Basic Mathematics for College Students







Put more simply, this rule says that subtraction is the same as adding the opposite.

After rewriting a subtraction as addition of the opposite, we then use one of the
rules for the addition of signed numbers discussed in Section 2.2 to find the result.
You won’t need to use this rule for every subtraction problem. For example,
is obviously 2; it does not need to be rewritten as adding the opposite. But for more
complicated problems such as or , where the result is not obvious,
the subtraction rule will be quite helpful.

 6  4 3 (5)

6  4

2.3 Subtracting Integers 157

Rule for Subtraction

To subtract two integers, add the first integer to the opposite (additive inverse)

of the integer to be subtracted.

EXAMPLE (^1) Subtract and check the result:
a. b. c.
StrategyTo find each difference, we will apply the rule for subtraction: Add the
first integer to the opposite of the integer to be subtracted.
WHYIt is easy to make an error when subtracting signed numbers. We will
probably be more accurate if we write each subtraction as addition of the opposite.
Solution
a.We read as “negative six minusfour.” Thus, the number to be
subtracted is 4. Subtracting 4 is the same as adding its opposite,.
Change the subtraction to addition.
Use the rule for adding two
integers with the same sign.
Change the number being
subtracted to its opposite.
To check, we add the difference, , and the subtrahend,4. We should get the
minuend,.
Check:  10  4  6 The result checks.

 6

 10

 6  4   6 ( 4 ) 10

 4

 6  4

 6  4 3 (5) 7  23

Self Check 1

Subtract and check the result:

a.

b.

c.

Now TryProblems 21, 25, and 29

6  85

4 (8)

 2  3

Caution! Don’t forget to write the opposite of the number to be subtracted

within parentheses if it is negative.

 6  4  6 (4)

b.We read as “three minusnegative five.” Thus, the number to be
subtracted is. Subtracting is the same as adding its opposite, 5.

Add...

... the opposite

Check: 8 (5) 3 The result checks.

3 ( 5 )  3  5  8

 5  5

3 (5)