Page 73 - Start Up Mathematics_7

5 13 –6 –7 1
Example 11: Find: (a) – (b) – (c) –3 – 7
12 18 5 15 5
Solution: (a) 5 – 13
12 18
LCM of 12 and 18 is 36.
Express each rational number with denominator 36.
5 × 3 13 × 2 15 26 15 –26
∴ – = – = +
12 × 3 18 × 2 36 36 36 36

15 + (–26 ) 15 – 36 –11
= = =
36 36 36
–6 –7 –6 (–7)
(b) – = –
5 15 5 15
LCM of 5 and 15 is 15.
Express each rational number with denominator 15.

–6 3 (–7) 1 –18 –7 –18 – (–7) –18 + 7 –11
∴ 5 × – 15 × = 15 – 15 = 15 = 15 = 15
3
1
1 –16 7
(c) –3 – 7 = –
5 5 1
LCM of 5 and 1 is 5.
Express each rational number with denominator 5.

–16 × 1 7 × 5 –16 35 –16 –35 –16 – 35 –51
∴ – = – = + = =
5 × 1 1 × 5 5 5 5 5 5 5
29 13
Example 12: What should be added to to get ?
75 15
Solution: We have, Required number + given fraction = 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 13: What should be subtracted from – to get ?
2 3 5
1 1 –1
Solution: We have, – – Required number = 5
3
2
1 –1
⇒ – Required number =
6 5
1 1 5 + 6 11
⇒ Required number = + = =
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

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