# 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 2/3 ÷ 1/3

= 2/3 / 1/3

= 2/3 × 3/1/3 × 3

= 2/3 × 3/1

= 2/3 × 3

= 6/3

= 2

Therefore, 2/3 ÷ 1/3 = 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. 1/3 ÷ 2/5

[First Fraction × Reciprocal of the Second Fraction]

= 1/3 × 5/2

= (1 × 5)/(3 × 2)

= 5/6

2. 6/19 ÷ 12/38

= 6/19 × 38/12

= 1

3. 2 1/7 ÷ 7/2

= (2 × 7 + 1)/7 ÷ 7/2

= 15/7 ÷ 7/2

= 15/7 × 2/7

= (15 × 2)/(7 × 7)

= 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