Divide a Proper Fraction by a Proper Fraction

1. If a pizza is cut into quarters, how many slices do you get?

dividing a fraction by a fraction
1  ÷ 
1
4
 =  4

You get 4 slices.

2. If you have half a pizza and you cut that into quarters, how many slices do you get?

dividing a fraction by a fraction
1
2
 ÷ 
1
4
 =  2

You get 2 slices.

3. If you have   
2
3
of a pizza that you cut into one-sixths, how many slices do you get?

dividing a fraction by a fraction
2
3
 ÷ 
1
6
 =  4

You get 4 slices.

Steps for dividing a proper fraction by a proper fraction

Dividing a fraction by another fraction is the same as multiplying the first fraction by the inverse of the second fraction. Here are the steps:

Step 1:   Change  ÷  to  × .
Step 2:   Invert the second fraction.
Step 3:   Simplify the expression.

Example:
Divide
4
9
by
2
3
.
4
9
 ÷ 
2
3
 = 
4
9
 × 
3
2
 = 
2
3

4. Ray has    
5
6
litre of tea in a kettle.
He pours    
1
12
litre of tea into each of some teacups.
How many teacups does he fill?

dividing a fraction by a fraction
   
5
6
 ÷ 
1
12

5
6
 × 
12
1

=  10

She fills 10 teacups.

5. Maya had    
3
4
kg of rice.
She packed the rice into bags of    
1
10
kg each.
a)   How many bags did she make?
b)   How much rice was left unpacked?
c)   How much more rice does she need to make another bag of    
1
10
kg?

dividing a fraction by a fraction
a)    
3
4
 ÷ 
1
10

    = 
3
4
 × 
10
1

    = 
30
4

    = 
6 1
2


    She made 6 bags.

b)     6  × 
1
10
 = 
3
5


    There was
3
5
kg of rice in 6 bags altogether.

   
3
4
 − 
3
5
 = 
1
20

    There was
1
20
kg rice that was left unpacked.

c) dividing a fraction by a fraction
   
1
10
 − 
1
20
 = 
1
20

    She needs
1
20
kg more rice to make another bag of
1
10
kg.

6. A rectangular piece of land    
1
3
km long has an area of    
1
12
km2.
Find the length of fence needed to border the land.

dividing a fraction by a fraction
    Area of the rectangular land  =  length  ×  breadth
    
1
12
km2  = 
1
3
km  ×  breadth

      Breadth
1
12
 ÷ 
1
3

1
12
 × 
3
1

1
4
km

     Border or Perimeter
=  (2  ×  length)  +  (2  ×  breadth)
=  (2  × 
1
3
)  +  (2  × 
1
4
)
2
3
 + 
1
2

7
6
km
1 1
6
km

The length of fence needed to border the land is  
1 1
6
  km.