Page 72 - Start Up Mathematics_7

–7 11
(c) +
10 15

LCM of 10 and 15 is 30.
We express each rational number with denominator 30.

2
–7 × + 11 × = –21 + 22 = –21 + 22 = 1
3
10 3 15 2 30 30 30 30
–6 –2
(d) +
19 57
LCM of 19 and 57 is 57.

We express each rational number with denominator 57.

–6 3 (–2) 1 –18 (–2) –18 + (–2) –18 – 2 –20
∴ × + × = + = = =
19 3 57 1 57 57 57 57 57
1 3 –7 18
(e) –2 + 3 = +
3 5 3 5

LCM of 3 and 5 is 15.

We express each rational number with denominator 15.

–7 5 18 3 –35 54 –35 + 54 19
∴ × + × = + = =
3 5 5 3 15 15 15 15
3
0
0
0
(f) –1 + 0 = –1 + = –1 + × = –1 + = –1 + 0 = –1
3 3 1 3 1 3 3 3 3 3
Additive inverse of a rational number
p –p
Additive inverse of a rational number q is q .

5 –5 –2 2
For example, additive inverse of is and that of is .
3 3 3 3
Subtraction of Rational Numbers

Case I: Subtraction of rational numbers with same denominators
p r
Let and be two rational numbers to be subtracted:
q q

We add the additive inverse of the rational number that is to be subtracted from the other rational
p r p –r p + (–r) p – r
number, i.e., – = + = =
q q q q q q

Case II: Subtraction of rational numbers with different denominators
(i) Express each rational number with positive denominator.
(ii) Find the LCM of the denominators.

(iii) Find equivalent rational numbers with denominators equal to the LCM obtained.
(iv) Now subtract the rational numbers as in case I.

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