How to do Division of Fraction?

Keep-Switch-Flip is the basic rule for dividing fractions, which means Keep the first number, Switch the division sign to the multiplication sign, and Flip the other number. We can also say that to divide a fraction, the following steps are involved:

• Find the multiplicative inverse of the second fraction (or number).
• Multiply the first fraction by the second fraction.
• Simplify the result if needed.

We can divide a fraction with another fraction, a mixed fraction, or a whole number. Further in this article, we will learn about the division of fractions with a whole number and, the division of fractions with other fractions or mixed fractions.

Division of a Fraction by a Whole Number

To find a division of a fraction with a whole number we can simply multiply the whole number with the denominator of the fraction or we can follow these steps:

Steps involved in the division of a fraction with a whole number

• First, find the multiplicative inverse of the whole number by taking 1 as its denominator.
• Reduce the fraction to its lowest term.
• Then multiply the fraction with the new divisor(i.e. the multiplicative inverse of the whole number).
• Lastly, reduce the result to its lowest term.

Let’s take an example for better understanding.

Question: Divide 7/5 by 14.

Solution:

Step 1: Find the multiplicative inverse of 14/1, which is 1/14.

Step 2: Reduce the fraction to its lowest term.

7/5 is already in its lowest term

Step 3: Find the product of 7/5 and 1/14:

7/5 × 1/14 = 7/70.

Step 4: Reduce the result to its lowest term

The lowest term of 7/70 is 1/10

Hence, 7/5 ÷ 14 = 1/10.

​Division of a Whole Number by a Fraction

While dividing a whole number with a fraction, we can follow these simple steps:

Steps involved in the division of a whole number with a fraction

• First, find the multiplicative inverse of the fraction.
• Reduce the fraction to its lowest term.
• Then multiply the whole number with the new divisor(i.e. the multiplicative inverse of the fraction).
• Lastly, reduce the result to its lowest term.

Question: Divide 8 by 4/14.

Solution:

Step 1: Find the multiplicative inverse of 4/14, which is 14/4.

Step 2: Reduce the fraction to its lowest term.

The lowest term of 14/4 is 7/2

Step 3: Find the product of 8 and 7/2:

8 × 7/2 = 56/2.

Step 4: Reduce the result to its lowest term

The lowest term of 56/2 is 28/1 = 28

Hence, 8 ÷ 4/14 = 28.

Division of a Fraction by Fraction

We can easily Divide a fraction with another fraction by following these simple steps:

Steps involved in the division of fraction by fraction

• First, find the multiplicative inverse of the divisor (or the second fraction).
• Reduce both fractions to their lowest term.
• Then, multiply the dividend with the new divisor.
• Lastly, reduce the result to its lowest term.

Question: Divide 3/5 by 15/6.

Solution:

Step 1: Find the reciprocal of 15/6, which is 6/15

Step 2: Reduce both fractions to their lowest term.

3/5 is already in its lowest term and the lowest term of 6/15 = 2/5

Step 3: Find the product of 3/5 and 6/15:

3/5 × 2/5 = 6/25.

Step 4: Reduce the result to its lowest term

6/25 is already in its lowest term.

Hence, 3/5 ÷ 15/6 = 6/25.

Division of a Fraction by a Mixed fraction

In this case, we first convert the mixed fraction to an improper fraction, the rest of the steps are the same as a division of a fraction with a fraction.

Steps involved in the division of a fraction by a mixed fraction

• First, convert the mixed fraction into an improper fraction.
• Then, find the multiplicative inverse of the divisor (or the second fraction).
• Reduce both fractions to their lowest term.
• Then, multiply the dividend with the new divisor.
• Lastly, reduce the result to its lowest term.

Question: Divide 2/5 by 1 5/6.

Solution:

Step 1: Convert mixed fraction to improper fraction

1 5/6 = 11/6

Step 2: Find the reciprocal of 11/6, which is 6/11

Step 3: Reduce both fractions to their lowest term.

2/5 and 6/11 are already in their lowest term

Step 4: Find the product of 2/5 and 6/11:

2/5 × 6/11 = 12/55.

Step 5: Reduce the result to its lowest term

12/55 is already in its lowest term

Hence, 2/5 ÷ 1 5/6 = 12/55.

Division Of Fractions by Decimal

For the division of decimals and fractions, we first convert the decimal number into a fraction and then multiply the reciprocal of the divisor with the dividend.

Steps involved in the division of a fraction with a decimal

• First, convert the decimal into a fraction.
• Then, find the multiplicative inverse of the divisor (or the second fraction).
• Reduce both fractions to their lowest term.
• Then, multiply the dividend with the new divisor.
• Lastly, reduce the result to its lowest term.

Question: Divide 6/20 by 0.12

Solution:

Step 1: Convert the decimal into a fraction

0.12 = 12/100

Step 2: Find the reciprocal of 12/100, which is 100/12

Step 3: Reduce both fractions to their lowest term.

The lowest term of 6/20 is 3/10 and the lowest term of 100/12 is 25/3.

Step 4: Find the product of 3/10 and 25/3:

3/10 × 25/3 = 75/30.

Step 5: Reduce the result to its lowest term

The lowest term of 75/30 is 5/2.

Hence, 6/20 ÷ 0.12 = 5/2.

Division means sharing something equally. For example, if we divide 20 sweets equally among 5 children, each child will get 4 sweets. Similarly, Division of fractions means dividing a fraction into equal parts. Like if we want to divide 2/3 of the cake among 6 people, each person will get 2/3 ÷ 6 = 1/9 part of the cake. For division in fractions, we multiply the first fraction with the reciprocal of the second fraction.

In this article, we will learn about fractions, the reciprocal of fractions, the division of a fraction with whole numbers, another fraction, and decimals along with some solved examples for better understanding.