## Word Problems Calculator

Solve word problems step by step.

- One-Step Addition
- One-Step Subtraction
- One-Step Multiplication
- One-Step Division
- One-Step Decimals
- Two-Step Integers
- Two-Step Add/Subtract
- Two-Step Multiply/Divide
- Two-Step Fractions
- Two-Step Decimals
- Multi-Step Integers
- Multi-Step with Parentheses
- Multi-Step Rational
- Multi-Step Fractions
- Multi-Step Decimals
- Solve by Factoring
- Completing the Square
- Quadratic Formula
- Biquadratic
- Logarithmic
- Exponential
- Rational Roots
- Floor/Ceiling
- Equation Given Roots New
- Substitution
- Elimination
- Cramer's Rule
- Gaussian Elimination
- System of Inequalities
- Perfect Squares
- Difference of Squares
- Difference of Cubes
- Sum of Cubes
- Polynomials
- Distributive Property
- FOIL method
- Perfect Cubes
- Binomial Expansion
- Logarithmic Form
- Absolute Value
- Partial Fractions
- Is Polynomial
- Leading Coefficient
- Leading Term
- Standard Form
- Complete the Square
- Synthetic Division
- Rationalize Denominator
- Rationalize Numerator
- Interval Notation New
- Pi (Product) Notation New
- Induction New
- Boolean Algebra
- Truth Table
- Mutual Exclusive
- Cardinality
- Caretesian Product
- Age Problems
- Distance Problems
- Cost Problems
- Investment Problems
- Number Problems
- Percent Problems

## Most Used Actions

- \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?}

## Frequently Asked Questions (FAQ)

How do you solve word problems.

## How do you identify word problems in math?

## Is there a calculator that can solve word problems?

## What is an age problem?

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## Generating PDF...

## Solving Word Questions

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.

The trick is to break the solution into two parts:

Turn the English into Algebra.

## Turning English into Algebra

To turn the English into Algebra it helps to:

- Read the whole thing first
- Do a sketch if possible
- Assign letters for the values
- Find or work out formulas

## 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?

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?

( 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.

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.

## 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

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

## 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?

- Use V for Volume
- Use A for Area
- Use s for side length of cube
- Volume of a cube: V = s 3
- Surface area of a cube: A = 6s 2

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

## 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?

- Joel's normal rate of pay: $N per hour
- Joel works for 40 hours at $N per hour = $40N
- When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
- Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
- And together he earned $660, so:

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

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

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:

- Present Value PV = $2,000
- Interest Rate (as a decimal): r = 0.11
- Number of Periods: n = 3
- Future Value (the value we want): FV

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:

- Present Value PV = $1,000
- Interest Rate (the value we want): r
- Number of Periods: n = 9
- Future Value: FV = $1,551.33

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?

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

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

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

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 .

And now for some Quadratic Equations :

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

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

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":

## 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!:

- the length of the room: L
- the width of the room: W
- the total Area including veranda: A
- the width of the room is half its length: W = ½L
- the total area is the (room width + 3) times the length: A = (W+3) × L = 56

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 :

So the length of the room is 8 m

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

## Mathematical Word Problems

## Word Problems

Solve a word problem and explore related facts.

## Solve a word problem:

## Solving Word Problems in Mathematics

Steps of solving a word problem.

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

## Praxis Core Math

- 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?

- 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 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text
- (Choice A) $ 4 \$4 $ 4 dollar sign, 4 A $ 4 \$4 $ 4 dollar sign, 4
- (Choice B) $ 5 \$5 $ 5 dollar sign, 5 B $ 5 \$5 $ 5 dollar sign, 5
- (Choice C) $ 9 \$9 $ 9 dollar sign, 9 C $ 9 \$9 $ 9 dollar sign, 9
- (Choice D) $ 14 \$14 $ 1 4 dollar sign, 14 D $ 14 \$14 $ 1 4 dollar sign, 14
- (Choice E) $ 20 \$20 $ 2 0 dollar sign, 20 E $ 20 \$20 $ 2 0 dollar sign, 20
- (Choice A) 10 10 1 0 10 A 10 10 1 0 10
- (Choice B) 12 12 1 2 12 B 12 12 1 2 12
- (Choice C) 24 24 2 4 24 C 24 24 2 4 24
- (Choice D) 30 30 3 0 30 D 30 30 3 0 30
- (Choice E) 32 32 3 2 32 E 32 32 3 2 32
- (Choice A) 4 4 4 4 A 4 4 4 4
- (Choice B) 10 10 1 0 10 B 10 10 1 0 10
- (Choice C) 14 14 1 4 14 C 14 14 1 4 14
- (Choice D) 18 18 1 8 18 D 18 18 1 8 18
- (Choice E) 22 22 2 2 22 E 22 22 2 2 22

## Things to remember

Want to join the conversation.

