, geometry, statistics, and more. They can also get instant feedback and explanations for their answers. https://www.ixl.com/math/grade-6 .
- Math Goodies : This website has a lot of worksheets and lessons that teach 6 th graders how to solve different types of word problems, such as percent, ratio, proportion, and more. They can also find tips and tricks for solving word problems faster and easier. https://www.mathgoodies.com/math-mammoth/worksheets/pdf/grade_6_word_problems.pdf .

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Math word problems can be challenging for many 6th-graders, but they are also important for developing their mathematical thinking and reasoning skills.

Using the strategies and steps we discussed in this article, your student's ability to solve different types of word problems in Grade 6 math can be improved.

You can also use the diagrams and models we have shown you to help your students visualize the problem and find the solution. Encourage them to practice as much as possible, and they must not be afraid to ask for help if needed.

You can also use the web links that we have provided to reinforce your student’s learning and have fun with math. We hope this article has helped your 6th-grade students feel more confident and prepared for tackling Grade 6 math word problems.

Happy problem-solving!

## WHAT’S THIS ALL ABOUT?

This is mathskills4kids.com a premium math quality website with original Math activities and other contents for math practice. We provide 100% free Math ressources for kids from Preschool to Grade 6 to improve children skills.

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## Word Problem Practice Questions with Answer Key

- Posted by Brian Stocker
- Date February 13, 2019
- Comments 11 comments

## Problem Solving – Word Problems

Word problems are mathematical problems using everyday language and real-world situations. Some information is given and one or more pieces or information (variables) are missing. You must understand the given information, identify the mathematical operations necessary to solve the problem, and then carry out those operations to obtain the missing information or variables.

## The Biggest Tip!

Tackling word problems is much easier if you have a systematic approach which we outline below.

Here is the biggest tip for word problems practice. Practice regularly and systematically. Sounds simple and easy right? Yes it is, and yes it really does work. Word problems are a way of thinking and require you to translate a real world problem into mathematical terms.

Some math instructors go so far as to say that learning how to think mathematically is the main reason for teaching word problems. So what do we mean by Practice regularly and systematically? Studying word problems and math in general requires a logical and mathematical frame of mind. The only way that you can get this is by practicing regularly, which means everyday.

## How to Solve Word Problems

Types of Word Problems

## Most Common Word Problem Mistakes on a Test

It is critical that you practice word problems everyday for the 5 days before the exam as a bare minimum. If you practice and miss a day, you have lost the mathematical frame of mind and the benefit of your previous practice is pretty much gone. Anyone who has done any number of math tests will agree – you have to practice everyday.

See Also Algebra Word Problems

Effective problem-solving skills are essential in many areas of life, from academia to the workplace and beyond. Developing the ability to solve word problems requires practice and patience, as well as a strong understanding of basic mathematical concepts and operations.

## Try a FREE Quiz

Word problem practice questions.

1. A box contains 7 black pencils and 28 blue ones. What is the ratio between the black and blue pens?

a. 1:4 b. 2:7 c. 1:8 d. 1:9

2. The manager of a weaving factory estimates that if 10 machines run at 100% efficiency for 8 hours, they will produce 1450 meters of cloth. Due to some tech¬nical problems, 4 machines run of 95% efficiency and the remaining 6 at 90% efficiency. How many meters of cloth can these machines will produce in 8 hours?

a. 1334 meters b. 1310 meters c. 1300 meters d. 1285 meters

3. In a local election at polling station A, 945 voters cast their vote out of 1270 registered voters. At poll¬ing station B, 860 cast their vote out of 1050 regis¬tered voters and at station C, 1210 cast their vote out of 1440 registered voters. What is the total turnout from all three polling stations?

a. 70% b. 74% c. 76% d. 80%

4. If Lynn can type a page in p minutes, what portion of the page can she do in 5 minutes?

a. p/5 b. p – 5 c. p + 5 d. 5/p

5. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both to paint a house?

