**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 2/3 = 2/5 ⋅ 17/3

2/5 ⋅ 5 2/3 = (2 ⋅ 17) / (5 ⋅ 3)

2/5 ⋅ 5 2/3 = 34/15

2/5 ⋅ 5 2/3 = 2 4/15

**Problem 4 :**

Find the value of :

6 3/4 ⋅ 7/10

**Solution : **

6 3/4 ⋅ 7/10 = 27/4 ⋅ 7/10

6 3/4 ⋅ 7/10 = (27 ⋅ 7) / (4 ⋅ 10)

6 3/4 ⋅ 7/10 = 189/40

6 3/4 ⋅ 7/10 = 4 29/40

**Problem 5 :**

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.

**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.

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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