Page 31 - Start Up Mathematics_8 (Non CCE)

Example 47: Find four rational numbers between –4 and 8.

1
1
Solution: Add –4 and 8 and multiply by , i.e., ×− ( 48+ ) = 1 × 4 = 2
2 2 2
So, the first rational number = 2 (∴ –4, 2, 8)
1
1
Add –4 and 2 and multiply by , i.e., ×− ( 42+ ) = 1 × −( 2 = −) 1
2 2 2
So, the second rational number = –1 (∴ –4, –1, 2, 8)
1
1
Add 2 and 8 and multiply by , i.e., ×( 28+ ) = 1 × 10 5=
2 2 2
So, the third rational number = 5 (∴ –4, –1, 2, 5, 8)

1 1 1 1 − 5
{
41 } =
Add –4 and –1 and multiply by , i.e., ×− { 4 +− } =( 1) × −− × − ( 5) =
2 2 2 2 2
−5
So, the fourth rational number =
2
−5 −5
–4, , –1, 2, 5, 8 or –4 < < –1 < 2 < 5 < 8
2 2

EXERCISE 1.9
1. Represent the following rational numbers on a number line:
3 −2 1 4 −5
(a) (b) (c) (d) (e)
5 3 4 7 8
−9 1 1 8 3
(f) (g) 2 (h) −3 (i) (j) −4
11 3 4 5 4
−2 1
2. Find two rational numbers between and .
3 4
3. Write four rational numbers less than 2.
−3 5
4. Find five rational numbers between and .
2 3
5. Write five rational numbers greater than –2.
3 3
6. Find ten rational numbers between and .
5 4
−2 −1
7. Find three rational numbers between and .
3 3

At a Glance
p p p × n pn
1. (a) If q is a rational number and n is an integer with n ≠ 0, then q = q × n = qn .

p p p ÷ n
(b) If q is a rational number and n is an integer with n ≠ 0, then q = q ÷ n .

p r
2. q = s only when (p × s) = (q × r)

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