a. 2 hours and 24 minutes b. 3 hours and 12 minutes c. 3 hours and 44 minutes d. 4 hours and 10 minutes

6. Employees of a discount appliance store receive an additional 20% off the lowest price on any item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?

a. $280.90 b. $287.00 c. $292.50 d. $306.00

7. The sale price of a car is $12,590, which is 20% off the original price. What is the original price?

a. $14,310.40 b. $14,990.90 c. $15,108.00 d. $15,737.50

8. Richard gives ‘s’ amount of salary to each of his ‘n’ employees weekly. If he has ‘x’ amount of money, how many days he can employ these ‘n’ employees.

a. sx/7n b. 7x/nx c. nx/7s d. 7x/ns

9. A distributor purchased 550 kilograms of potatoes for $165. He distributed these at a rate of $6.4 per 20 kilograms to 15 shops, $3.4 per 10 kilograms to 12 shops and the remainder at $1.8 per 5 kilo¬grams. If his total distribution cost is $10, what will his profit be?

a. $10.40 b. $8.60 c. $14.90 d. $23.40

10. How much pay does Mr. Johnson receive if he gives half of his pay to his family, $250 to his land¬lord, and has exactly 3/7 of his pay left over?

a. $3600 b. $3500 c. $2800 d. $175042

11. The cost of waterproofing canvas is .50 a square yard. What’s the total cost for waterproofing a canvas truck cover that is 15’ x 24’?

a. $18.00 b. $6.67 c. $180.00 d. $20.00

1. A The ratio between black and blue pens is 7 to 28 or 7:28. Bring to the lowest terms by dividing both sides by 7 gives 1:4.

2. A At 100% efficiency 1 machine produces 1450/10 = 145 m of cloth. At 95% efficiency, 4 machines produce 4 * 145 * 95/100 = 551 m of cloth. At 90% efficiency, 6 machines produce 6 * 145 * 90/100 = 783 m of cloth. Total cloth produced by all 10 machines = 551 + 783 = 1334 m Since the information provided and the question are based on 8 hours, we did not need to use time to reach the answer.

The turnout at polling station A is 945 out of 1270 registered voters. So, the percentage turnout at station A is:

(945/1270) × 100% = 74.41%

The turnout at polling station B is 860 out of 1050 registered voters. So, the percentage turnout at station B is:

(860/1050) × 100% = 81.90%

The turnout at polling station C is 1210 out of 1440 registered voters. So, the percentage turnout at station C is:

(1210/1440) × 100% = 84.03%

To find the total turnout from all three polling stations, we need to add up the total number of voters and the total number of registered voters from all three stations:

Total number of voters = 945 + 860 + 1210 = 3015

Total number of registered voters = 1270 + 1050 + 1440 = 3760

The overall percentage turnout is:

(3015/3760) × 100% = 80.12%

Therefore, the total turnout from all three polling stations is 80.12% — rounding to 80%.

4. D This is a simple direct proportion problem: If Lynn can type 1 page in p minutes, then she can type x pages in 5 minutes We do cross multiplication: x * p = 5 * 1 Then, x = 5/p

5. A This is an inverse ratio problem. 1/x = 1/a + 1/b where a is the time Sally can paint a house, b is the time John can paint a house, x is the time Sally and John can together paint a house. So, 1/x = 1/4 + 1/6 … We use the least common multiple in the denominator that is 24: 1/x = 6/24 + 4/24 1/x = 10/24 x = 24/10 x = 2.4 hours. In other words; 2 hours + 0.4 hours = 2 hours + 0.4•60 minutes = 2 hours 24 minutes

The original price of the dishwasher is $450. During a 15% off sale, the price of the dishwasher will be reduced by:

15% of $450 = 0.15 x $450 = $67.50

So the sale price of the dishwasher will be:

$450 – $67.50 = $382.50

As an employee, the person receives an additional 20% off the lowest price, which is $382.50. We can calculate the additional discount as:

20% of $382.50 = 0.20 x $382.50 = $76.50

So the final price that the employee will pay for the dishwasher is:

$382.50 – $76.50 = $306.00

Therefore, the employee will pay $306.00 for the dishwasher.

