Class 7 - Multiplication Of Fractions

Multiplication of fractions is a fundamental concept in mathematics that helps solve a wide range of problems. Unlike addition or subtraction, to multiply fractions, you simply multiply the numerators and denominators. Understanding this concept is essential to work with ratios, proportions, and real-life calculations. In this guide, you’ll learn easy steps, key rules, and clear examples to master the multiplication of fractions .

Table of Contents

• How to Multiply Fractions
• Rules for Multiplying Fractions
• Understanding ‘of’ in Fractions (Multiplication Concept)
• Multiplication of fractions with whole numbers
• Multiplication of fractions with fractions
• Multiplication of Mixed Fractions
• Frequently Asked Questions on Multiplication of Fractions

 

How to Multiply Fractions

Multiplying fractions is different from adding or subtracting them. It does not require the denominators to be the same. Any two fractions can be multiplied directly, even with different denominators. However, it is important to first convert mixed fractions into either proper or improper fractions before multiplying them. 

Steps:

1. Multiply the numerators (top numbers)

2. Multiply the denominators (bottom numbers)

3. Simplify the fraction to the lowest form, if possible.

Basic formula:

$\frac{a​}{b}×\frac{c}{d}​= \frac{a×c}{b×d}​$

Rules for Multiplying Fractions

For multiplying fractions, follow the rules given below:

• There is no requirement for a common denominator. Just multiply numerators and denominators directly.

• Simplify Before Multiplying (Cross-Cancellation): Cancel common factors to make the calculation easier and faster.

• Mixed fractions must be converted into improper fractions before multiplication.

• Keep the answer in the simplest form: Always reduce your final answer to the simplest form possible.
  
  

Understanding ‘of’ in Fractions (Multiplication Concept)

Consider 6 flowers and divide them between two flower vases. We divide them into two equal groups of 3 flowers each in each vase. Three flowers are half of the total of 6 flowers.

 

3 can be written as 1/2 of 6

$\frac{1}{2}×6 = \frac{6×1}{2} = 3$

We can write it as, 1/2 of 6 = 3

The operator ‘of’ represents multiplication.

Let us consider another example: Riya has a chocolate cake. She eats 1/2 of 1/4 the chocolate cake.

 

1/2 of 1/4 of chocolate cake = $\frac{1}{2}×\frac{1}{4}  = \frac{1}{8}$
i.e., she ate \frac{1}{8} of the chocolate cake.

 

Multiplication of fractions with whole numbers

Multiplication is repeated addition. Multiplication of fractions with whole numbers is similar to that of multiplication in whole numbers.

Let us multiply  $3×\frac{1}{4}  = \frac{1}{4} +  \frac{1}{4}+ \frac{1}{4} =  \frac{3}{4}$
Or we can directly multiply the numerators and denominators to obtain  $3×\frac{1}{4} = \frac{3× 1}{4} = \frac{3}{4}$

Let us look at a few more examples of multiplication of fractions with whole numbers 

Example 1:   $3×\frac{2}{5}  =  \frac{3×2}{5} = \frac{6}{5}$

Example 2:  $\frac{3}{4} of 100 =  \frac{3}{4}× 100 = \frac{3× 100}{4}  =  \frac{300}{4}$
Further simplifying the fractions we get  $\frac{300}{4} = 75$

Multiplication of fractions with fractions

Multiplication of a fraction by another fraction means that one of the fractions is broken down further by the other fraction. To multiply a fraction by another fraction, multiply the numerators and denominators of the fractions separately.

• When two proper fractions are multiplied, the product is less than each of the fractions.

Let us look at a few examples of multiplication of fractions by another fraction.

Example 1: Multiplication of Proper Fractions:

Multiply $\frac{5}{7} ×\frac{1}{6}$
 $\frac{5}{7} ×\frac{1}{6}  =  \frac{5 × 1 }{ 7×6} =  \frac{5}{42}.$

Example 2: Multiplication of Improper Fractions:

Multiply $\frac{4}{3} ×\frac{7}{5}$
 $\frac{4}{3} ×\frac{7}{5}  =  \frac{4 × 7 }{ 3×5} =  \frac{28}{15}.$

Example 3 : $Multiply \frac{2}{3} ×\frac{9}{4}$
 $\frac{2}{3} ×\frac{9}{4}  = \frac{1}{1} ×\frac{3}{2}$( simpifying the fractions)
 $=  \frac{1 × 3 }{ 1×2} =  \frac{3}{2} = 1\frac{1}{2}.$
Converting to mixed fractions,  $\frac{3}{2} = 1\frac{1}{2}$.

 

Multiplication of Mixed Fractions

When multiplying mixed fractions, we need to change the mixed fractions into an improper fraction before multiplying. 

• When two improper fractions are multiplied, their product is greater than each of the two fractions.

Let us look at a few examples of the multiplication of improper fractions.

Example 1:  $Multiply  3\frac{2}{5}× 6\frac{6}{9}$
Converting to improper fractions ,  $3\frac{2}{5}× 6\frac{6}{9}= \frac{17}{5}× \frac{60}{9}$

$\frac{17}{5}× \frac{60}{9} = \frac{340}{15}= 22\frac{2}{3}$

Example 2: If the cost of 1 kg of sugar is ₹  $7\frac{3}{4},$ what will be the cost of 28 kg of sugar?

Solution: Given, Cost of 1 kg of sugar is Rs  $7\frac{3}{4}$. 
The cost of 28 kg  =  $7\frac{3}{4}× 28$

$7\frac{3}{4}× 28 = \frac{31}{4}× 28 = \frac{31× 28}{4}$

∴ 31× 7 = 217

∴ The cost of 28 kg of sugar is ₹217.

Example 3: If a farmer ploughs $9\frac{1}{6}$square metres in an hour, how much area will he plough in  $1\frac{8}{10}$hours?

Solution: Given,the farmer ploughs  $9\frac{1}{6}$square metres of area in an hour

Area he will plough in $1\frac{8}{10}$hours = $9\frac{1}{6}× 1\frac{8}{10}$square metres.
= $\frac{55}{6}×  \frac{18}{10}$square metres

= $\frac{55× 18}{6×10}$  square metres

=  $11× \frac{3}{2}$square metres =   $\frac{33}{2}$square metres
=  $16 \frac{1}{2}$ square metres

Therefore, the farmers will plough  $16 \frac{1}{2}square$ metres in $1\frac{8}{10}$ hours.