Page 70 - Start Up Mathematics_7

Example 9: Insert five rational numbers and represent them on a number line in each of the
following:
–1 2
(a) –1 and 0 (b) –3 and –2 (c) and
2 3
Solution: (a) Let’s convert –1 and 0 into rational numbers with denominator 6.
–6 0
i.e., –1 = and 0 =
6 6
–6 0
Five rational numbers between and are
6 6
–6 –5 –4 –3 –2 –1 0
–1 = < < < < < < = 0
6 6 6 6 6 6 6

–1 –5 –4 –3 –2 –1 0
6 6 6 6 6
(b) Let’s convert –3 and –2 into rational numbers with denominator 6
–18 –12
i.e., –3 = and –2 =
6 6
–18 –12
Five rational numbers between and are
6 6
–18 –17 –16 –15 –14 –13 –12
–3 = < < < < < < = – 2
6 6 6 6 6 6 6

–3 –17 –16 –15 –14 –13 –2
6 6 6 6 6
–1 2
(c) and
2 3
LCM of 2 and 3 = 6
We convert both rational numbers with denominator 6.

–1 –1 3 –3 2 2 2 4
∴ = × = and = × =
2 2 3 6 3 3 2 6
–3 4 –2 –1 1 2 3
Rational numbers between and are , , 0, , ,
6 6 6 6 6 6 6

–1 –1 –2 –1 0 1 2 3 2 1
2 6 6 6 6 6 3
EXERCISE 4.1

–1 3
1. List three rational numbers between: (a) –1 and 1 (b) and
2 2
–1 –5
2. Write three rational numbers equivalent to: (a) and (b) .
3 3
3. Which of the following pairs represent the same rational number?

–3 –21 4 –4 2 –6 5 –7
(a) and (b) and (c) and (d) and
7 49 –5 5 3 9 –7 5

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