Easy Algebra Step-by-Step

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.