# DIVIDING FRACTION BY FRACTION

The following steps would be useful to understand how to divide a fraction by another fraction.

Step 1 :

In division of two fractions, change the division as multiplication.

Step 2 :

Take reciprocal of the second fraction.

Step 3 :

Multiply the two fractions (numerator times numerator and denominator times denominator).

Example 1 :

Simplify :

2/5 ÷ 6/7

Solution :

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.

2/5 ÷ 6/7  =  2/5 ⋅ 7/6

Simplify.

2/5 ÷ 6/7  =  (2 ⋅ 7)/(5 ⋅ 6)

2/5 ÷ 6/7  =  (1 ⋅ 7)/(5 ⋅ 3)

2/5 ÷ 6/7  =  7/15

Example 2 :

Simplify :

7/5 ÷ 3/2

Solution :

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.

7/5 ÷ 3/2  =  7/5 ⋅ 2/3

Simplify.

7/5 ÷ 3/2  =  (7 ⋅ 2)/(5 ⋅ 3)

7/5 ÷ 3/2  =  (7 ⋅ 2)/(5 ⋅ 3)

7/5 ÷ 3/2  =  14/15

Example 3 :

Simplify :

5/12 ÷ 20/13

Solution :

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.

5/12 ÷ 20/13  =  5/12 ⋅ 13/20

Simplify.

5/12 ÷ 20/13  =  (5 ⋅ 13)/(12 ⋅ 20)

5/12 ÷ 20/13  =  (1 ⋅ 13)/(12 ⋅ 4)

5/12 ÷ 20/13  =  13/48

Example 4 :

Simplify :

2/19 ÷ 6 1/2

Solution :

2/19 ÷ 6 1/2  =  2/19 ÷ 13/2

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.

2/19 ÷ 6 1/2  =  2/19  2/13

Simplify.

2/19 ÷ 6 1/2  =  (⋅ 2)/(19 ⋅ 13)

2/19 ÷ 6 1/2  =  4/247

Example 5 :

David can make one pizza in 1/2 hour. How many pizzas can he make in 5/2 hours ?

Solution :

Time taken to make one pizza is 1/2 hour.

No. of pizzas made in 5/2 hours is

=  5/2 ÷ 1/2

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.

=  5/2  2/1

=  (5 ⋅ 2)/(2 ⋅ 1)

=  10/2

=  5

So, David can make 5 pizzas in 5/2 hours.

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