Basic Mathematics for College Students

Success Tip We can use rounding to check the results when multiplying

mixed numbers. If the fractional part of the mixed number is or greater,

round up by adding 1 to the whole-number part and dropping the fraction.

If the fractional part of the mixed number is less than , round down by

dropping the fraction and using only the whole-number part. To check the

answer from Example 5, part a, we proceed as follows:

Since is greater than , round up to 2.

Since is less than , round down to 2.

Since 4 121 is close to 4, it is a reasonable answer.

31 21 2 31

1

3

4

 2

1

3

 2  2  4

43 21 1 43

4121

1

2

1

2

262 Chapter 3 Fractions and Mixed Numbers

b. Write and as improper fractions.

To prepare to simplify, factor 26 as 2 13 and 15 as 3 5.

Any whole number divided by 1 remains the same.

c. Write as an improper fraction and write 3 as a fraction.

Write the negative improper fraction

as a negative mixed number.

^373

 12

1

3

12

(^3)  37
 3
7
 6
1
Multiply the remaining factors in the
numerator and in the denominator.
The result is an improper fraction.



37

3

To simplify, factor 9 as 33, and

then remove the common factor of 3

from the numerator and denominator.



37  3

1

3

1

 3  1

Multiply the numerators and multiply the denominators.

Since the fractions have unlike signs, make the answer negative.



37  3

9  1

 4  4 91

1

9

 3 

37

9



3

1

 6

Multiply the remaining factors in the numerator:

2  1  3  1 6.

Multiply the remaining factors in the denominator: 1 1 1.



6

1

Remove the common factors of 13 and 5 from the

 (^) numerator and denominator.

2  13

1

 3  5

1

5

1

 13

1



2  13  3  5

5  13

Multiply the numerators.

 (^) Multiply the denominators.

26  15

5  13

5 5 51 1 132

1

5

a 1

2

13

b

26

5



15

13

Self Check 6

Divide and simplify, if possible:

a.

b.

Now TryProblems 59 and 65

5

3

5



7

8

 3

4

15

a 2

1

10

b

EXAMPLE (^6) Divide and simplify, if possible:
a. b.
StrategyWe will write the mixed numbers as improper fractions.
WHY Then we can use the rule for dividing two fractions from Section 3.3.
Solution
a. Write and as improper fractions.
Use the rule for dividing two fractions.:
Multiply ^27 8 by the reciprocal of  49 , which is  94.

 

27

8

a

4

9

b

 3  3 38  2 41

3

8

a 2

1

4

b

27

8

a

9

4

b

1

11

16



3

4

 3

3

8

a 2

1

4

b