Using the Definition of SubtractionSubtract.
Change to.No change Additive inverse of 3(a)
(b) (c)
Change to.No change Additive inverse of(d)
(e) or 1 NOW TRY
5
6
4
3
- a-
1
2
b =
4
3
+
1
2
=
8
6
+
3
6
=
11
6
,
- 3 - 1 - 52 = - 3 + 152 = 2
- 5
5 - 7 = 5 + 1 - 72 =- 2 - 6 - 9 = - 6 + 1 - 92 =- 15
12 - 3 = 12 + 1 - 32 = 9
EXAMPLE 6
40 CHAPTER 1 The Real Number System
NOW TRY
EXERCISE 6
Subtract.
(a)
(b)
(c) -
5
7
-
1
3
4 - 15
- 5 - 1 - 112
NOW TRY ANSWERS
- (a) 6 (b)
(c) - 2221 , or - 1 211- 11
Uses of the SymbolWe use the symbol for three purposes:
1. to represent subtraction,as in
2. to represent negative numbers,such as and
3. to represent the opposite (or negative) of a number,as in “the opposite
(or negative) of 8 is ”
We may see more than one use of in the same expression, such as
where is subtracted from The meaning of the symbol depends on its
position in the expression.
- 9 - 6. -
- - 6 - 1 - 92 ,
- 8.
- 10, -2, -3;
9 - 5 = 4;
-
OBJECTIVE 4 Use the rules for order of operations with real numbers.
Adding and Subtracting with Grouping SymbolsPerform each indicated operation.
(a) Start within the innermost parentheses.
Add.
Definition of subtraction
Add.
Definition of subtraction= 3 Add.
=- 6 + 192
=- 6 - 3 - 94
=- 6 - 32 + 1 - 1124
=- 6 - 32 - 114
- 6 - 32 - 18 + 324
EXAMPLE 7
Definition of SubtractionFor any real numbers xand y,
To subtract y from x, add the additive inverse (or opposite) of y to x .That is,
change the subtrahend to its opposite and add.
Example: 4 - 9 = 4 + 1 - 92 =- 5
xyx 1 y 2.
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