## Divide a Proper Fraction by a Proper Fraction

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

1 ÷

1 |

4 |

You get

**4**slices.

#### 2. If you have half a pizza and you cut that into quarters, how many slices do you get?

1 |

2 |

1 |

4 |

You get

**2**slices.

#### 3. If you have

2 |

3 |

2 |

3 |

1 |

6 |

You get

**4**slices.

#### Steps for dividing 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:

Divide

by

.

÷

=

×

=

**Step 1:**Change ÷ to × .**Step 2:**Invert the second fraction.**Step 3:**Simplify the expression.*Example:*Divide

4 |

9 |

2 |

3 |

4 |

9 |

2 |

3 |

4 |

9 |

3 |

2 |

2 |

3 |

#### 4. Ray has

5 |

6 |

He pours

1 |

12 |

How many teacups does he fill?

5 |

6 |

1 |

12 |

=

5 |

6 |

12 |

1 |

= 10

She fills

**10**teacups.

#### 5. Maya had

3 |

4 |

She packed the rice into bags of

1 |

10 |

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 |

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 |

5 |

3 |

4 |

3 |

5 |

1 |

20 |

There was

**kg rice that was left unpacked.**

1 |

20 |

c)

1 |

10 |

1 |

20 |

1 |

20 |

She needs

**kg more rice to make another bag of**

1 |

20 |

1 |

10 |

#### 6. A rectangular piece of land

1 |

3 |

1 |

12 |

^{2}.

Find the length of fence needed to border the land.

Area of the rectangular land = length × breadth

1 |

12 |

^{2}=

1 |

3 |

**Breadth**

=

1 |

12 |

1 |

3 |

=

1 |

12 |

3 |

1 |

=

**km**

1 |

4 |

**Border or Perimeter**

= (2 × length) + (2 × breadth)

= (2 ×

1 |

3 |

1 |

4 |

=

2 |

3 |

1 |

2 |

=

7 |

6 |

=

1 | 1 |

6 |

The length of fence needed to border the land is

**km.**

1 | 1 |

6 |