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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.

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Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

Example: Sam and Alex play tennis.

On the weekend Sam played 4 more games than Alex did, and together they played 12 games.

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

You should also write down what is actually being asked for , so you know where you are going and when you have arrived!

Also look for key words:

Thinking Clearly

Some wording can be tricky, making it hard to think "the right way around", such as:

Example: Sam has 2 dollars less than Alex. How do we write this as an equation?

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")

Example: on our street there are twice as many dogs as cats. How do we write this as an equation?

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")

Let's start with a really simple example so we see how it's done:

Example: A rectangular garden is 12m by 5m, what is its area ?

Turn the English into Algebra:

Formula for Area of a Rectangle : A = w × h

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

Now let's try the example from the top of the page:

Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?

We know that Sam played 4 more games than Alex, so: S = A + 4

And we know that together they played 12 games: S + A = 12

We are being asked for how many games Alex played: A

Which means that Alex played 4 games of tennis.

Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!

A slightly harder example:

Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?

12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?

We know there are seven days in the week, so: d + e = 7

And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27

We are being asked for how many days she trains for 5 hours: d

The number of "5 hour" days is 3

Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.

3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours

Some examples from Geometry:

Example: A circle has an area of 12 mm 2 , what is its radius?

And the formula for Area is: A = π r 2

We are being asked for the radius.

We need to rearrange the formula to find the area

Example: A cube has a volume of 125 mm 3 , what is its surface area?

Make a quick sketch:

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?

$40N + $(12 × 1¼N) = $660

We are being asked for Joel's normal rate of pay $N.

So Joel’s normal rate of pay is $12 per hour

Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

More about Money, with these two examples involving Compound Interest

Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?

This is the compound interest formula:

So we will use these letters:

We are being asked for the Future Value: FV

Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?

The compound interest formula:

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33

And an example of a Ratio question:

Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1

b + 4 g − 2 = 2 1

Which can be rearranged to b + 4 = 2(g − 2)

We are being asked for how many students there are altogether now: b + g

There are 12 girls !

And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys

So there are now 12 girls and 16 boys in the class, making 28 students altogether .

There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1

And now for some Quadratic Equations :

Example: The product of two consecutive even integers is 168. What are the integers?

Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.

We will call the smaller integer n , and so the larger integer must be n+2

And we are told the product (what we get after multiplying) is 168, so we know:

We are being asked for the integers

That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.

Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES

Check 12: 12(12 + 2) = 12×14 = 168 YES

So there are two solutions: −14 and −12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check":

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).

Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?

Let's first make a sketch so we get things right!:

We are being asked for the length of the room: L

This is a quadratic equation , there are many ways to solve it, this time let's use factoring :

And so L = 8 or −14

There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

So the length of the room is 8 m

L = 8, so W = ½L = 4

So the area of the rectangle = (W+3) × L = 7 × 8 = 56

There we are ...

... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?

Mathematical Word Problems

Math word problems is one of the most complex parts of the elementary math curriculum since translating text into symbolic math is required to solve the problem. Because the Wolfram Language has powerful symbolic computation ability, Wolfram|Alpha can interpret basic mathematical word problems and give descriptive results.

Word Problems

Solve a word problem and explore related facts.

Solve a word problem:

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Solving Word Problems in Mathematics

Steps of solving a word problem.

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Praxis Core Math

Unit 1: lesson 4.

Algebraic word problems | Lesson

What are algebraic word problems?

What skills are needed.

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Strategies for Solving Word Problems

word problems to solve

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. read the entire word problem.

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. what exactly is the question.

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

word problems to solve

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

3rd Grade Math Task Cards Mega Bundle | 3rd Grade Math Centers Bundle

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

th Grade 960 Math Task Cards Mega Bundle | 4th Grade Math Centers

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

5th Grade Math Task Cards Mega Bundle - 5th Grade Math Centers

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

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How to Solve Word Problems in Algebra

Last Updated: December 19, 2022 References

This article was co-authored by Daron Cam . Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College. This article has been viewed 53,927 times.

You can solve many real world problems with the help of math. In order to familiarize students with these kinds of problems, teachers include word problems in their math curriculum. However, word problems can present a real challenge if you don't know how to break them down and find the numbers underneath the story. Solving word problems is an art of transforming the words and sentences into mathematical expressions and then applying conventional algebraic techniques to solve the problem.

Assessing the Problem

Image titled Solve Word Problems in Algebra Step 1

Image titled Solve Word Problems in Algebra Step 3

For example, you know that Jane bought two books. You know that the second book was $80. You also know that the second book cost $10 less than 3 times the price of the first book. You don't know the price of the first book.

Image titled Solve Word Problems in Algebra Step 4

Finding the Solution

Image titled Solve Word Problems in Algebra Step 6

Completing a Sample Problem

Image titled Solve Word Problems in Algebra Step 10

Robyn and Billy run a lemonade stand. They are giving all the money that they make to a cat shelter. They will combine their profits from selling lemonade with their tips. They sell cups of lemonade for 75 cents. Their mom and dad have agreed to double whatever amount they receive in tips. Write an equation that describes the amount of money Robyn and Billy will give to the shelter.