7. D Original price = x, 80/100 = 12590/X, 80X = 1259000, X = 15,737.50.

8. D We are given that each of the n employees earns s amount of salary weekly. This means that one employee earns s salary weekly. So; Richard has ‘ns’ amount of money to employ n employees for a week. We are asked to find the number of days n employees can be employed with x amount of money. We can do simple direct proportion: If Richard can employ n employees for 7 days with ‘ns’ amount of money, Richard can employ n employees for y days with x amount of money … y is the number of days we need to find. We can do cross multiplication: y = (x * 7)/(ns) y = 7x/ns

9. B The distribution is done at three different rates and in three different amounts: $6.4 per 20 kilograms to 15 shops … 20•15 = 300 kilograms distributed $3.4 per 10 kilograms to 12 shops … 10•12 = 120 kilograms distributed 550 – (300 + 120) = 550 – 420 = 130 kilograms left. This 50 amount is distributed in 5 kilogram portions. So, this means that there are 130/5 = 26 shops. $1.8 per 130 kilograms. We need to find the amount he earned overall these distributions. $6.4 per 20 kilograms : 6.4•15 = $96 for 300 kilograms $3.4 per 10 kilograms : 3.4 *12 = $40.8 for 120 kilograms $1.8 per 5 kilograms : 1.8 * 26 = $46.8 for 130 kilograms So, he earned 96 + 40.8 + 46.8 = $ 183.6 The total distribution cost is given as $10 The profit is found by: Money earned – money spent … It is important to remember that he bought 550 kilograms of potatoes for $165 at the beginning: Profit = 183.6 – 10 – 165 = $8.6

10. B We check the fractions taking place in the question. We see that there is a “half” (that is 1/2) and 3/7. So, we multiply the denominators of these fractions to decide how to name the total money. We say that Mr. Johnson has 14x at the beginning; he gives half of this, meaning 7x, to his family. $250 to his landlord. He has 3/7 of his money left. 3/7 of 14x is equal to: 14x * (3/7) = 6x So, Spent money is: 7x + 250 Unspent money is: 6×51 Total money is: 14x Write an equation: total money = spent money + unspent money 14x = 7x + 250 + 6x 14x – 7x – 6x = 250 x = 250 We are asked to find the total money that is 14x: 14x = 14 * 250 = $3500

11. D First calculate total square feet, which is 15 * 24 = 360 ft 2 . Next, convert this value to square yards, (1 yards 2 = 9 ft 2 ) which is 360/9 = 40 yards 2 . At $0.50 per square yard, the total cost is 40 * 0.50 = $20.

- Not reading the problem carefully and thoroughly, so that you either misunderstand or solve the problem incorrectly.
- Not identifying the important information in the problem, such as the quantities, units, and the operation to be performed.
- Not translating the information in the problem into mathematical language and equations.
- Not checking the units of measure and making sure they match your final answer.
- Not double-checking the answer to ensure it makes sense.
- Not understanding the underlying mathematical concept or operation the problem is asking for.
- Not using estimation or approximations as a tool to check the reasonableness of your answer.

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11 comments.

Will we need to know units and their conversions such as yards to feet? Should we memorise those?

are we allowed to use a calculator? To expect someone to complete these in their head is absurd especially with a time limit. The second question requires multiplication by decimals, which would be okay if you got a whole number but you dont, you get a fraction and the only way to get it to 551 is by then multiplying that number by 4. Doubt anyone would be required to do these kind of calculations in a real world scenario especially unaided and under time constraints.

Hi Depends on the test – what test are you studying for?

is this preparation for the CAAT level C???

