Page 61 - ICSE Math 7

We express each rational number with denominator 15.
–7 5 18 3 7 –35 54 7 –35 + 54 + 7 26 11
∴ × + × + = + + = = = 1
3 5 5 3 15 15 15 15 15 15 15
–1 –1 0 –1 0 3 –1 0 –1 + 0 –1
(c) + 0 = + = + × = + = =
3 3 1 3 1 3 3 3 3 3

Additive inverse of a rational number
p –p
Additive inverse of a rational number is . Try This
q q
5 –5 –2 2 What will be the additive
For example, additive inverse of is and that of is . inverse of –3 ?
3 3 3 3 –5
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.
5 13 –6 –7 1
Example 10: Find: (a) – (b) – (c) –3 – 7
12 18 5 15 5

Solution: (a) 5 – 13 Try This
12 18 Find the value of the following.
LCM of 12 and 18 is 36. 4 2 1 1
5
5
Express each rational number with denominator 36. (a) – (b) 4 – 1 5
9
5 × 3 13 × 2 15 26 15 –26 15 + (–26) 15 – 26 –11
∴ – = – = + = = =
12 × 3 18 × 2 36 36 36 36 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 3 15 1 15 15 15 15 15
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

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