# Dividing a Proper Fraction by a Proper Fraction

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

*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?*

*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?

If you have | 23 | 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:

**Change ÷ to ×.**

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

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

*Step 3:*

*Example:*

Divide | 49 | by | 23 | . |

4

9÷ 2

3= 4

9× 3

2= 2

3

*Word Problem 1*

*Word Problem 1*

Ray has 5

6litre of tea in a kettle. He pours 1

12litre 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*

*Word Problem 2*

Maya had 3

4kg of rice. She packed the rice into bags of 1

10kg 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

10kg?

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

5kg of rice in 6 bags altogether.

3

4− 3

5= 1

20

There was 1

20kg rice that was left unpacked.

c)

1

10− 1

20= 1

20

She needs 1

20kg more rice to make another bag of 1

10kg.

*Word Problem 3*

*Word Problem 3*

A rectangular piece of land 1

3km long has an area of 1

12km ^{2}.

Find the length of fence needed to border the land.

Area of the rectangular land = len gth × breadth 1

12km ^{2}= 1

3km × breadth Breadth= 1

12÷ 1

3= 1

12× 3

1= 1

4km

Border or perimeter = (2 × length) + (2 × breadth)

= (2 × 1

3km) + (2 × 1

4km)

= 2

3km + 1

2km

= 7

6km

= 1 1

6km

The length of fence needed to border the land is 1 1

6km.