Dividing a Proper Fraction by a Proper Fraction

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



1 ÷  1
4
  =  4
You get 4 slices.

Now, if you have only half a pizza to begin with and you cut that into quarters, how many slices do you get?



1
2
  ÷  1
4
  =  2
You get 2 slices.

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



2
3
  ÷  1
6
  =  4
You get 4 slices.


What are the steps to divide 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
  

Word Problem 1

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 use?


5
6
  ÷   1
12
  =  5
6
 × 12
 1
 
     =  10

He uses 10 teacups.

Word Problem 2

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?


a)  3
4
  ÷   1
10
  =  3
4
  ×  10
 1
      =  30
 4
      =   61
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)
         1
10
  −   1
20
  =   1
20
        She needs   1
20
  kg more rice to make another bag of   1
10
  kg.

Word Problem 3

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.



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
 km) + (2 × 1
4
 km)
                             =  2
3
 km + 1
2
 km
                             =  7
6
 km
                             =  11
6
 km
The length of fence needed to border the land is 11
6
 km.