MULTIPLYING FRACTIONS BY FRACTIONS

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

To multiply a proper or improper fraction by another proper or improper fraction, we have to multiply the numerators and denominators. 

For example, 

2/3 ⋅ 4/5   =  (2 ⋅ 4)/(3 ⋅ 5)  =  8/15

1/3 ⋅ 7/11  =  (1 ⋅ 7)/(3 ⋅ 11)  =  7/33

Problem 1 :

Find the value of :

1/5 of 3/8

Solution :

1/5 of 3/8  =  1/5  3/8

1/5 of 3/8  =  (1 ⋅ 3)/(5 ⋅ 8)

1/5 of 3/8  =  3/40

Problem 2 :

Find the value of :

2/9 ⋅ 3/2

Solution :

2/9 ⋅ 3/2  =  (2 ⋅ 3)/(9 ⋅ 2)

2/9 ⋅ 3/2  =  6/18

Problem 3 :

Find the value of :

 2/5 ⋅ 5 2/3

Solution :

2/5 ⋅ 5  =  2/5  17/3

2/5  5  =  (2 ⋅ 17)/(5 ⋅ 3)

2/5 ⋅ 5  =  34/15

2/5 ⋅ 5  =  2⁴⁄₁₅

Problem 4 :

Find the value of :

 6 3/4 ⋅ 7/10

Solution :

6¾ ⋅ 7/10  =  27/4 ⋅ 7/10

6¾ ⋅ 7/10  =  (27  7)/(4 ⋅ 10)

6¾ ⋅ 7/10  =  189/40

6¾ ⋅ 7/10  =  4²⁹⁄₄₀

Problem 5 :

Lily reads 1/4 th of a book in 1 hour. How much of the book will she read in 3½ hours ?

Solution :

The part of the book read by Lily in 1 hour is 1/4.   

So, the part of the book read by Lily in 3½ hours is

=  3½ ⋅ 1/4

=  7/2 ⋅ 1/4

=  (7 ⋅ 1)/(2 ⋅ 4)

=  7/8

Hence, Lily will read 7/8 part of the book in 3 1/2 hours.

Problem 6 :

David ate 1/3 of the pizza and gave 3/4 th of the remaining to his friend. What is the part of the pizza did David give his friend ?  

Solution :

The part of the pizza eaten by David is 1/3. 

So, the remaining pizza is 2/3.

The part of the pizza given to his friend is

=  3/4 of the remaining

=  3/4 of 2/3

=  3/4 ⋅ 2/3

=  (3 ⋅ 2)/(4 ⋅ 3)

=  (1 ⋅ 1)/(2 ⋅ 1)

=  1/2

Hence,  David gave 1/2 of the pizza to his friend. 

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