**Multiplying fractions by fractions :**

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 x 4/5 = 8/15

1/3 x 7/11 = 7/33

**Example 1 :**

Find 1/5 of 3/8

**Solution : **

1/5 of 3/8 = 1/5 x 3/8

1/5 of 3/8 = 3/40

**Example 2 :**

Find 2/9 x 3/2

**Solution : **

2/9 x 3/2 = 1/3

**Example 3 :**

Find 2/5 x 5 2/3

**Solution : **

2/5 x 5 2/3 = 2/5 x 17/3

2/5 x 5 2/3 = 34/15

2/5 x 5 2/3 = 2 4/15

**Example 4 :**

Find 6 3/4 x 7/10

**Solution : **

6 3/4 x 7/10 = 27/4 x 7/10

6 3/4 x 7/10 = (27x7) / (4x10)

6 3/4 x 7/10 = 189 / 40

6 3/4 x 7/10 = 4 29/40

**Example 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 = 1/4

So, the part of the book read by Lily in 3 1/2 hours is

= 3 1/2 x 1/4

= 7/2 x 1/4

= (7x1) / (2x4)

= 7/8

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

**Example 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 = 1/3

So, the remaining pizza = 2/3

The part of the given to his friend is

= 3/4 of the remaining

= 3/4 of 2/3

= 3/4 x 2/3

= 1/2

Hence, he 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 "Multiplication of fractions by fractions".

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