Fraction Multiplication and Division

Review Topic 7

Look at the following examples. Decide what the rule is for multiplying fractions.

Examples: 2/3 x 1/5 = 2/15

4/5 x 3/ 4 =12/20=3/5 3 3 9

4 4 16

,

5 5 3 15 73 1

8 8 1 8 8

Rule

Notice: Fraction numbers must be written as the ratio of two integers to be multiplied.

a c a c

b d b d

Thus to multiply 2 ½ x 1 ¾ x 12

First change the mixed numbers to improper fractions 5/2 x 7/4 x12/1

to get 420/8

This can be reduced to 52 ½.

Cancellation

One other step can save time.

Canceling reduces the answer before you multiply the numbers.

15 7 12 15

2 4 25

3

1

7 12

2 4

3

25 5

3 7 3 63 36 102 1 5 10

Fraction Division

To divide fractions, invert the second fraction and multiply.

2/3 ½ = 2/3 x 2/1 = 4/3 = 1 1/3.

Rule:

a c a d a dx

b d b c b c

Things to Remember

Notice: DON”T cancel until after the divisor (second number) is inverted.

For word problems, be very careful which number to write first in the problem.

The thing being split, cut apart, or sorted goes first.

Example:

1 1 10 5 10 2 2 2 4 13 2 13 2 3 2 3 5 3 1 3 3

Steps

Change to improper

Invert and Multiply

Cancel

Multiply

Simplify