Introduction
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.
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 |
12 | |
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
EXPLORE! |
Self-Check
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? |
[show answer] |
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? |
[show answer] |
Question 3 If the initial temperature is d degrees how many degrees will it be if the temperature goes up 3 degrees? |
[show answer] |