Image titled Solve Word Problems in Algebra Step 11

Since you are combining their profits and tips, you will be adding two terms. So, x = __ + __.

$.75c$

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About This Article

To solve word problems in algebra, start by reading the problem carefully and determining what you’re being asked to find. Next, summarize what information you know and what you need to know. Then, assign variables to the unknown quantities. For example, if you know that Jane bought 2 books, and the second book cost $80, which was $10 less than 3 times the price of the first book, assign x to the price of the 1st book. Use this information to write your equation, which is 80 = 3x - 10. To learn how to solve an equation with multiple variables, keep reading! Did this summary help you? Yes No

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120 Math Word Problems To Challenge Students Grades 1 to 8

word problems to solve

Engage and motivate your students with our adaptive, game-based learning platform!

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.

$A teacher is teaching three students with a whiteboard happily.$

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?

$A glimpse of the Prodigy Math Game world and a sample math question a kid could receive while playing.$

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

A hand holding a pen is doing calculation on a pice of papper

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

A female teacher is instructing student math on a blackboard

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

A student is drawing on a notebook, holding a pencil.

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

Four students are sitting together and discussing math questions

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

A girl is doing math practice

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?

A tablet showing an example of Prodigy Math's battle gameplay.

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

$Two students are calculating on a whiteboard$

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

$A hand is calculating math problem on a blacboard$

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

Two teachers are discussing math with a pen and a notebook

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

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.

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

How to Solve Word Problems

Help kids solve word problems!

A proven step-by-step method for solving word problems is actually quite simple.

Read the problem out loud to yourself

Let’s put these steps into practice. Consider the word problem below.

Example: Kevin loves to read. He likes many different types of books. He has 3 large bookcases that each have 9 shelves on it all filled with his books. If each shelf can hold 16 books, how many books does Kevin have?

Read the Problem Out Loud

Kids have a tendency to rush through every problem. This is due to time limits on classwork and tests. If your child does not know what the problem is asking, then they cannot solve the problem. When your child reads the problem aloud, they are saying and hearing the problem. They can form a clearer picture in their head of the problem and they are more prepared to solve it.

Students need to visualize a problem to understand it, especially younger students. As they get older, they can start to visualize in their head but at a young age they should be drawing out a picture that explains to them what the problem is about. The picture should take into account all of the aspects of the problem.

Draw a picture to visualize the problem

Ask “What Do I Need to Find?”

Some word problems are straight forward with their questions. It can be as simple as “Molly has two dogs, Jason has three. How many dogs do Molly and Jason have together?” This one, however, we have to think about. There is more than one step for this problem. We first have to find how many shelves he has and then find out how many books are on all of the shelves to know how many books he has altogether.

List What is Given

It is always good to start with listing the things you know. If you try to solve the problem without knowing what tools you are given to solve it, you will not get the right answer. Think about the last time you tried to fill in the blanks or assume an answer without knowing all the facts. Your outcome probably did not turn out well. It is for this reason that we need to list what is given before any problem. The student should write it down at the top or side of the scrap paper so they always have it as a reference when doing the problem. For this problem, my list of what is given would be:

Find the Key Words

Every word problem has key words to look out for that tell you what operation to do. As your child gets more practice with word problems, finding the key words will get easier. Here are some of the most popular key words for word problems:

*this can be a key word for addition and multiplication

According to the chart above, we should use multiplication. First, we should multiply the number of shelves per case by the number of cases. 9 shelves per case x 3 book cases = 27 shelves. Next, we must multiply the number of books per shelf by the number of shelves. 27 shelves x 16 books per shelf = 432 books.

Check your answer

The last step of course is to check your work by seeing if the answer fits the question asked. Mathematically, we can check our work by doing the opposite of whatever operation we used. So for this problem, we can divide 432 by 16 and we will get 27, then divide 27 by 3 and get 9.

As challenging as word problems can be for children, having them follow these simple 7 steps will help them better understand word problems and see beyond the complicated words. Soon enough, world problems will not be so troubling for them after all and they will grow to become more confident, eager learners.

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This online math calculator can answer a number of problems in a wide range of subjects, not just strictly math. Below is a list of the available subjects to choose from. You can switch the calculator subject by clicking or tapping the menu in the upper left hand corner of the calculator.

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.

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

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Algebra Solutions

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Trigonometry Solutions

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Precalculus Solutions

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Calculus Solutions

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Statistics Solutions

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Finite Math Solutions

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Linear Algebra Solutions

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Chemistry Solutions

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Geometry Graphing Solutions

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120 Math Word Problems for Grades 1 to 8
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Math Word Problem Solutions · Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. · Rhonda has 12 marbles more than Douglas. Douglas has 6