Class 7 - Division Of Fractions

Division of fractions is a fundamental concept in mathematics that helps solve a wide range of problems. Unlike addition or subtraction, for division of fractions, you multiply that whole number by the reciprocal of that fraction. 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 division of fractions.

Table of Contents

• How to Divide Fractions
• Rules to Divide Fractions
• Division of Whole Numbers by Fractions
• Division of Fractions by Whole Numbers
• Division of Fractions with Fractions
• Frequently Asked Questions on Division of Fractions

How to Divide Fractions

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by interchanging the fraction's numerator and denominator.
Formula: $\frac{a​}{b}÷\frac{d​}{c}​=\frac{a​}{b}×\frac{c}{d} = \frac{a​c}{bd}​$

Rules to Divide Fractions

1. Do not divide directly: You cannot divide fractions directly. Always convert division into multiplication using the reciprocal.

2. Reciprocal is essential: The reciprocal of a fraction is obtained by  simply flipping it

3. Simplify when possible: Before or after multiplying, simplify the fractions to make calculations easier.

4. Convert mixed fractions first: If a fraction is in mixed form, convert it into an improper fraction before dividing.

5. If the result is an improper fraction, convert it into a mixed number if required.

Division of whole numbers by fractions

To divide a whole number by any fraction, we multiply that whole number by the reciprocal of that fraction.

• To divide a whole number by a mixed fraction, we first convert the mixed fraction into an improper fraction and then multiply the whole number by the reciprocal of the improper fraction.

Let us look at a few examples of division of whole numbers by fractions.
Example 1: Divide  $4÷\frac{2}{3}$
Solution: $4÷\frac{2}{3} = 4× \frac{3}{2} = 6$

Example 2: Divide$16 ÷\frac{2}{3}$
Solution: $16÷\frac{2}{3} =  16×\frac{3}{2} =  8×3 = 24$

Example 3: Divide  $6 ÷ 5\frac{1}{3}$
Solution: $6 ÷ 5\frac{1}{3} = 6 ÷ \frac{16}{3}$

$= 6 × \frac{3}{16} = \frac{6 × 3}{16} = \frac{9}{8}$

Converting  $\frac{9}{8}$to improper fraction we get  $6 ÷ 5\frac{1}{3} = 1\frac{1}{8}$

 

Division of fractions by whole numbers

To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number.

 

• To divide a mixed fraction by a whole number, convert the mixed fraction into an improper fraction, and then multiply it by the reciprocal of the whole number.

Let us look at a few examples of division of fractions by whole numbers.

Example 1: Divide  $\frac{2}{3} ÷ 12$
Solution:  $\frac{2}{3} ÷ 12 =  \frac{2}{3} ×  \frac{1}{12}$
 $=  \frac{1}{18}$

Example 2: Divide $5\frac{1}{3} ÷ 12$
Solution: Converting  $5\frac{1}{3}$to improper fractions we get $\frac{16}{3}$
 $5\frac{1}{3} ÷ 12  =  \frac{16}{3} ÷ 12$
 $=  \frac{16}{3}  × \frac{1}{12}$ $=  \frac{4}{9}$

Division of fractions with fractions

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction. 

 

• To divide a mixed fraction by another fraction, convert the mixed fraction into an improper fraction, and then multiply the first fraction by the reciprocal of the second fraction. 

Let us look at a few examples of division of fractions by whole numbers.

Example 1: Divide $\frac{9}{7} ÷ \frac{12}{7}$
Solution:  $\frac{9}{7} ÷ \frac{12}{7} =  \frac{9}{7} ×  \frac{7}{12}$
 $= \frac{9}{12} = \frac{3}{4}$

Example 2: Divide  $\frac{5}{6} ÷ 2\frac{1}{3}$
Solution: Converting  $2\frac{1}{3}$ into improper fractions we get $\frac{7}{3}$
 $\frac{5}{6} ÷ 2\frac{1}{3} =  \frac{5}{6} ÷ \frac{7}{3}$=   $\frac{5}{6} × \frac{3}{7}$
 $=  \frac{5}{14}$

Example 3: Divide  $7\frac{1}{2} ÷ 3\frac{1}{2}$
Solution: Converting to improper fractions,
 $7\frac{1}{2} ÷ 3\frac{1}{2} = \frac{15}{2} ÷ \frac{7}{2}$
 $= \frac{15}{2}  ×  \frac{2}{7}$
 $=   \frac{15}{7}$