# Dividing a Proper Fraction by a Proper Fraction

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

 1 ÷ 14 =  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?

 12 ÷ 14 =  2
 You get 2 slices.

### If you have 23 of a pizza that you cut into one-sixths, how many slices do you get?

 23 ÷ 16 =  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 49 by 23 .
 49 ÷ 23 = 49 × 32 = 23

### Word Problem 1

 Ray has 56 litre of tea in a kettle. He pours 112 litre of tea into each of
 some teacups. How many teacups does he use?

 56 ÷ 112 = 56 × 12 1 = 10

He uses 10 teacups.

### Word Problem 2

 Maya had 34 kg of rice. She packed the rice into bags of 110 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 110 kg?

 a) 34 ÷ 110 = 34 × 10 1 = 30 4 = 6 12

 b)  6 × 110 = 35
 There was 35 kg of rice in 6 bags altogether.

 34 − 35 = 120
 There was 120 kg rice that was left unpacked.

 c)
 110 − 120 = 120
 She needs 120 kg more rice to make another bag of 110 kg.

### Word Problem 3

 A rectangular piece of land 13 km long has an area of 112 km2.
 Find the length of fence needed to border the land.

 Area of the rectangular land = len gth × breadth 112 km2 = 13 km × breadth Brea dth = 112 ÷ 13 = 112 × 31 = 14 km

 Border or perimeter = (2 × length) + (2 × breadth)
 = (2 × 13 km) + (2 × 14 km)
 = 23 km + 12 km
 = 76 km
 = 1 16 km
 The length of fence needed to border the land is 1 16 km.