As we know, we do various operations in mathematics like addition, subtraction, multiplication, and division. In this article, we will discuss fractions and how fractions multiplication works.

The following points we will cover on it:

- Definition of fraction
- How to multiply fractions with same denominators?
- How to multiply fractions with different denominators?
- How to multiply improper fractions with different denominators?
- How to multiply fraction by whole number?
- How to solve fractions multiplication word problems?

Let's start with the definition of fraction.

### 1. Definition of fraction

A fraction is a part of the whole.

It means a piece of cake is part of the whole cake. So we can say that the piece of cake is a fraction of the whole cake.

Example: 1/3, 2/3, 5/7, etc.

### 2. How to multiply fractions with same denominators?

We do multiply, both numerators by each other and both same denominators by each other to find the answer.

For better understanding, we are multiplying fractions with same denominator:

1. Multiply 1/3 ✕ 2/3

Solve:

= 1/3 ✕ 2/3

= (1✕2)/(3✕3)

= 2/9

=0.222....

2. Multiply 9/2 ✕ 5/2

Solve:

= 9/2 ✕ 5/2

= (9✕5)/(2✕2)

= 45/4

= 11.25

### 3. How to multiply fractions with different denominators?

If fractions have different denominators so we will multiply both the denominators by each other and both the numerators by each other.

Let's understand with some examples here we are multiplying fractions with different denominators:

1. Multiply 2/3 x 6/7

Solve:

= 2/3 ✕ 6/7

= (2✕6)/(3✕7)

= 12/21

= 0.571....

2. Multiply 1/10 x 17/18

= 1/10 ✕ 17/18

= (1✕17)/(10✕18)

= 17/180

= 0.0944....

### 4. How to multiply improper fractions with different denominators?

To multiply improper fractions with different denominators we need to multiply both numerators by each other and both denominators by each other to get the answer.

Take examples for better understanding:

1. Multiply 11/3 x 20/7

= 11/3 x 20/7

= (11✕20)/(3✕7)

= 220/21

= 10.476....

2. Multiply 33/4 x 7/2

= 33/4 x 7/2

= (33✕7)/(4✕2)

= 231/8

= 28.875

### 5. How to multiply fraction by whole number?

We multiply the numerator of fraction by the whole number to get the answer.

Let's take some examples:

1. Multiply 14/3 x 7

= 14/3 x 7

= (14✕7)/3

= 98/3

= 32.66...

2. Multiply 55/6 x 20

= 55/6 x 20

= (55✕20)/6

= 1100/6

= 183.33...

### 6. How to solve fractions multiplication word problems?

1. A car runs 16 km using 1 litre of petrol. How much distance will it cover using 7/4 litres of petrol?

Solve:

In 1-litre petrol dist. covered by car = 16 km

In 7/4 litre petrol dist. covered by car = 7/4✕16

= 7/4✕16

= (7✕16)/4

= 112/4

= 28

28 km dist. covered by car in 7/4 litre petrol.

2. David reads 1/3 part of a book in 1 hour. How many parts of the book will be read in 11/6 hours?

Solve:

Book read by David in 1 hr = 1/3 part

Book read by David in 11/6 hours = 1/3✕11/6

= 1/3✕11/6

= (1✕11)/(3✕6)

= 11/18

David will read the 11/18 part of the book in 11/6 hours.