Page 274 - Basic College Mathematics with Early Integers

S E C T I O N 3.7 I OPERATIONS ON MIXED NUMBERS 251

3 7
Example 23 Add: 6 + a -9 b PRACTICE 23
5 10
2 3
Solution: Here we are adding two numbers with different signs. Recall that we Add: 6 3 + a -12 b
4
then subtract the absolute values and keep the sign of the larger absolute value.
7
Since -9 has the larger absolute value, the answer is negative.
10
First, subtract absolute values:
7 7
9 = 9
10 10
#
3 2 6
- 6 # =- 6
5 2 10
1
3
10
Thus,

3 7 1 7
6 + a -9 b = -3 The result is negative since -9 has the larger absolute value.
5 10 10 10
Work Practice 23

5 4
Example 24 Subtract: -11 - 20 PRACTICE 24
6 9
5 4 2 11
Solution: Let’s write as an equivalent addition: -11 + a -20 b. Here, we are Subtract: -9 7 - 30 14
6 9
adding two numbers with like signs. Recall that we add their absolute values and
keep the common negative sign.
First, add absolute values:
#
5 3 15
11 # = 11
6 3 18
#
4 2 8
+ 20 # + 20
9 2 = 18

23 5
31 or 32
18 18
c c
23 5
Since = 1
18 18
Thus,
5 4 5
-11 - 20 = -32
6 9 c 18
Keep the common sign.
Work Practice 24

Answers
1 1
23. -6 24. -40
12 14