+

Fractions Multiplication and Division

+Multiplication

Multiply the numerators and put in the numerator of the result

Multiply the denominators and put in the denominator of the result

8 9 8 x 9 72

47 7 x 4 28= =x

+Multiplication - Let’s Try It!

9 2

17=x

5 3

17=x

7 11

94=x

4 14

730=x

18

7

15

7

77

36

56

210

+

56

210 These numbers get pretty big!

What if we needed to multiply again?

Let’s make the fraction more simple, so it will be easier to use in the future.

+Simplification

Divide by the Greatest Common Factor

72

28But what is a Common Factor?

+Factors

A factor is a number that can be divided into another number with no remainder 8’s factors are:

1 (8/1 =8) 2 (8/2 = 4) 4 (8/4 = 2) 8 (8/8 = 1)

3 is NOT a factor of 8, because 8 is not evenly divisible by 3 (8/3 = 2 with R=3)

+Common Factors

A common factor is a factor that two numbers have in common

For example, 7 is a factor of both 21 and 105, so it is a common factor of the two.

The greatest common factor is the largest factor that the two number share

So let’s go back to our simplification problem from before…

+Simplification

Divide both numerator and denominator by the Greatest Common Factor

72

28 Factors are 1, 2, 4, 7, 14, 28

Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 48, 72

Greatest Common Factor is 4

2872 ÷

÷ 44

==

718

So7228

=7

18

+Simplification - Let’s Try It!

3

1

7

2

3

1

63

18=

5

2

114

78=

7

2

19

13

9

3=

84

24=

21

7=

15

6=

+Division

Just like multiplication with one more step

Invert the second fraction and multiply

8 2

13=÷

8 1

23x =

8

6

+Division - Let’s Try It!

9 217

=÷

=5 3

17÷

7 1194

=÷

=4 10

720÷

914

5

21

6344

7

50

+Addition

To add two fractions, you must make sure they have a Common Denominator

8

3

16

5+

What is a Common Denominator?

+Common Denominator

A common denominator is a number with which both of the denominators share at least one factor that is not the number 1

For example, if the denominators are 4 and 7, then a common denominator is 28.

28 shares the factors 1, 2 and 4 with the

number 4, and the factors 1 and 7 with the number 7.

So let’s go back to our simplification problem from before…

+Review

A fraction has a numerator and a denominator

The denominator can never be 0

You can multiply, divide, add and subtract fractions

A common factor is a number that both denominators are evenly divisible by

A common denominator is a number that both denominators share a factor with