When solving problems it is sometimes necessary to translate words, a table of data, or a physical model into expressions. There are two types of expressions: variable and numerical.

Variable expressions have at least one variable (sometimes called an unknown) in them. Numerical expressions involve only numbers. Here are examples of each:

Variable expressions Numerical expressions

8 + m

g - 17


8 + 13

29 - 17


Here is a table of key words that indicate addition and subtraction.


Verbal expressions (key words)

Variable expression

  • add 3 to a number
  • a number plus 3
  • the sum of a number and 3
  • 3 more than a number
  • a number increased by 3
  • subtract 12 from a number
  • a number minus 12
  • the difference of a number and 12
  • 12 less than a number
  • a number decreased by 12


Example 1

  • Anglea and Bill are siblings. When Angela was 5 years old, her brother was 8 years old. When Angela was 6 years old, her brother was 9 years old. If Angela is n years old, how old is Bill?


To find Bill's age, begin by placing their ages in a table...

When Angela's age is... Bill's age is...
5 8
6 9
7 10
n n+3

Notice that Bill is always 3 years older than Angela. So when Angela is 12 years old Bill will be 15 years old.

When Angela is n years old, Bill will be (n+3) years old.


Example 2

Alan is 8 years old.

  • Question: How old will he be in 5 years' time? Answer: 8 + 5
  • Question: How old will he be in x years? Answer: 8 + x 


Example 3

  • Question: Suppose that you buy something that costs b dollars. Suppose that you pay with a $10 dollar note. Write an expression for the change that you get. If needed, this diagram might help you understand the situation.
  • Answer: 10 - b



  • Move the red point up and down the number line and observe how the blue point moves in relation.
  • What variable expression describes the blue point, if we consider the red point as \large~x?



Question 1

Two sticks are laid end-to-end. Their combined length is 18 inches. The shorter stick is m inches long. What is the length of the longer stick?

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Question 2

Let a, b, and c represent the three lengths of the three sides of a triangle. What is the perimeter of the triangle?

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Question 3

If the initial temperature is d degrees how many degrees will it be if the temperature goes up 3 degrees?

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Last modified: Wednesday, 16 March 2016, 8:13 PM