Dividing a Whole Number by a Proper Fraction

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

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

You get 2 slices.

2. If 1 whole pizza is cut into one-thirds, how many slices do you get?

dividing a number by a fraction
1  ÷ 
1
3
 =  3

You get 3 slices.

3. If 2 pizzas are cut into two-thirds, how many slices do you get?

dividing a number by a fraction
2  ÷ 
2
3
 =  3

You get 3 slices.

4. How many two-thirds are there in 3 wholes?

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


There are  
4 1
2
  two-thirds in 3 wholes.

Steps for dividing a whole number by a proper fraction

Dividing a whole number by a proper fraction is the same as multiplying the whole number by the inverse of the proper fraction. Here are the steps:

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

Example:
Divide 8 by
4
5
.
8  ÷ 
4
5
 =  8  × 
5
4
 =  10

5. Nina had 2 m of lace that she used for making bows.
If she needed    
2
7
m of lace for each bow, how many bows did she make?

dividing a number by a fraction
    2  ÷ 
2
7

=  2  × 
7
2

=  7

She made 7 bows.

6. Mr. Lee buys 25 kg of decorative shells from a wholesale market.
He then repacks the shells into small bags of    
1
4
kg each.
a)   How many bags does he get?
b)   If he sells each bag at $3.50, how much money does he collect from the sale of all bags?

dividing a number by a fraction
a)     25  ÷ 
1
4

    =  25  × 
4
1

    =  100

    He gets 100 bags.

b)     $3.50  ×  100  =  $350

    He collects $350.

7. A chemist fills 5 litres of perfume into bottles that have a capacity of    
2
11
litre each.
a)   What is the greatest number of bottles that he can fill completely?
b)   In the end, there is one bottle that is not completely filled. How much perfume does that bottle contain?

dividing a number by a fraction
a)     5  ÷ 
2
11

    =  5  × 
11
2

    = 
27 1
2


    He can fill 27 bottles completely.

b)     27  × 
2
11
 = 
54
11

      There are
54
11
litres of perfume in the 27 bottles altogether.

      5  − 
54
11

      = 
55 - 54
11

      = 
1
11
litre
      The bottle contains
1
11
litre of perfume.