Basic Mathematics for College Students

Chapter 3 Summary and Review 305

To multiply mixed numbers,first change the
mixed numbers to improper fractions. Then
perform the multiplication of the fractions.
Write the result as a mixed number or whole
number in simplest form.

Multiply and simplify:

Write and as improper fractions.

Write the improper fraction

as a mixed number.

49

 121 4

4

Multiply the remaining factors in the

numerator and in the denominator.

The result is an improper fraction.



49

4

To simplify, factor 21 as 3 7, and then

remove the common factor of 3 from

the numerator and denominator.



3

1

 7  7

2  2  3

1

Use the rule for multiplying two fractions.

Multiply the numerators.

 Multiply the denominators.

21  7

2  6

10 10 12 1 61

1

2

 1

1

6



21

2



7

6

10

1

2

 1

1

6

To divide mixed numbers, first change the
mixed numbers to improper fractions. Then
perform the division of the fractions. Write the
result as a mixed number or whole number in
simplest form.

Divide and simplify:

Write and as improper

fractions.

Multiply by the reciprocal of ,

which is.

Write the negative improper

fraction as a negative mixed

number.

 1  (^32)

1

2

Multiply the remaining factors

in the numerator and in the

denominator. The result is a

negative improper fraction.



3

2

To simplify, factor 9 as 3 3 and

34 as 2 17. Then remove the

common factors of 3 and 17 from

the numerator and denominator.



17

1

 3

1

 3

3

1

 2  17

1

Multiply the numerators.

Multiply the denominators.

Since the fractions have unlike

signs, make the answer negative.



17  9

3  34

 349

^17173 ^349

3

a

9

34

b

5 5 23 3 97

2

3

a 3

7

9

b

17

3

a

34

9

b

5

2

3

a 3

7

9

b

69. In the illustration below, each triangular region
    outlined in black represents one whole. Write a
    mixed number and an improper fraction to
    represent what is shaded.
    70. Graph , , , and on a number line.

− 5 − 4 − 3 − 2 − 1012345

59

 (^24)
3
4
8
 2 9
2
3
REVIEW EXERCISES
12
(^4)  49
 4
09
 8
1