Formula for Dividing Fractions

Before going to know what is the formula for dividing fractions, let us recall what is division. The division is dividing/distributing things equally among several things/people. We already know how to divide a whole number by another number. Here, we will learn how to divide fractions using the formula for dividing fractions.

What Is the Formula for Dividing Fractions?

For dividing one fraction by another, we always keep the first (dividend) fraction the same, flip the second (divisor) fraction, and change the division symbol into the multiplication symbol. This method can be remembered using the phrase KFC (Keep Flip Change). Thus, the formula for dividing fractions using KFC is:

Important Note: If we have an integer instead of a fraction here, then we write 1 in its denominator. For example, if we have 2, we write it as 2 / 1.

Example: Divide 2 / 5 by 4 / 7.

Solution:

Using the formula for dividing fractions:

2 / 5 ÷ 4 / 7 = 2 / 5 × 7 / 4 = 14 / 20 = 7 / 10

Answer: Therefore, 2 / 5 ÷ 4 / 7 = 7 / 10.

Let us see more applications of the formula for dividing fractions in the solved examples section below.

Examples Using Formula for Dividing Fractions

Example 1: A pizza is divided into 4 parts to share it equally among 4 children. But one of the children doesn't like pizza and he gives away his part to his 3 friends equally. Then what fraction of pizza is eaten by each of these 3 children apart from the part that they already had?

Solution:

To find: The extra part of pizza eaten by each of 3 children.

The fraction of pizza shared to each of the 4 children = 1 / 4.

It is given that one such fraction is divided equally among 3 friends. 

Using the formula for dividing fractions, the fraction of pizza obtained by each of these 3 friends is,

1 / 4 ÷ 3 = 1 / 4 ÷ 3 / 1 = 1 / 4 × 1 / 3 = 1 / 12

Answer: The extra part of pizza eaten by each of 3 children = 1 / 12.

Example 2: The area of a rectangular room is 45 3/4 square feet. If the length of the room is 5 1/2 ft then what is its width?

Solution:

To find: To find the width of the room.

It is given that:

• Area of the room = 45 3/4 square feet = 183 / 4 square feet.
• Length = 5 1/2 ft = 11 / 2 ft.

We know that area of a rectangle is length × width. From this, width = area / length. 

Using the formula for dividing fractions,

Width = 183 / 4 ÷ 11 / 2

= 183 / 4 × 2 / 11

= 183 / 22

= 8 (7/22) ft

Answer: The width of the room = 8 (7 22) ft.