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Single Variable Expressions

Use symbols and operations to understand and define variables.

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Single Variable Expressions

Let's Think About It

Credit: MENI from ASO! & Soothe.
Source: https://www.flickr.com/photos/menieeleegelles/8004925492
License: CC BY-NC 3.0

Ayako just got her first job at her local arcade. In her interview, the manager said she would earn either $8 or $9 an hour. When he called to offer her the job, Ayako was so excited that she forgot to ask what she would be paid. Ayako plans to work 20 hours per week. How can Ayako figure out how much she will get paid each week?

In this concept, you will learn how to evaluate single variable expressions with given values.

Guidance

A variable is a letter that is used to represent an unknown quantity. Often,  or  represents the unknown quantity, but any letter, usually lowercase, can be used as a variable. 

A variable can be used in any sort of mathematical expressionA variable expression is an expression with one or more operations that has variables but no equals sign.

To understand variable expressions a little better, let’s think about some ways that you can show addition, subtraction, multiplication and division in mathematics.

Addition can be shown by using a + sign.

Subtraction can be shown using a subtraction or minus sign .

Multiplication can be shown in different ways:

  • Using the times symbol, e.g. 
  • Using two sets of parentheses, e.g. 
  • Using a variable next to a number, e.g.  indicates 6 multiplied by the unknown
  • Using one number next to parentheses, e.g. 4(3) = 12 

Division can be shown in different ways:

  • Using the division symbol, e.g. 
  • Using the fraction bar, e.g.  

Depending on the situation, you should expect to see operations shown in different ways.

Often you will be asked to evaluate variable expressions with a given value for the variable.

Evaluate 5 + a when a = 18.

First, substitute the given value for the variable. In this case, substitute 18 in for a.

Next, add.

The answer is 23.

Let's look at an example.

Evaluate when is 40.

First, substitute the given value for the variable. In this case, substitute 40 in for

Then subtract.

The answer is 18.

Let's look at another example.

Evaluate when is 12. 

First, substitute the given value for the variable. In this case, substitute 12 in for . Then multiply.

The answer is 84.

Let's look at one more example.

Evaluate  when  is 2.

This expression includes a fraction bar, which tells you that this is a division problem.

First, substitute the given value of 2 in for .

The answer is 7.

Examples

Example 1

Evaluate when is 12.

The answer is 29.

Example 2

Evaluate when is 9.

The answer is 45.

Example 3

Evaluate when is 4.

The answer is 2.

Follow Up

Credit: Steven Depolo
Source: https://www.flickr.com/photos/stevendepolo/3354726208
License: CC BY-NC 3.0

Remember Ayako and her new job?

Ayako needs to figure out how much she will get paid for working 20 hours a week if she gets paid $8 or $9 an hour.

First, write an expression.

  ?

The given values for the unknown variable, , are 8 and 9.

Next, substitute 8 in for the variable.

20(8)=160

The answer is 160.

Then, substitute 9 in for the variable.

20(9)=180

The answer is 180.

The answer is 160 or 180.

Ayako will get paid $160 or $180 per week at her new arcade job.

Video Review

Explore More

Evaluate each of the variable expressions when

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3.  

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7.  

8.  

9.  

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12.  

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15.  

Vocabulary

Algebraic Expression

Algebraic Expression

An expression that has numbers, operations and variables, but no equals sign.
Evaluate

Evaluate

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

Expression

An expression is a mathematical phrase containing variables, operations and/or numbers. Expressions do not include comparative operators such as equal signs or inequality symbols.
Variable Expression

Variable Expression

A variable expression is a mathematical phrase that contains at least one variable or unknown quantity.

Image Attributions

  1. [1]^ Credit: MENI from ASO! & Soothe.; Source: https://www.flickr.com/photos/menieeleegelles/8004925492; License: CC BY-NC 3.0
  2. [2]^ Credit: Steven Depolo; Source: https://www.flickr.com/photos/stevendepolo/3354726208; License: CC BY-NC 3.0

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