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Multiplicative inverse (reciprocal)

Before learning division of fractions, we need to know the concept of the ‘multiplicative
inverse’. Two numbers are said to be reciprocal to each other, if their product is 1.

2
6
3
For example: × = 3 × 2 = = 1. Knowledge Desk
2 3 2 × 3 6
3 2
So, the reciprocal of is . The reciprocal of 0 does
2 3 not exist.
To find the multiplicative inverse (reciprocal) of a fraction, interchange the positions of the
numerator and denominator.

Example: Find the reciprocal of the following.
( a) 8 (b) 3 ( c) 1 2 ( d) 9
5 7 5
8 8 1
Solution: (a) We can write 8 as . So, the multiplicative inverse of =
1 1 8
3
(b) Multiplicative inverse of = 5
5 3
2 1 × 7 + 2 9 9 7
(c) 1 = = . So, the multiplicative inverse of =
7 7 7 7 9
9
5
(d) Multiplicative inverse of =
5 9
division oF Fractions

division of a Fraction by a whole number

To divide a fraction by a whole number, we multiply the fraction with the multiplicative
inverse (reciprocal) of the whole number.

Rule: Fraction ÷ Whole number = Fraction × Reciprocal of the whole number.
1
1
1
1
Example: Divide by 3 = × Reciprocal of 3 = × = 1
3 3 3 3 9
division of a whole number by a Fraction
To divide a whole number by a fraction, we multiply the whole number with the multiplicative
inverse (reciprocal) of the fraction.
Rule: Whole number ÷ Fraction = Whole number × Reciprocal of the fraction
1 1
Example: 4 ÷ = 4 × Reciprocal of = 4 × 3 = 12
3 3

Example 1: Divide the following.
1 4 1 2
( a) ÷ 3 (b) ÷ 20 (c) 12 ÷ ( d) 15 ÷
5 9 9 5
1
1
1
Solution: (a) 1 ÷ 3 = × Reciprocal of 3 = × = 1
5 5 5 3 15
4
4
( b) 4 ÷ 20 = × Reciprocal of 20 = × 1 = 4 × 1 = 1
9 9 9 20 9 × 20 45
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