Dividing Fractions

To Divide Fractions:

• Rewrite the first fraction.• Change the division sign to a

multiplication sign.• Flip the second fraction upside

down.• Multiply.

Reciprocal

• When you flip the second fraction, you are writing that fraction’s reciprocal.

35

53

Finding Reciprocals

2

5= 5

2

6

13=

6

13

Example 1

1

3÷ 1

2Rewrite:

13

x 21 = 2

3

Example 2

4

5÷

4

9Rewrite:

45

x94

11

=95

= 1 45

Example 3

12 ÷ 351

Rewrite:

121

x 53

41

=20

1= 20

Example 4

16

÷21

Rewrite:

16

x 12

=1

12

Classwork: Try these Visual models to help you

learn Division with fractions. See if you can guess with

whole numbers!

Dividing Mixed

Numbers

Strategy:

• Change mixed numbers into improper fractions.

• Instead of dividing, multiply by the reciprocal.

• Factor when possible, multiply, and put your answer in simplest form.

Example 1

6 25 ÷ 2 2

7

÷32

5167

32

5 x 716

21 = 14

5 = 2 45

Example 2

1 19 ÷ 6 2

3

÷10

9203

x10

9320

123

1=

16

Example 3

8 113 ÷ 5

÷105

1351

10513 x 1

521

1= 21

13 =1 813

Classwork: Visit the Visual Fractions modeling mixed number

site.

Solving Fraction Equations by

Multiplying

If the variable is in the fraction…

• When the variable is the numerator of the fraction, then it suggests a division problem.

• To solve a division problem, the inverse operation is multiplying.

Example

y

8= 20

This equation reads “y divided by 8 equals 20.”

The opposite of dividing by 8 is multiplying by 8.

Multiply both sides by 8.

y

8= 208

1·

11

y1

=

·8

160

y =160

Example 2

m2

= 3·21

11

m1 =

· 2

6

m =6

Check answers in the original equation.

m2 =362 =3

3 =3

If the variable is being multiplied by a fraction…

• To isolate a variable that is being multiplied by a fraction, multiply by the reciprocal.

• Perform the same operation on the other side of the equation.

Example

23

r = 10·32

1111

1r =

· 321

5

1151

r = 15

Classwork: Try this interactive site that

reminds us to balance equations!

Next Play Connect 4 with a partner and solve

equations

Homework Time-Dividing Fractions HO