Division of a Fractional Number

We will discuss here about division of a fractional number by a fractional number.

Now, let us consider the division $\frac{2}{3}$ ÷ $\frac{1}{3}$

= $\frac{\frac{2}{3}}{\frac{1}{3}}$

= $\frac{2}{3}$ × $\frac{1}{\frac{1}{3}}$

= $\frac{2}{3}$ × $\frac{3}{1}$

= $\frac{2}{3}$ × 3

= $\frac{6}{3}$

= 2

Therefore, $\frac{2}{3}$ ÷ $\frac{1}{3}$ = $\frac{2}{3}$ × 3 = 2

Therefore, the rules for the division of a fraction by a fraction is

A Fraction ÷ Another Fraction = First Fraction × Reciprocal of the Second Fraction.

Hence, we conclude that to divide a fractional number by another fractional number, we multiply the first fractional number by the multiplicative inverse of the second fraction number.

1. $\frac{1}{3}$ ÷ $\frac{2}{5}$

[First Fraction × Reciprocal of the Second Fraction]

= $\frac{1}{3}$ × $\frac{5}{2}$

= $\frac{1 × 5}{3 × 2}$

= $\frac{5}{6}$

2. $\frac{6}{19}$ ÷ $\frac{12}{38}$

= $\frac{6}{19}$ × $\frac{38}{12}$

= 1

3. 2$\frac{1}{7}$ ÷ $\frac{7}{2}$

= $\frac{2 × 7 + 1}{7}$ ÷ $\frac{7}{2}$

= $\frac{15}{7}$ ÷ $\frac{7}{2}$

= $\frac{15}{7}$ × $\frac{2}{7}$

= $\frac{15 × 2}{7 × 7}$

= $\frac{30}{49}$

4. 6 2/3 ÷ 4 1/5

= (6 × 3 + 2)/3 ÷ (4 × 5 + 1)/5

= 20/3 ÷ 21/5

= 20/3 × 5/21

= (20 × 5)/(3 × 21)

= 100/63

5. 12/11 ÷ 144/121

= 12/11 × 121/144