# Dividing a Whole Number by a Proper Fraction

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

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

1 ÷ 1

2= 2

You get 2 slices.

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

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

1 ÷ 1

3= 3

You get 3 slices.

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

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

2 ÷ 2

3= 3

You get 3 slices.

How many __2__

3 s are there in 3 wholes?

How many | 23 | s are there in 3 wholes? |

3 ÷ 2

3= 4 1

2

There are 4 1

2two-thirds in 3 wholes.

**What are the steps to divide 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:

**Change ÷ to ×.**

*Step 1:***Invert the fraction.**

*Step 2:***Simplify the expression.**

*Step 3:*

*Example:*

Divide 8 by | 45 | . |

8 ÷ 4

5= 8 × 5

4= 10

*Word Problem 1*

*Word Problem 1*

Nina had 2 m of lace that she used for making bows.

If she needed 2

7m of lace for each bow, how many bows did she make?

2 ÷ 2

7= 2 × 7

2= 7

She made 7 bows.

*Word Problem 2*

*Word Problem 2*

Mr. Lee buys 25 kg of decorative shells from a wholesale market.

He then repacks the shells into small bags of 1

4kg 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?

a) 25 ÷ 1

4= 25 × 4

1= 100

He gets 100 bags.

b) $3.50 × 100 = $350

He collects $350.

*Word Problem 3*

*Word Problem 3*

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?

a) 5 ÷ 2

11= 5 × 11

2= 27 1

2

He can fill 27 bottles completely.

b) 27 × 2

11= 54

11

There is 54

11litres of perfume in the 27 bottles altogether.

5 litres − 54

11litres = 55 − 54

11= 1litre

11

The bottle not completely filled contains 1

11litre of perfume.