Chapter 1 Rational and Irrational Numbers Set 1.2

Question 1.
Compare the following numbers.

Solution:
i. 7, -2
If a and b are positive numbers such that a < b, then -a > -b.
Since, 2 < 7 ∴ -2 > -7

Here, the denominators of the given numbers are not the same.
LCM of 12 and 16 = 48

Alternate method:
15 × 16 = 240
12 × 7 = 84
Since, 240 > 84
∴ 15 × 16 > 12 × 7

Here, the denominators of the given numbers are not the same.
LCM of 8 and 4 = 8

Here, the denominators of the given numbers are not the same.
LCM of 15 and 5 = 15

Here, the denominators of the given numbers are not the same.
LCM of 11 and 4 = 44

Questions and Activities

Question 1.
Verify the following comparisons using a number line. (Textbook pg. no, .3)

Solution:

We know that, on a number line the number to the left is smaller than the other.
∴ 2 < 3 and -3 < -2
i.e. 2 < 3 and -2 > -3