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## How to Solve Word Problems

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

- Read the problem out loud to yourself

Draw a Picture

- Think “What do I need to find?”
- List what is given
- Find the key words
- Check your work

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.

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:

- Kevin has 3 book cases
- Each book case has 9 shelves
- Each shelve holds 16 books

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.

Topics: Math , Child Education , Math Skills , Parenting Tips , Child Anxiety , Math Anxiety , Word Problems

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## How to Solve Word Problems in Algebra

Last Updated: December 19, 2022 Fact Checked

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 fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 65,147 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

- For example, you might have the following problem: Jane went to a book shop and bought a book. While at the store Jane found a second interesting book and bought it for $80. The price of the second book was $10 less than three times the price of he first book. What was the price of the first book?
- In this problem, you are asked to find the price of the first book Jane purchased.

- 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.

- Multiplication keywords include times, of, and f actor. [9] X Research source
- Division keywords include per, out of, and percent. [10] X Research source
- Addition keywords include some, more, and together. [11] X Research source
- Subtraction keywords include difference, fewer, and decreased. [12] X Research source

## Finding the Solution

## Completing a Sample Problem

- 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.

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

## Expert Q&A

## Video . By using this service, some information may be shared with YouTube.

- Word problems can have more than one unknown and more the one variable. Thanks Helpful 2 Not Helpful 1
- The number of variables is always equal to the number of unknowns. Thanks Helpful 1 Not Helpful 0
- While solving word problems you should always read every sentence carefully and try to extract all the numerical information. Thanks Helpful 1 Not Helpful 0

## You Might Also Like

- ↑ Daron Cam. Academic Tutor. Expert Interview. 29 May 2020.
- ↑ http://www.purplemath.com/modules/translat.htm
- ↑ https://www.mathsisfun.com/algebra/word-questions-solving.html
- ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut8_probsol.htm
- ↑ http://www.virtualnerd.com/algebra-1/algebra-foundations/word-problem-equation-writing.php
- ↑ https://www.khanacademy.org/test-prep/praxis-math/praxis-math-lessons/praxis-math-algebra/a/gtp--praxis-math--article--algebraic-word-problems--lesson

## 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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## Appendix A: Applications

Apply a problem-solving strategy to basic word problems, learning outcomes.

- Practice mindfulness with your attitude about word problems
- Apply a general problem-solving strategy to solve word problems

## Approach Word Problems with a Positive Attitude

The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?

Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student in the cartoon below?

Negative thoughts about word problems can be barriers to success.

When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.

Start with a fresh slate and begin to think positive thoughts like the student in the cartoon below. Read the positive thoughts and say them out loud.

When it comes to word problems, a positive attitude is a big step toward success.

If we take control and believe we can be successful, we will be able to master word problems.

Think of something that you can do now but couldn’t do three years ago. Whether it’s driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!

## Use a Problem-Solving Strategy for Word Problems

In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then you’ve increased your math vocabulary as you learned about more algebraic procedures, and you’ve had more practice translating from words into algebra.

You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.

Now we’ll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We’ll demonstrate the strategy as we solve the following problem.

Pete bought a shirt on sale for $[latex]18[/latex], which is one-half the original price. What was the original price of the shirt?

Solution: Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.

- In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

- In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

- Let [latex]p=[/latex] the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

Step 6. Check the answer in the problem and make sure it makes sense.

- We found that [latex]p=36[/latex], which means the original price was [latex]\text{\$36}[/latex]. Does [latex]\text{\$36}[/latex] make sense in the problem? Yes, because [latex]18[/latex] is one-half of [latex]36[/latex], and the shirt was on sale at half the original price.

Step 7. Answer the question with a complete sentence.

- The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was [latex]\text{\$36}[/latex].”

If this were a homework exercise, our work might look like this:

We list the steps we took to solve the previous example.

## Problem-Solving Strategy

- Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the internet.
- Identify what you are looking for.
- Name what you are looking for. Choose a variable to represent that quantity.
- Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
- Solve the equation using good algebra techniques.
- Check the answer in the problem. Make sure it makes sense.
- Answer the question with a complete sentence.

For a review of how to translate algebraic statements into words, watch the following video.

Let’s use this approach with another example.

Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought [latex]11[/latex] apples to the picnic. How many bananas did he bring?

In the next example, we will apply our Problem-Solving Strategy to applications of percent.

Nga’s car insurance premium increased by [latex]\text{\$60}[/latex], which was [latex]\text{8%}[/latex] of the original cost. What was the original cost of the premium?

- Write Algebraic Expressions from Statements: Form ax+b and a(x+b). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Hub7ku7UHT4 . License : CC BY: Attribution
- Question ID 142694, 142722, 142735, 142761. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License, CC-BY + GPL
- Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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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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## Strategies for Solving Word Problems – Math

## 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:

## 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:

- Circle any numbers you’ll use.
- Lightly cross out any information you don’t need.
- Underline the phrase or sentence which tells exactly what you’ll need to find.

## 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:

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:

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:

## 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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- \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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Math homework can sometimes feel like an insurmountable challenge. From complex equations to confusing word problems, it’s easy to get overwhelmed. However, with the right techniques and strategies, you can conquer any math problem that com...

The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...

Maytag washers are reliable and durable machines, but like any appliance, they can experience problems from time to time. Fortunately, many of the most common issues can be solved quickly and easily. Here’s a look at how to troubleshoot som...

How to Solve Word Problems · Read the Problem Out Loud. Kids have a tendency to rush through every problem. · Draw a Picture. Students need to

Steps of Solving a Word Problem · 1. Read the problem: first, students should read through the problem once. · 2. Highlight facts: then, students should read

Assessing the Problem · Step 1 Read the problem carefully. · Step 2 Determine what you are asked to find.

Read it the first time. Read it again but this time you highlight, underline, circle any key words and numbers. Such as maybe it says “ Less

Analyze the data given to you in question and try to visualise them by making a figure if possible. · Underline or Mark all the data given to you. · Now

A video model showing how to teach a step by step process to solve word problems. This video shows a simple way to solve word problems

Once you've finished school, most of the math problems you encounter will likely come in the form of word problems. In word problems, you're

Problem-Solving Strategy · Read the word problem. Make sure you understand all the words and ideas. · Identify what you are looking for. · Name what you are

and a single variable. Usually, the

3. Write on the Word Problem · Circle any numbers you'll use. · Lightly cross out any information you don't need. · Underline the phrase or sentence which tells

To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as