Basic Mathematics for College Students

The figure below shows that for each whole number on the number line, there is
a corresponding whole number, called its opposite,to the left of 0. For example, we see
that 3 and  3 are opposites, as are  5 and 5. Note that 0 is its own opposite.

2.1 An Introduction to the Integers 137

Caution! Absolute value expresses distance. The absolute value of a number

is always positive or 0. It is never negative.

EXAMPLE (^4) Find each absolute value: a. b. c.
StrategyWe need to determine the distance that the number within the vertical
absolute value bars is from 0 on a number line.
WHYThe absolute value of a number is the distance between 0 and the number
on a number line.
Solution
a.On the number line, the distance between 8 and 0 is 8. Therefore,
b.On the number line, the distance between and 0 is 5. Therefore,
c.On the number line, the distance between 0 and 0 is 0. Therefore,
000  0

0  50  5

 5

080  8

080 0  50 000

Self Check 4

Find each absolute value:

a.

b.

Now TryProblems 47 and 49

040

0  90

5 Find the opposite of an integer.

To write the opposite of a number, a symbol is used. For example, the opposite
of 5 is (read as “negative 5”). Parentheses are needed to express the opposite of a
negative number. The opposite of is written as. Since 5 and are the same
distance from 0, the opposite of is 5. Therefore,. This illustrates the
following rule.

 5 (5) 5

 5 (5)  5

 5



–5 –4 –3 –2 –1 0

Opposites

1 2 3 4 5

Absolute Value

The absolute valueof a number is the distance on the number line between

the number and 0.

The Opposite of the Opposite Rule

The opposite of the opposite (or negative) of a number is that number.

Opposites or Negatives

Two numbers that are the same distance from 0 on the number line, but on

opposite sides of it, are called oppositesor negatives.