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\\November 22, 2023 3:12 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Multiplicative inverse (reciprocal)

Before knowing division of fractions, we need to know the concept of ‘multiplicative inverse’.

Two numbers are said to be reciprocal to each other, if their product is 1.
2
3
6
For example: × = 3 × 2 = = 1.
2 3 2 × 3 6
3 2 Knowledge Desk
So, the reciprocal of is .
2 3 ‘Reciprocal of 0 does not
To find the reciprocal (multiplicative inverse) of a fraction, exist’.

interchange the position 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, multiplicative inverse of =
1 1 8
3
(b) Multiplicative inverse of = 5
3
5
2 1 × 7 + 2 9 9 7
(c) Since, 1 = = . So, 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 reciprocal
(multiplicative inverse) 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 reciprocal
(multiplicative inverse) of the fraction.
rule: Whole number ÷ Fraction = Whole number × Reciprocal of 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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