In this module, we will learn how we can multiply fractions. **Multiplication of Fractions**:- Multiplying fractions can be defined as the product of a fraction with any whole number, integer or a fraction itself. The product of multiplication can be a fraction or an integer.

**Multiplication of Fractions ** is quite different from addition and subtraction of fractions as the same denominator is not necessary here. We can easily multiply any 2 fractions having different denominators. The fractions can be proper and improper both.

Part 1: Fractions From Basics

Part 2: Subtraction of Fractions

Part 3: Fractions From Basics

Table of Contents

## Definition

Multiplying fractions can be defined as the product of a fraction with any whole number, integer or fraction itself.

## How we can Multiply Fractions?

**We can multiply fractions very easily using 3 simple steps: –**

- Firstly, multiply the numerator of one fraction by the numerator of another fraction.
- Now, multiply the denominators of both fractions.
- At last, simplify the fractions if possible.

### Example 1: Multiply 5/2 and ⅔ ?

**Answer: **

Multiplication of two fractions can be done by:

**Step 1** = Firstly, multiply the numerators

= 5*2 = 10

**Step** 2 = Now, multiply the denominators.

= 2*3 = 6

**Step 3** = Simplify the fraction.

= 10/6 = 5/3

Hence, the answer of multiplication of 5/2 & ⅔ = 5/3

#### Example 2:: Multiply 9/5 and 7/3 ?

**Answer:**

Multiplication of two fractions can be done by:

**Step 1** = Firstly, multiply the numerators

= 9*7 = 63

**Step 2** = Now, multiply the denominators.

= 5*3 = 15

**Step 3** = Simplify the fraction.

= 63/15 = 21/5

Hence, the answer of multiplication of 9/5 & 7/3 = 21/5

Read More : How to find HCF in 10 seconds

**Rule of Multiplication of Fractions**

- If any fraction is in mixed form, first convert it into an improper fraction and then multiply the numerators and denominators.
- Simplify the product as much as possible.
- Multiply the numerators and denominators individually.

## Multiplication of Fractions with the Same Denominator

When we multiply fractions with the same denominator, it also follows the same rule discussed previously. As you all know fractions having the same denominator are known as like fractions. Firstly, we multiply the numerators of the fractions, then the denominators, and finally the fraction is reduced to its lowest terms or we can say it is simplified.

**Example 1** : Multiply 7/5 × 9/5

Solution: We can multiply the fractions by using the following simple steps: –

**Step 1** = First, Multiply the numerators.

= 7 × 9 = 63.

**Step 2** = Then, multiply the denominators.

= 5 × 5 = 25.

**Step 3** = The product of the fractions 7/5 and 9/5 is 63/25 which cannot be simplified.

Hence, 63/25 is the answer.

**Example 2:** Multiply 3/7 × 2/7.

Solution: We can multiply the fractions by using the following simple steps: –

**Step 1** = First, Multiply the numerators.

= 3 × 2 = 6.

**Step 2** = Then, multiply the denominators.

= 7 × 7 = 49.

**Step 3 =** The product of the fractions 3/7 and 2/7 is 6/49 which cannot be simplified.

Hence, 6/49 is the answer.

Read More: METHODS FOR SOLVING QUADRATIC Equations

## Multiplication of Fractions with Different Denominators

Multiplication of fractions with unlike ( fractions having different denominators are known as unlike fractions)denominators is the same as multiplication of like fractions.

Let us understand by using an example.

#### Example 1 : Multiply 3/2 × 6/7.

Solution: We can multiply the fractions by using the following simple steps: –

**Step 1** = First, Multiply the numerators.

= 3 × 6 = 18.

**Step 2 =** Then, multiply the denominators.

= 2 × 7 = 14.

**Step 3** = The product of the fractions 3/2 and 6/7 is 18/14 which can be simplified into 9/7.

Hence, 9/7 is the answer.

Read More : Find your LCM in 10 seconds

## Multiplication of Fractions with Whole Numbers

Multiplication of fractions by whole numbers is a very easy concept. You can multiply the fraction with a whole number by using a few simple steps.

### Steps of Multiplication of Fractions with whole numbers: –

In the case of whole numbers, we write the whole number in the fractional form. For eg: – 5 is written as 5/1 in fraction. You can simply place “1” in the denominator.by placing ‘1’ in the denominator. And then we use the basic rule of multiplication: –

Firstly, multiply the numerator of one fraction by the numerator of another fraction.

Now, multiply the denominators of both fractions.

At last, simplify the fractions if possible.

Let us understand with an example.

#### Example: Multiply: 7 × 3/5.

**Solution:**

**Step 1** = As, 7 is a whole number, it can be written as 7/1. Now, it can be multiplied as simple fractions.

**Step 2** = Now, we have to multiply, 7/1 × 3/5.

**Step 3 =** Firstly, multiply the numerators

= 7 × 3 = 21.

**Step 4** = Now, multiply the denominators.

= 1 × 5 = 5.

**Step 5 =** The product of 7 x ⅗ is 21/5 which cannot be further simplified.

**Step 6** = Hence, 21/5 is the answer.

Read More : Sum of cubes of n natural numbers

**Multiplication of Fractions with Mixed Numbers or fractions**

Mixed numbers or mixed fractions are fractions having a whole number and a proper fraction.

For eg: – 3 ½ , here 3 is the whole number and ½ is the proper fraction.

To multiply fractions with mixed numbers , you simply have to convert the mixed fraction into an improper fraction.

Let us understand the concept with the help of an example.

Example: Multiply 3 ⅕ and 2 ⅔ .

.Solution:

**Step 1** = Firstly, change the mixed fractions to improper fractions.

3 ⅕ = 16/5

2 ⅔ = 8/3

**Step 2** = Now, multiply the numerators of the improper fractions.

= 16 x 8 = 128

**Step 3** = Multiply the denominators now.

= 5 x 3 = 15

**Step 4** = 128/15 cannot be simplified further.

**Step 5** = Now, convert the answer into a mixed fraction or number which is 8 8/15.

**Quizzes: –**

**Question 1** : What is the product of 3/2 and ⅘?

Options:

- 12/5
- 12/2
- 6
**6/5 ( Correct answer)**

**Question 2** : Find the product of 9 x ⅜

Options:

- 27
**27/8 (Correct answer )**- 72/8
- 9

**Question 3** : Which of the following is a product of 1 ½ x 3 ⅓ ?

Options:

**5 ( Correct answer )**- 6/2
- 3/3
- 4 ½

## PRACTICE: –

- ⅗ x 9/5
- 4/7 x ⅗
- 9 x 2/6
- 32 x 14/26
- 2 ⅗ x 4 2/7
- 3 ½ x ⅘
- 3 x 1 ½