Page 141 - Basic College Mathematics with Early Integers

118 C HAPTE R 2 I INTEGERS AND INTRODUCTION TO VARIABLES

Objective Finding the Absolute Value of a Number

If you think of The absolute value of a number is the number’s distance from 0 on a number line.
6 and 7 as arrowheads,notice The symbol for absolute value is ƒ ƒ . For example, ƒ 3 ƒ is read as “the absolute
that in a true statement the value of 3.”
arrow always points to the
ƒ 3 ƒ = 3 because 3 is 3 units from 0. 3 units
smaller number.
5 7-4 -3 6 -1 2 1 0 1 2 3 4
c c
ƒ -3 ƒ = 3 because -3 is 3 units from 0. 3 units
smaller smaller
number number
4 3 2 1 0 1 2

PRACTICE 4 Example 4 Simplify.
Simplify.
a. ƒ -2 ƒ b. ƒ 5 ƒ c. ƒ 0 ƒ
a. ƒ -4 ƒ b. ƒ 2 ƒ
c. ƒ -8 ƒ Solution:
a. ƒ -2 ƒ = 2 because -2 is 2 units from 0.
b. ƒ 5 ƒ = 5 because 5 is 5 units from 0.
c. ƒ 0 ƒ = 0 because 0 is 0 units from 0.
Work Practice 4

Since the absolute value of a number is that number’s distance from 0, the absolute
value of a number is always 0 or positive. It is never negative.
ƒ 0 ƒ = 0 ƒ -6 ƒ = 6
c c
zero a positive number

Objective Finding Opposites

Two numbers that are the same distance from 0 on a number line but are on opposite
sides of 0 are called opposites.

4 units 4 units
4 and -4 are opposites.
5 4 3 2 1 0 1 2 3 4 5

When two numbers are opposites, we say that each is the opposite of the other.
Thus 4 is the opposite of -4 and -4 is the opposite of 4.
The phrase “the opposite of” is written in symbols as “-.” For example,

The opposite of 5 is -5
T T T T
Copyright 2012 Pearson Education, Inc.
- 152 = -5

The opposite of -3 is 3
T T T T
- (-3) = 3 or
-(-3) = 3
Answers
4. a. 4 b. 2 c. 8