Fractions

Multiplication and Division of Fractions

Multiplication of fractions

To multiply fractions, there is no need to have the same denominators. We can multiply any fractions by the following steps.

Step 1: If there is a whole number, write the whole number in the form of a fraction with denominator 1.

Step 2: Multiply the numerators.

Step 3: Multiply the denominators.

Step 4: Simplify the new fraction.

Multiplication of fraction and a whole number

Example:

Question: Find the product: x 4

Answer:

Step 1: Write the whole number in the form of a fraction.

4 =

Step 2: Multiply the numerators.

4 × 3 = 12

Step 3: Multiply the denominators.

1 × 4 = 4

We can do steps 2 and 3 as:

x = =

Step 4: Simplify the new fraction.

HCF of 4 and 12 = 4

Divide numerator and denominator by 4.

= = = 3
Therefore, x = 3

Visual representation:

The fraction is repeated 4 times. (Multiplication is repeated addition.)
x 4 So, 4 of is 3

Multiplication of two fractions

Example:

Question: Find the product: x

Answer:

Step 1: Multiply the numerators.

Step 2: Multiply the denominators.

x = =
So, of is

Visual representation:

Division of Fractions

To do division of fractions, we need to know the term ‘reciprocal of a fraction’.

Reciprocal of a fraction:

• Reciprocal of a fraction is the fraction obtained by interchanging the numerator and denominator with each other.
• The product of a fraction with its reciprocal is always 1

Example:

Reciprocal of is
Reciprocal of is
Reciprocal of 5 is (We can write 5 as .)

Steps for division of fractions:

Step 1: If there is a whole number, write the whole number in the form of a fraction

Step 2: Find the reciprocal of the second fraction.

Step 3: Multiply the first fraction and reciprocal of the second fraction.

Examples:

Question 1: ÷ 2 = ?

Answer:

÷ 2 = x (Here, is the reciprocal of the 2.)
÷2= x = =

Now, simplify the answer.

HCF of 9 and 24 = 3

Divide both numerator and denominator by 3.

=
So, ÷ 2 =

Visual representation:

Question 2: ÷ =?

Answer:

Step 1: Find the reciprocal of the second fraction.

Step 2: Multiply the first fraction and the reciprocal of the second fraction.

÷ = x = =

Step 3: Simplify the fraction.

HCF of 45 and 36 = 9

Divide both numerator and denominator by 9.

= So, ÷ = =1

Visual representation: