Page 62 - ICSE Math 7

29 13
Example 11: What should be added to to get ?
75 15
Solution: We have, Required number + given number = 13
15
29 13
Thus, Required number + 75 = 15

13 29 65 – 29 36 12
⇒ Required number = – = = =
15 75 75 75 25

1 1 –1
Example 12: What should be subtracted from – to get ?
2 3 5
1 1 –1
Solution: We have, – – Required number =
2 3 5
1 –1
⇒ – Required number =
6 5
1
1
⇒ Required number = + = 5 + 6 = 11
6 5 30 30
Multiplication of rational numbers

Multiplication of rational numbers is similar to the multiplication of fractions.

Product of numerators p r p × r
Product of rational numbers = , i.e., × =
Product of denominators q s q × s
Points to remember
• To multiply a rational number and an integer, we multiply the numerator of the rational number
p p r p × r p × r
with the integer, keeping the denominator same, i.e., × r = × = = .
q q 1 q × 1 q
p r r p
• Multiplication of rational numbers is commutative, i.e., × = × .
q
s
s
q
• When a rational number is multiplied by 0, the product is always 0, i.e.,
p p 0 p × 0 0
• × 0 = × = = = 0.
q q 1 q × 1 q
Example 13: Find the following products.

9 –7 3 5 2 2 –5
(a) × (b) × (–9) (c) × (d) ×
4 5 11 11 5 –5 2
9 –7 9 × (–7) –63 3 3 –9 3 × –9 –27
Solution: (a) × = = (b) × (–9) = × = =
4 5 4 × 5 20 11 11 1 11 × 1 11

5 2 5 × 2 10 2 2 –5 2 × –5 –10
(c) × = = = (d) × = = = 1
11 5 11 × 5 55 11 –5 2 –5 × 2 –10
Reciprocal of a rational number
The reciprocal of a non-zero rational number is its multiplicative Try This
p q 3 7
inverse, i.e., reciprocal of is . For example, reciprocal of is
q p 7 3 What will be the reciprocal of
–7
–5 11 –11 ?
and reciprocal of is , i.e., 12
11 –5 5

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