These questions vary in subject and difficulty level to give students practice on different types of questions for different types of tests. They are not specific to one test or one level.

Yes the LEAST common multiple of 6 and 4 is 12 – i did it with 24 – it will give the same answer no matter which way you do it. Good point though – perhaps for simplicity sake 12 would be better.

Are these questions appeared on the Cbest?

The are the same TYPE of questions – not exactly

sorry for the message above, i like your site and i have won 1st place in an exam due to this site

I used Chat GPT. Solved every one…. perfectly. I’m still dumb as a rock though.

Oh Really? You may want to check that again!! It gave me wrong answers and weird steps to calculate for 2 of them!

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## 20 Word Problems For Year 6: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma johnson.

Word problems for Year 6 are an important part of the curriculum. For children to achieve success in the Year 6 SATs, in particular the more challenging reasoning element of the SATs assessments, it is essential they have the confidence to tackle a wide range of word problems.

Key to this success is regular exposure to the style and type of questions, covering the topics children could be presented with. Our collection of year 6 maths worksheets are is a great place to start.

To help child practice their problem solving skills, we have put together a collection of 20 word problems , organised by topic. This collection encompasses the types of questions children may encounter in the two reasoning papers.

## All Kinds of Word Problems Four Operations

Download this free pack of word problems. With questions covering all four operations, your students will have a great opportunity to practice their problem solving skills across KS2 topics.

## Place value

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The National Curriculum states that children need to be able to solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into simpler steps and persevering in seeking solutions.

By Year 6, children can expect to be tackling a range of one-step, two-step and multi-step word problems. To achieve at least the expected standard in Year 6, pupils need to demonstrate the ability to solve word problems across a range of topics.

Solving problems including ordering, rounding and negative numbers.

Solving multiplication, division and addition and subtraction word problems including one and two-step word problems and multi-step word problems in context, deciding which operations and methods to use and why.

Solving problems involving comparing, ordering and sequencing fractions; using the four operations and problems which require answers to be rounded to specified degrees of accuracy.

Solving problems involving the relative sizes of two quantities; the calculation of percentages; involving similar shapes where the scale factor is known and can be found; and unequal sharing and grouping, using knowledge of fractions and multiples.

Solving problems including time word problems and involving the calculation and conversion of units of measure, using decimal notation up to three decimal places, where appropriate.

Interpret and construct pie and line graphs and use these to solve problems.

Word problems are an essential element of the Year 6 curriculum, because they require children to apply the knowledge they have learnt to ‘real life’ situations, for example, in money word problems . They shouldn’t just be taught as stand alone topics, but should be incorporated in lessons throughout the year, to ensure children have as much exposure as possible.

Solving word problems helps children learn the skills needed to apply their knowledge of maths beyond the classroom and into the real world.

When teaching problem solving in Year 6, children need to firstly look carefully at the key information and think about what they already know. Secondly, what is the word problem actually asking? Which calculation(s) would be required and would it help to draw/represent the problem pictorially?

Here is an example:

Ahmed is buying clothes. He buys a t-shirt for £12.99 and a pair of jeans which cost £12.26 more than the T-shirt. He pays with a £50 note. What change does Ahmed get?

How to solve:

What do you already know?

- More than means I will need to add the price of the T-shirt and jeans together.
- Decimals numbers means I need to remember to line up the decimal points in my calculations.
- Calculating change means I will need to subtract the total for the jeans and T-shirt from the original amount.

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

- To calculate the cost of the jeans, we need to add £12.99 and £12.26 = £25.25
- Ahmed pays using a £50 note.
- To calculate the change Ahmed will get, we need to subtract £25.25 from £50.
- £50 – £25.25 = £24.75

Problem solving is an important part of the preparation for the Key Stage 2 SATs, as this is the area children tend to find the most challenging. With two reasoning papers to complete, children will be expected to answer a wide range of word and number problem style questions. The best preparation for this is through regular exposure to these types of questions.

