Basic Mathematics for College Students

Solve application problems by multiplying

and dividing mixed numbers.

6

3.5 Multiplying and Dividing Mixed Numbers 263

Write the improper fraction as a mixed number by dividing

3 by 2.

b. Write as an improper fraction.

Multiply by the reciprocal of , which is.

Write the improper fraction as a mixed

number by dividing 9 by 4.

9

 21 4

4

Multiply the remaining factors in the

numerator and in the denominator.

The result is an improper fraction.



9

4

To simplify, factor 27 as 39 and 16 as 44.

Then remove the common factors of 3 and 4

from the numerator and denominator.



3

1

 9  4

1

4

1

 4  3

1

Multiply the numerators.

 Multiply the denominators.

27  4

16  3

4

3

3

4

27

 16

27

16



4

3

1 1 1611

11

16



3

4



27

16



3

4

 1 1 32

2

Multiply the remaining factors in the numerator:

3  1  1 3. Multiply the remaining factors in the

denominator: 2 1  1 2.



3

2

To simplify, factor 27 as 3 9 and 8 as 2 4.

Then remove the common factors of 9 and 4

from the numerator and denominator.



3  9

1

 4

1

2  4

1

 9

1

Multiply the numerators.

Multiply the denominators.



27  4

8  9

Since the product of two negative fractions

 (^) is positive, drop both  signs and continue.

27

8

a

4

9

b

Self Check 7

BUMPER STICKERSA

rectangular-shaped bumper

sticker is inches long

by inches wide. Find its

area.

Now TryProblem 99

3 14

8 14

EXAMPLE (^7) To y s The dimensions of the rectangular-shaped screen of
an Etch-a-Sketch are shown in the illustration below. Find the area of the screen.
Strategy To find the area, we will multiply by.
WHY The formula for the area of a rectangle is Area length width.

6 14 4 12

(^1) –
2
(^1) –
4
4 in.
6 in.