Page 268 - Basic College Mathematics with Early Integers

S E C T I O N 3.7 I OPERATIONS ON MIXED NUMBERS 245

11
#
Example 5 Multiply: 7 2 . Check by estimating. PRACTICE 5
14
Multiply. Check by estimating.
1
#
#
11 7 39 7 39 7 39 39 1 7
#
#
Solution: 7 2 = # = = = or 19 Exact 3 6
# #
#
14 1 14 1 14 1 2 7 2 2 15
1
To estimate,
11
#
2 rounds to 3 and 7 3 = 21. Estimate
14
The estimate is close to the exact value, so our answer is reasonable.
Work Practice 5
Concept Check Find the error.
#
1 1 1 1 1
2 # = 2 = 2
#
4 2 4 2 8
Examples Divide. PRACTICE 6–8
Divide.
#
3 3 5 3 1 3 1 3
6. , 5 = , = # = = 4 8 4
#
4 4 1 4 5 4 5 20 6. , 7 7. , 3
9 15 5
1
#
#
11 5 11 17 11 6 11 6 11 6 11 2 3
7. , 2 = , = # = = = 8. 3 , 2
# #
#
18 6 18 6 18 17 18 17 6 3 17 51 7 14
1
1
# #
#
2 5 17 23 17 9 17 9 17 3 3 51 5
8. 5 , 2 = , = # = = = or 2
#
#
3 9 3 9 3 23 3 23 3 23 23 23
1
Work Practice 6–8
Objective Adding or Subtracting Mixed Numbers
We can add or subtract mixed numbers, too, by first writing each mixed number as
an improper fraction. But it is often easier to add or subtract the whole number
parts and add or subtract the proper-fraction parts vertically.
Adding or Subtracting Mixed Numbers
To add or subtract mixed numbers, add or subtract the fraction parts and then
add or subtract the whole number parts.
1 3
Example 9 Add: 2 + 5 . Check by estimating. PRACTICE 9
3 8
1 2
Solution: The LCD of the denominators 3 and 8 is 24. Add: 2 + 4 .
6 5
#
1 8 8
2 # = 2 Check by estimating.
3 8 24
#
3 3 9
+ 5 # = 5
8 3 24
Answers
17
7 d Add the fractions. 5. 19 2 6. 4 7. 8 8. 1 15
24 5 63 57 31
c Add the whole numbers.
1 3 17
9. 6
To check by estimating, we round as usual.The fraction 2 rounds to 2, 5 30
3 8
rounds to 5, and 2 + 5 = 7 , our estimate.
Our exact answer is close to 7, so our answer is reasonable. Concept Check Answer
forgot to change mixed number to
Work Practice 9 improper fraction