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

= 11/12

6. 5 1/8 ÷ 8 2/16

= (5 × 8 + 1)/8 ÷ (8 × 16 + 2)/16

= 41/8 ÷ 130/16

= 41/8 × 16/130

= 41/65