DIVIDING FRACTION BY FRACTION

Dividing Fraction by Fraction :

In this section, you will learn, how to divide a fraction by another fraction.

Dividing Fraction by Fraction - Steps

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).

Dividing Fraction by Fraction - Examples

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 ⋅ 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.

After having gone through the stuff given above, we hope that the students would have understood, how to divide a fraction by another fractions. 

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