## Writing & Grammar

## Strategies for Solving Word Problems

## 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.

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

1. read the entire word problem.

## 2. Think About the Word Problem

## Here are the questions:

A. what exactly is the question.

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

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

- 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

## 5. Estimate the Answer Before Solving

## 6. Check Your Work When Done

## 7. Practice Word Problems Often

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

CLICK HERE to take a look at 3rd grade:

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

Thanks so much for stopping by!

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## How to Solve Word Problems in Algebra

Last Updated: December 19, 2022 References

## 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.

- 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

## 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. ⧼thumbs_response⧽ Helpful 2 Not Helpful 1
- The number of variables is always equal to the number of unknowns. ⧼thumbs_response⧽ Helpful 1 Not Helpful 0
- While solving word problems you should always read every sentence carefully and try to extract all the numerical information. ⧼thumbs_response⧽ 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

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

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

- Teaching Tools
- Subtraction
- Multiplication
- Mixed operations
- Ordering and number sense
- Comparing and sequencing
- Physical measurement
- Ratios and percentages
- Probability and data relationships

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

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

Best for: 1st grade, 2nd grade

## Subtraction word problems

Best for: 1st grade, second grade

## Practice math word problems with Prodigy Math

## Multiplication word problems

Best for: 2nd grade, 3rd grade

## Division word problems

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

## Mixed operations word problems

## Ordering and number sense word problems

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

## Fractions word problems

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

## Decimals word problems

Best for: 4th grade, 5th grade

## 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?

## Time word problems

## Money word problems

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

## Physical measurement word problems

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

## Ratios and percentages word problems

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

## Probability and data relationships word problems

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

## Geometry word problems

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

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

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

## Variables word problems

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

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

- 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.

## Final thoughts about math word problems

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## How to Solve Word Problems

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

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

*this can be a key word for addition and multiplication

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Disclaimer: IntMath.com does not guarantee the accuracy of the Mathway Problem Solver solutions.

## Problem Solver Subjects

## Basic Math Solutions

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

- Long Arithmetic
- Rational Numbers
- Operations with Fractions
- Ratios, Proportions, Percents
- Measurement, Area, and Volume
- Factors, Fractions, and Exponents
- Unit Conversions
- Data Measurement and Statistics
- Points and Line Segments

## Math Word Problem Solutions

Simplified Equation: 17 - x = 8

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

## 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.

## Chemistry Solutions

Below are examples of Chemistry problems that can be solved.

- Unit Conversion
- Atomic Structure
- Molecules and Compounds
- Chemical Equations and Reactions
- Behavior of Gases
- Solutions and Concentrations

## Physics Solutions

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## Geometry Graphing Solutions

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

## IMAGES

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## COMMENTS

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...

An example of a ratio word problem is: “In a bag of candy, there is a ratio of red to green candies of 3:4. If the bag contains 120 pieces of candy, how many red candies are there?” Another example of a ratio word problem is: “A recipe call...

When multiplying or dividing different bases with the same exponent, combine the bases, and keep the exponent the same. For example, X raised to the third power times Y raised to the third power becomes the product of X times Y raised to th...

Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems

Examples · Example: A rectangular garden is 12m by 5m, what is its area? · Example: Sam and Alex play Tennis. · Example: Alex and Sam also build tables. · Example:

Solve a word problem: · Rachel has 17 apples. · Jack has 8 cats and 2 dogs. · if there are 40 cookies all together and A takes 10 and B takes 5 how many are left.

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

Five steps for solving word problems shown in a couple of sample word problems. These word problems use basic one step expressions.

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

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

Solve an equation for

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 to Solve Word Problems · Read the problem out loud to yourself · Draw a Picture · Think “What do I need to find?” · List what is given · Find the

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