USING RECIPROCAL TO DIVIDE FRACTIONS

We have to do the following steps to divide a fraction by another fraction.   

Step 1 :

When we divide a fraction by another fraction, first we have to change the division sign 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 : 

Divide  2/5  by  6/7.

Solution : 

Using the method explained above, we have 

 2/5 ÷ 6/7  =  2/5 ⋅ 7/6

2/5 ÷ 6/7  =  (2 ⋅7) / (5 ⋅ 6)

2/5 ÷ 6/7  =  7/15

Example 2 :

Divide  7/5  by  3/2.

Solution : 

Using the method explained above, we have 

7/5 ÷ 3/2  =  7/5 ⋅ 2/3

7/5 ÷ 3/2  =  (7 ⋅ 2) / (5 ⋅ 3)

7/5 ÷ 3/2  =  14/15

Example 3 :

Divide  5/12  by  20/13.

Solution : 

Using the method explained above, we have 

5/12 ÷ 20/13  =  5/12 ÷ 20/13

5/12 ÷ 20/13  =  5/12 ⋅ 13/20

5/12 ÷ 20/13  =  (5 ⋅ 13) /  (12 ⋅ 20)

5/12 ÷ 20/13  =  13/48

Example 4 :

Divide 2/19  by  6 1/2.

Solution : 

First, let us convert the mixed number 6 1/2 in to improper fraction.

6 1/2  =  13/2

Now,m we have 2/19 ÷ 6 1/2  =  2/19 ÷ 13/2

 Using the method explained above, we have 

2/19 ÷ 13/2 =  2/19 ⋅ 13//2

2/19 ÷ 13/2 =  (2 ⋅ 13) / (19 ⋅ 2)

2/19 ÷ 13/2 =  13 / 19

Example 5 :

One pizza can be made in 1/2 hour. How many pizzas can be made in 5/2 hours ?

Solution : 

Time taken to make one pizza  =  1/2 hour  

No. of pizzas made in 5/2 hours  =  5/2 ÷ 1/2

No. of pizzas made in 5/2 hours  =  5/2 ⋅ 2/1

No. of pizzas made in 5/2 hours  =  (5 ⋅ 2) / (2 ⋅ 1)

No. of pizzas made in 5/2 hours  =  5

How to divide a fraction by a whole number ?

We have to do the following steps to divide a fraction by a whole number.  

Step 1 :

When we divide a fraction by a whole number, first we have to write the whole number as fraction with denominator 1.

Step 2 :

Change the division sign as multiplication.

Step 3 :

Take reciprocal of the second fraction (Whole number with denominator 1).

Step 4 :

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

Example 1 : 

Divide 2/5 by 6.

Solution : 

Using method 1, we have 

2/5 ÷ 6  =  2/5 ÷ 6/1

 2/5 ÷ 6  =  2/5 ⋅ 1/6

2/5 ÷ 6  =  (2 ⋅ 1) / (5 ⋅ 6)

2/5 ÷ 6  =  1/15

Example 2 :

Divide 5/12 by 20.

Solution : 

Using method 2, we have 

5/12 ÷ 20  =  5 / (12 ⋅ 20)

5/12 ÷ 20  =  1/48

Example 3 :

David eats 1/4 of a pizza and divides the remaining in to two equal parts for his two kids. What is the part of the pizza will each kid receive ?

Solution : 

Part of the pizza eaten by David  =  1/4

Remaining pizza  =  3/4

Given : Remaining pizza is divided in to equal parts for his two kids. 

So, part of the pizza received by each kid is 

=  3/4 ÷ 2

=  3/(4 ⋅ 2)

=  3/8

Hence, each kid will receive 3/8 part of the pizza.

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