Addition word problems at Year 6 include larger 6 or 7 digit numbers, decimal numbers and problems involving finding the inverse. These can be one, two and multi-step problems

## Addition question 1

A shopping centre had 124,713 visitors in January, 102,539 in February and 118,768 in March. How many shoppers visited the shopping centre from January to March?

Answer (1 mark): 346,020

## Addition question 2

A shop has an offer on all T-shirts.

Buy one T-shirt, get one for half price.

If Tom buys 2 T-shirts, how much does he pay altogether?

Answer (2 marks): £7.35

## Addition question 3

The table below shows the number of visitors to the planetarium and the transport museum each day. Which day had the most visitors?

Answer (2 marks): Saturday

Subtraction word problems in Year 6 include larger 6 or 7 digit numbers, decimal numbers and problems involving finding the inverse. These can be one, two and multi-step problems

## Subtraction question 1

In the Autumn term, the total number of English and maths worksheets printed by a school was 63,502. 39,756 were maths worksheets. How many worksheets were printed out for English?

Answer (1 mark): 23,746

## Subtraction question 2

6 cars were weighed before being loaded onto the car transporter.

They weight of the cars was:

What is the difference in weight between the heaviest and lightest car?

Answer (1 mark): 1043kg

## Subtraction question 3

Two decimal numbers add together to make 37.53.

One number is 23.86.

What is the other number?

Answer (1 mark): 13.67

Multiplication word problems can include multiplying whole and decimal numbers by 1 and 2-digit numbers. A secure knowledge of times tables is helpful for children solving these questions confidently.

## Multiplication question 1

A box of chocolate contains 2 trays of chocolates.

There are 18 chocolates on each tray.

How many chocolates are there in 35 boxes of chocolates?

Answer (2 marks): 1260

## Multiplication question 2

Zara buys 4 large boxes of cupcakes and 3 small boxes of cupcakes.

Each large box contains 28 cupcakes. Each small box contains 16 cupcakes.

How many cupcakes does Zara buy altogether?

Answer (2 marks): 160

## Multiplication question 3

A cyclist cycled a route of 123.6 miles once a week for a year. How far did he cycle over the whole year?

Answer (2 marks): 6427.2

Division word problems in Year 6 can include division with whole numbers and decimal numbers, dividing by 1 and 2-digit numbers.

## Division question 1

A 940ml bottle of blackcurrant makes 20 drinks.

How many millilitres of blackcurrant are in each drink?

Answer (2 marks): 47

## Division question 2

Mr Jones is organising mini buses for a Year 6 school trip. Each minibus seats 12 people

120 Year 6 pupils are going on a school trip.

There needs to be one adult for every 10 pupils

How many coaches will Mr Jones need to book?

Answer (2 marks): 12 mini buses

125 pupils will need 13 adults = 138 in total

## Division question 3

A factory is packaging eggs in boxes of 12.

The factory has 878 eggs to box-up.

How many boxes will they have, to send to the supermarket?

Answer (2 marks): 73 boxes

Decimals, percentage word problems and fraction word problems can be stand alone, or they can involve converting between. For example, in questions using measures.

## Fractions, decimals and percentages question 1

By the end of the Autumn term, Chloe had used ⅔ of her maths book. If the book had 96 pages, how many pages had she used?

Answer (1 mark): 64 pages

⅓ of 96 = 32

⅔ of 96 = 64

## Fractions, decimals and percentages question 2

Abdullah received £600 for his birthday. He spent 45% of him money on a VR headset. How much did the headset cost him?

Answer (1 mark): £270

## Fractions, decimals and percentages question 3

Mrs Jones went to the local supermarket to buy some vegetables.

She bought:

- 1 3/10kg of potatoes
- 840.5g of apples
- 4/5kg of peaches
- 520.6g of grapes

What was the total weight of the shopping Mrs Jones bought?

