Page 14 - Maths Skills - 8

12 Maths

63
6 2 2
Similarly, standard form of

21 21 3 7 7
Clearly, 2 2
9 7
Hence, the given rational numbers are not equal.

Example 6: Show that −15 and 24 are equal.
40 − 64

Solution: Given rational numbers are −15 and 24 .
40 − 64
Now, check whether: Numerator of first rational number × Denominator of second rational number
= Numerator of second rational number × Denominator of first rational number
i.e., – 15 × (– 64) = 960 and 40 × (24) = 960
Clearly, – 15 × (– 64) = 40 × 24

Hence, 15 24 .
40 64

Example 7: Are the rational numbers − 35 15 and 185 equal? 3 63, 27, 333
,
− 63 27 333 3 21, 9, 111
3 7, 3, 37
− 35 35 15 185
Solution: Given rational numbers are or , and 7 7, 1, 37
− 63 63 27 333
LCM of 63, 27 and 333 is 3 × 3 × 3 × 7 × 37 = 6993 37 1, 1, 37
1, 1, 1
To make the denominators equal,

35 35 111 3885
= [ 6993 ÷ 63 = 111]

63 63 111 6993
15 15 259 3885
Similarly, = [ 6993 ÷ 27 = 259]

27 27 259 6993
and 185 = 185 21 3885 [ 6993 ÷ 333 = 21]

6993
333 21
333
Hence, the three rational numbers are equal.

Exercise 1.1

1. Draw the number line and represent the following rational numbers on it.

(i) − 3 (ii) 5 (iii) − 2 3 (iv) − 7 (v) 6 1
7 12 4 − 9 5

(vi) 15 (vii) −7 1 (viii) 13 (ix) 22 (x) 5 3
− 5 5 7 4
7
2. Arrange the following in ascending order.

3 − 4 − 15 − 11 19 4 6 1 − 2
(i) , , , , (ii) 0 ,, − ,,
10 15 28 20 30 7 9 7 10