Page 60 - ICSE Math 7

EXERCISE 4.1

–1 –5
1. Write three rational numbers equivalent to: (a) and (b) .
3 3
2. Which of the following pairs represent the same rational number?
–3 –21 4 –4 2 –6
(a) and (b) and (c) and
7 49 –5 5 3 9
3. Rewrite the following rational numbers in the simplest form.
–45 34 16
(a) 115 (b) 48 (c) 128

4. Draw a number line and represent the following rational numbers on it.
4 3 –7
(a) 5 (b) 8 (c) 5
5. Compare the following.

(a) 4 and 7 (b) –5 and 7 (c) –19 and 7
15 10 6 –18 24 –18

Addition of rational numbers
Case I: Addition of rational numbers with same denominator
p r
Let and be two rational numbers to be added.
q q
(i) Express each rational number with a positive denominator.
p r p + r
(ii) Add the numerators keeping the denominator same, i.e., + = .
q q q
Case II: Addition of rational numbers with different denominators
(i) Express each rational number with a positive denominator.
(ii) Find the LCM of the denominators.
(iii) Express each rational number with common denominator equal to the LCM obtained.
(iv) Now add the rational numbers as in case I.

Example 9: Find the sum.
–6 –2 1 3 7 –1
(a) + (b) –2 + 3 + (c) + 0
19 57 3 5 15 3

–6 –2
Solution: (a) +
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)
∴ × + × = + = Try This
19 3 57 1 57 57 57
–18 – 2 –20 Find the value of the following.
= = 2 –5 1
57 57 (a) + 3 (b) 6 + 3
3
1 3 –7 18 9 –11 –7 11
(b) –2 + 3 = + (c) + (d) +
3 5 3 5 4 4 10 15
LCM of 3 and 5 is 15.

46