The preceding example suggests the following definition of subtraction.
16 CHAPTER 1 Review of the Real Number System
SubtractionFor all real numbers aand b,
That is, to subtract bfrom a, add the additive inverse (or opposite) of bto a.
aba 1 b 2.
NOW TRY
EXERCISE 3
Find each difference.
(a)
(b)
(c)
4
9
-
3
5
- 5.67- 1 - 2.34 2
- 4 - 11
Subtracting Real NumbersFind each difference.
Change to addition.
The additive inverse of 8 is(a)
Change to addition.
The additive inverse of 4 is(b)
(c) The additive inverse of is 7.
(d)
(e)
=
29
24
=
20
24
+
9
24
5
6
- a-
3
8
b =
5
6
+
3
8
=5.7
=-2.4+8.1
- 2.4- 1 - 8.1 2
=- 3
- 10 - 1 - 72 =- 10 + 7 - 7
- 12 - 4 =- 12 + 1 - 42 =- 16
6 - 8 = 6 + 1 - 82 =- 2
EXAMPLE 3
To subtract, add the additive
inverse (opposite).Write each fraction with the least
common denominator, 24.Add numerators.
Keep the same denominator. NOW TRYWhen working a problem that involves both addition and subtraction, add and
subtract in order from left to right. Work inside brackets or parentheses first.
Adding and Subtracting Real NumbersPerform the indicated operations.
(a)
Work from left to right.
Add inside parentheses.
Subtract from left to right.= 1 Subtract.
= 13 - 12
= 18 - 5 - 12
= 115 + 32 - 5 - 12
15 - 1 - 32 - 5 - 12
EXAMPLE 4
NOW TRY ANSWERS
- (a)- 15 (b) -3.33 (c)- 457