Page 33 - ICSE Math 7

Multiplication

To multiply a fraction by one or more whole numbers or fractions, follow the given steps.
(a) Multiply the corresponding numerators to get the numerator of the resulting fraction.
(b) Multiply the corresponding denominators to get the denominator of the resulting fraction.

(c) Reduce the resulting fraction by cancelling the common factors from the numerator and denominator.
Alternatively, cancel out the common factors from the numerator and denominator of the fractions
and then multiply to get the required product.
Example 10: Multiply.
4
3
1
(a) 1 × 20 (b) 3 × 1 (c) 6 × × 3 3
8 4 5 12 5
5
1× 20
1
5
Solution: (a) 1 × 20 = × 20 = = = 2 1
8 8 1 2 8 ×1 2 2
3 15 ×9
15
4
3
3
9
(b) 3 × 1 = × = = 27 = 6
4 5 4 5 4× 5 4 4
1 3 6 1 18 6 ×1× 18 9 9 4
(c) 6 × × 3 = × × = = = 1
12 5 1 12 5 1× 12 ×5 5 5
2
Reciprocal of a fraction
The reciprocal or the multiplicative inverse of a given fraction can be obtained by interchanging the
numerator and denominator of the fraction. When the product of two fractions is 1, each fraction is
7
7
8
8
the reciprocal of the other. For example, is the reciprocal of , i.e., × = 1.
8 7 7 8
Example 11: Find the reciprocal of the following fractions.
5 4 1
(a) (b) 2 (c) 3
9 5 7
5
Solution: (a) Reciprocal of = 9 Maths Info
9 5
4
(b) Reciprocal 2 = Reciprocal of 14 = 5 To find the reciprocal of a
mixed fraction, convert it into
5 5 14 an improper fraction and then
1 22 7 interchange its numerator and
(c) Reciprocal of 3 = Reciprocal of =
7 7 22 denominator.
Division

To divide a fraction by another fraction, multiply the first fraction (dividend) by the reciprocal of the
second fraction (divisor) to get the result.

Example 12: Divide.
9 14 7 2 1
(a) by 3 (b) by (c) 2 by 1
10 15 25 7 14
1
Solution: (a) 9 ÷ 3 = 9 ×   Reciprocal of 3is 1 
10 10 3   3  

3 9 ×1 3
= =
10× 3 10

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