<meta http-equiv="refresh" content="1; url=/nojavascript/">
Skip Navigation
You are reading an older version of this FlexBook® textbook: CK-12 Middle School Math Concepts - Grade 8 Go to the latest version.

1.9: Translate Verbal Phrases into Variable Expressions

Difficulty Level: At Grade Created by: CK-12
Atoms Practice
Practice Mathematical Expressions
Practice Now

Have you ever had to figure out a math problem that was described in words? Look at this dilemma.

Kelly and her brother sold lemonade and cookies at the school fair. They sold the lemonade for two dollars per glass and the cookies for one dollar and fifty cents a piece. When finished, Kelly realized that they had sold fifty glasses of lemonade and twenty cookies. She said this to her brother.

"We sold fifty times two dollars and twenty times one dollar and fifty cents."

Kelly's brother isn't sure how to write this expression. Pay attention and you will be able to help him at the end of the Concept.


Do you know how to take a verbal phrase and write it as a variable expression?

To accomplish this task, you will need to think about what different words mean. A verbal expression is a mathematical statement that is expressed in words.

You will have to work as a detective to figure out what different words mean. Once you know what those words mean, you will be able to write different variable expressions.

Let’s start by looking at some mathematical operations written as words.




Increased by




Less than

Take away






Split up

This list does not include ALL of the ways to write the operations, but it will give you a good place to start.

Take a few minutes and write these words down in your notebook.

Now we can look at the following chart which starts with a verbal phrase and writes it as a variable expression.

Verbal Phrase Variable Expression
Three minus a number 3x
A number increased by seven n+7
The difference between an unknown quantity and twenty-six s26
A number decreased by nine w9
Ten times a number plus four 10f+4

Notice that words like “a number” and “an unknown quantity” let us know that we need to use a variable.

Example A

Write a variable expression that reads “The product of a number and six plus four.”

Solution: 6x+4

Example B

Write a variable expression that reads “Ninety divided by a number minus eight.”

Solution: 90b8

Example C

Write a variable expression that reads “Two less than a number, multiplied by thirty-six.”

Solution: 36(n2)

Now let's go back to the dilemma from the beginning of the Concept. Kelly explained the sales to her brother in this way.

"We sold fifty times two dollars and twenty times one dollar and fifty cents."

First, use the information in the statement to write an expression.


Notice that we have fifty times two dollars plus twenty times one dollar and fifty cents. This shows the number of glasses of lemonade and cookies times each price.

Next, we can figure out how much money they made.


This is our final answer.


Variable Expression
a group of numbers, operations and variables without an equal sign.
a letter used to represent an unknown number.
a number in an expression that does not have a variable.
Verbal Expression
using language to write a mathematical expression instead of numbers, symbols and variables.

Guided Practice

Here is one for you to try on your own.

Write a variable expression that reads “Eighty-five divided by a number minus thirteen.”


We could do this in several different ways. We could use a symbol, ÷, to show division or we could use a fraction bar to show division.

Because you are moving toward Algebra, let’s use a fraction bar.

The answer is 85a13.

Video Review

Writing Basic Algebraic Expressions


Directions: Write a variable expression for each verbal expression.

1. The sum of a number and twelve.

2. The difference between a number and eight.

3. Three times a number

4. A number squared plus five

5. A number divided by two plus seven

6. Four times the quantity of a number plus six

7. A number times two divided by four

8. A number times six plus the same number times two

9. A number squared plus seven take a way four

10. A number divided by three plus twelve

11. A number times five and another number times six

12. Sixteen less than a number times negative four

13. A number times eight divided by two

14. A number divided by six and another number times negative five

15. A number divided by four plus another number divided by sixteen




To evaluate an expression or equation means to perform the included operations, commonly in order to find a specific value.


A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n.
Verbal Expression

Verbal Expression

A verbal expression (or verbal model) uses words to decipher the mathematical information in a problem. An equation can often be written from a verbal model.

Image Attributions


Difficulty Level:

At Grade


Date Created:

Dec 19, 2012

Last Modified:

Aug 10, 2015
Files can only be attached to the latest version of Modality


Please wait...
Please wait...
Image Detail
Sizes: Medium | Original

Original text