Answer (1 mark):

- 1.3kg potatoes
- 0.8405kg apples
- 0.8kg peaches
- 0.520kg grapes

Ratio word problems are often linked with measures. Children should be encouraged to draw bar models to solve problems involving ratio, as these question really benefit from a visual representation.

## Ratio question 1

Sam and Zeyn were making drinks for the school fair. To make the jugs of squash, they were mixing 300ml of orange squash with 1500ml of water.

If they have 900ml of orange squash

- How much water will they need altogether?
- What will be the total volume of the squash?

Answer (2 marks):

- 4500ml of water
- 5400ml of squash

## Ratio question 2

A piece of ribbon is 72cm long. It is cut into pieces in the ratio of 2:3:4.

How long is each piece of ribbon?

Answer (1 mark): 16cm:24cm:32cm

Mixed operation word problems require two or more operations to solve. Alongside the four operations, they can also include other topics, including fractions and percentages These can be two-step or multi-step questions and are worth 2 or 3 marks in SATs papers.

Third Space Learning’s online one-to-one tutoring programmes include questions that combine skills students have learnt and test their understanding across a range of topics. Personalised to the needs of each individual student, our online tutoring programme works to identify gaps in learning, fill those gaps and reinforce students’ maths knowledge.

## Mixed four operations question 1

One bank-holiday weekend, a total of 346,728 people visited a theme park.

134,235 visited on Saturday

121,689 visited on Sunday.

How many visited on bank holiday Monday?

Answer (2 marks): 90,804

## Mixed four operations question 2

A pair of jeans in a shop cost £28.

In the sale, they were reduced in price by 25%.

What was the reduced price?

Answer (2 marks): £21

## Mixed four operations question 3

Sophie thinks of a number.

She multiplies her number by 6.

Then she adds 10

Finally she divides by 4.

Her answer is 13.

What was her original number?

Answer (1 mark): 7

Third Space Learning also offers a wide array of maths and word problems resources for other year groups such as word problems for Year 5 , word problems for Year 4 and word problems for Year 3

Do you have pupils who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Subsidised one to one maths tutoring from the UK’s most affordable DfE-approved one to one tutoring provider.

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## 4.OA.A.3 Solving Multi-Step Problems with Unknown Quantity

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## Wyoming Standards for Mathematics

Learning Domain: Operations and Algebraic Thinking

Standard: Solve multi-step word problems posed with whole numbers, including problems in which remainders must be interpreted.

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## Maryland College and Career Ready Math Standards

Standard: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Learning Domain: Mathematical Practices

Standard: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

## Common Core State Standards Math

Cluster: Use the four operations with whole numbers to solve problems

Cluster: Mathematical practices

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An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

Problem Solver Subjects. Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects. Here are example math problems within each subject that can be input into the calculator and solved.

Math Word Problem Worksheets. Read, explore, and solve over 1000 math word problems based on addition, subtraction, multiplication, division, fraction, decimal, ratio and more. These word problems help children hone their reading and analytical skills; understand the real-life application of math operations and other math topics.

Write your answer as a fraction, or as a whole or mixed number. Decimals word problems. Best for: 4th grade, 5th grade. 47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total? ... How to easily make your own math word problems & word problems worksheets.

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math ...

These mixed operations word problems worksheets will produce addition, multiplication, subtraction and division problems with 1 or 2 digit numbers. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Grade 5 word problems worksheets. Mixed 4 operations (addition, subtraction, multiplication, division) Estimating and rounding word problems (based on the 4 operations) Add and subtract fractions and mixed numbers (like and unlike denominators) Multiplying and dividing fractions. Mixed operations with fractions (add, subtract, multiply, divide)

This collection of printable math worksheets is a great resource for practicing how to solve word problems, both in the classroom and at home. There are different sets of addition word problems, subtraction word problems, multiplication word problems and division word problems, as well as worksheets with a mix of operations.

