Computation with Real Numbers 15
Problem Which is greater –7 or –2?
Solution
Step 1. Graph –7 and –2 on a number line.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
Step 2. Identify the number that is farther to the right as the greater
number.
–2 is to the right of –7, so –2 > –7.
The concept of absolute value plays an important
role in computations with signed numbers. The abso-
lute value of a real number is its distance from 0 on the
number line. For example, as shown in Figure 2.1, the
absolute value of −8 is 8 because −8 is 8 units from 0.
You indicate the absolute value of a number by placing the number between
a pair of vertical bars like this: |−8| (read as “the absolute value of negative
eight”). Thus, |−8| = 8.
Problem Find the indicated absolute value.
a. − 30
b. 04
c. − 21
3
Solution
a. − 30
Step 1. Recalling that the absolute value of a real number is its distance
from 0 on the number line, determine the absolute value.
|–30| = 30 because –30 is 30 units from 0 on the number line.
–10 –9 –8 –7 –6 –5
8 units
–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Figure 2.1 The absolute value of − 8
Absolute value is a distance,
so it is never negative.