Pre-Algebra Demystified

Subtraction of Integers

In arithmetic, subtraction is usually thought of as ‘‘taking away.’’ For exam-

ple, if you have six books on your desk and you take four to class, you have

two books left on your desk. The ‘‘taking away’’ concepts work well in

arithmetic, but with algebra, a new way of thinking about subtraction is

necessary.

In algebra, we think of subtraction as adding the opposite. For example, in

arithmetic, 8
 6 ¼2. In algebra, 8þð
 6 Þ¼2. Notice that in arithmetic, we

subtract 6 from 8. In algebra, we add the opposite of 6, which is
6, to 8. In

both cases, we get the same answer.

To subtract one number from another, add the opposite of the number that is

being subtracted.

EXAMPLE

Subtract (þ12)
ð
 8 Þ:

SOLUTION

Addþ8 (the opposite of
8) to 12 to get 20, as shown.

ðþ 12 Þ
ð
 8 Þ¼ðþ 12 Þþðþ 8 Þ (opposite of 
 8 Þ

¼ 20

Hence, (þ12)
ð
 8 Þ¼20.

EXAMPLE

Subtractð
 6 Þ
(þ3).

SOLUTION

ð
 6 Þ
ðþ 3 Þ¼ð
 6 Þþð
 3 Þ (opposite of þ 3 Þ

¼
 9

Hence,ð
 6 Þ
(þ3)¼
 9 :

Math Note: Sometimes the answers in subtraction do not look cor-

rect, but once you get the opposite, you follow the rules of addition. If

the two numbers have like signs, use Rule 1 for addition. If the two

numbers have unlike signs, use Rule 2 for addition.

24 CHAPTER 2 Integers