Math Playground has hundreds of interactive math word problems for kids in grades 1-6. Solve problems with Thinking Blocks, Jake and Astro, IQ and more. Model your word problems, draw a picture, and organize information!

Solving algebraic word problems requires us to combine our ability to create equations and solve them. To solve an algebraic word problem: Define a variable. Write an equation using the variable. Solve the equation. If the variable is not the answer to the word problem, use the variable to calculate the answer.

We provide word problems and math puzzles designed by experienced teachers. LogicLike helps children improve their math skills in a playfull way! ... Show Answer. 490 cents / $4.90. Michael had $9,896.00 in his checking account.

Khan Academy's 100,000+ free practice questions give instant feedback, don't need to be graded, and don't require a printer. Math Worksheets. Khan Academy. Math worksheets take forever to hunt down across the internet. Khan Academy is your one-stop-shop for practice from arithmetic to calculus. Math worksheets can vary in quality from ...

The following collection of free 3th grade maths word problems worksheets cover topics including addition, subtraction, multiplication, division, and measurement. These free 3rd 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 ...

One hose can fill a goldfish pond in 30 minutes, and two hoses can fill the same pond in 21 minutes. Find how long it takes the second hose alone to fill the pond. The larger of two numbers is __2__ more than four times the smaller number. The difference of the two numbers is __29__. Find each number.

Discover the best way to enhance your kid's mental math skills with our math word problems for kids. As a matter of fact, these easy math word problems for kids with answers will provide you with a daily practice of fun captivating word problems in all areas of math. 2. Adding, subtracting, comparing and ordering word problems. Second Grade. 15.

Here are some sample Grade 6 math word problems with answers and explanations available at Mathskills4kids.com: A cookie recipe calls for 2 cups of flour for every 3 cups of sugar. How much flour is needed for 9 cups of sugar? Answer: 6 cups of flour. Explanation: This is a ratio problem. We can use a tape diagram to show the relationship ...

Explore printable Math Word Problems worksheets for 8th Grade. Math Word Problems worksheets for Grade 8 are an essential resource for teachers looking to challenge their students and help them develop critical thinking and problem-solving skills. These worksheets cover a wide range of topics, including algebra, geometry, and statistics ...

5. A. This is an inverse ratio problem. 1/x = 1/a + 1/b where a is the time Sally can paint a house, b is the time John can paint a house, x is the time Sally and John can together paint a house. So, 1/x = 1/4 + 1/6 …. We use the least common multiple in the denominator that is 24: 1/x = 6/24 + 4/24. 1/x = 10/24.

Maths Word Problems and Solutions ... Hint: See problem 20 and solve by yourself. Answer: A) 120 hectares; B) 7 days; C) 8 days. Problem 22 A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minutes ahead of scheduled.

Explore printable Math Word Problems worksheets for 7th Grade. Math Word Problems worksheets for Grade 7 are an essential resource for teachers looking to challenge their students and help them develop critical thinking skills. These worksheets cover a wide range of topics, including fractions, decimals, percentages, algebra, geometry, and more.

Math Word Problems worksheets for Grade 6 are an essential resource for teachers who want to help their students develop strong problem-solving skills and a deep understanding of mathematical concepts. These worksheets provide a variety of engaging and challenging problems that require students to apply their knowledge of math in real-world ...

You will need to get assistance from your school if you are having problems entering the answers into your online assignment. Phone support is available Monday-Friday, 9:00AM-10:00PM ET. You may speak with a member of our customer support team by calling 1-800-876-1799.

Our collection of year 6 maths worksheets are is a great place to start. To help child practice their problem solving skills, we have put together a collection of 20 word problems, organised by topic. This collection encompasses the types of questions children may encounter in the two reasoning papers. All Kinds of Word Problems Four Operations.

Cluster: Use the four operations with whole numbers to solve problems Standard: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental ...