HOW TO MULTIPLY TWO FRACTIONS

How to Multiply Two Fractions ?

In this section, we will see how to multiply two fractions.

Procedure for multiplying any two factions :

1. First we need to multiply the numerator of the first fraction with the numerator of the second fraction

2. Then we have to multiply the denominator of the first fraction with the denominator of the second fraction

3. If it is possible to simplify we can simplify the answer.

Multiplying Two Fractions Examples

Question 1 :

Multiply (14/25) ⋅ (2/11)

Solution :

=  (14/25) ⋅ (2/11)

 =  (14 ⋅ 2) / (25 ⋅ 11)

=  25/275

Question 2 :

Multiply (49/56) ⋅ (4/7)

Solution :

  =  (49/56) ⋅ (4/7)

  =  (49 ⋅ 4) / (56 ⋅ 7)  

  =  (7 ⋅ 1)/(14 ⋅ 1)

  = 7/14

  = 1/2

Question 3 :

Multiply   (4/25) ⋅ (2/11)

Solution :

  =  (4/25) ⋅ (2/11)

  =  (4 ⋅2) / (25 ⋅ 11)  

  =  8/275

Question 4 :

Multiply   (7/12) ⋅ (24/11)

Solution :

  =  (7 ⋅ 24)/(12 ⋅ 11)

  =  168/132

We can simplify this using 2 times table. So we will get 84/61

Question 5 :

Multiply   (5/9) ⋅ (45/14)

Solution :

  =  (5 ⋅ 45)/(9 ⋅ 14)

  =  225/126

We can simplify this using 3 times table. So we will get 25/14.

Question 6 :

Lily reads 1/4^th of a book in 1 hour. How much of the book will she read in 3 1/2 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 3 1/2 hours is

=  3 1/2 ⋅ 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.

Question 7 :

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. 

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

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