Page 270 - Basic College Mathematics with Early Integers

S E C T I O N 3.7 I OPERATIONS ON MIXED NUMBERS 247

7 1 1
Then 3 simplifies to 3 . The difference is 3 .
21 3 3
3 2
To check, 8 rounds to 8, 5 rounds to 5, and 8 - 5 = 3 , our estimate.
7 21
Our exact answer is close to 3, so our answer is reasonable.
Work Practice 12

When subtracting mixed numbers, borrowing may be needed, as shown in the
next example.

3 6
Example 13 Subtract: 7 - 3 PRACTICE 13
14 7
7 3
Solution: The LCD of the denominators 7 and 14 is 14. Subtract: 9 - 4
15 5
3 3 Notice that we cannot subtract 12 from 3 , so we borrow
7 = 7
14 14
14 14 from the whole number 7.
6 12
- 3 =- 3
7 14
borrow 1 from 7
3 3 17 17
7 =6+1 =6+ or 6
14 14 14 14
Now subtract.
3 3 17
7 = 7 = 6
14 14 14
6 12 12
- 3 = - 3 =- 3
7 14 14
5
3 ; Subtract the fractions.
14
c
Subtract the whole numbers.
Work Practice 13

1 3 1
Concept Check In the subtraction problem 5 - 3 , 5 must be
3 1 4 4 4
rewritten because cannot be subtracted from . Why is it incorrect to rewrite
1 5 4 4
5 as 5 ?
4 4

3
Example 14 Subtract: 14 - 8 PRACTICE 14
7
2
7 7 Subtract: 25 - 10
Solution: 14 = 13 Borrow 1 from 14 and write it as . 9
7 7
3 3
– 8 = – 8 Answers
7 7 13 7
4 13. 4 15 14. 14 9
5 Subtract the fractions.
7
Concept Check Answer
Subtract the whole numbers.
1 5
Work Practice 14 Rewrite 5 4 as 4 4 by borrowing from
the 5.