Page 81 - ICSE Math 6

Reciprocals
1 x
If x is a natural number, then is its reciprocal. Similarly, if is a Maths Info
y x y
fraction, then is its reciprocal. The product of a number and
x its reciprocal is always 1.

Example 20: Find the reciprocal of the following fractions.

7 3
(a) (b) 2
9 5
7 9 3 (2×5) 3+ 13
Solution: (a) Reciprocal of = (b) As, 2 = =
9 7 5 5 5

3 5
\ Reciprocal of 2 =
5 13

a 7 b
Example 21: If = , then find . Maths Info
b 10 a
x a y b
a 7 b 10 If = , then = .
Solution: As = , \ = y b x a
b 10 a 7

Division of fractions
Multiply the first fraction (dividend) by the reciprocal of the other fraction (divisor) to get the result.

Example 22: Divide.
2 4 3 1 3
(a) by (b) 1by (c) 2 by1
3 5 5 3 4

2 4 25 1 2 ×5 5 3 5 1×5 5
Solution: (a) ÷ = × = = (b) 1÷ = 1× = =
3 5 3 4 3× 4 2 6 5 3 1×3 3

1 (2×3) 1+ 7 3 (1×4) 3+ 7
(c) As, 2 = = and 1 = =
3 3 3 4 4 4

1 3 7 7 7 4 7 ×4 4 1
\ 2 ÷ 1 = ÷ = × = = = 1
3 4 3 4 3 7 3× 7 3 3
Operation ’of’

The word ‘of’ written in between two fractions is to be treated just like multiplication. It is solved
before multiplication and division in a given expression.

Example 23: Evaluate.
3 4 10
(a) of 6 (b) of
2 5 11

3 3 3× 6 3 4 10 4× 10 2 8
Solution: (a) of 6 = ×6 = = 9 (b) of = =
2 2 2 1 5 11 1 5 ×11 11

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