Find five rational numbers between (i) 2/3 and 4/5 (ii) -3/2 and 5/3 (iii) 1/4 and 1/2

Find five rational numbers between  (i) 2/3 and 4/5 (ii) -3/2 and 5/3 (iii) 1/4 and 1/2

Source: NCERT CLASS 8 Maths Chapter 1 Rational Numbers Exercise 1.2 Question 5

Solution:

(i) Find five rational numbers between 2/3 and 4/5

The LCM of both denominators i.e. 3 and 5 is 15.

We shall multiply the numbers to get the denominator as a multiple of 15.

Multiplying both the numerator and denominator of 2/3 by 20, we get

2/3 = 2/3 × 20/20 = 40/60

Multiplying both the numerator and denominator of 4/5 by 12, we get

4/5 = 4/5 × 12/12 = 48/60

The five rational numbers between 2/3 and 4/5 can be taken as:

41/60, 42/60, 43/60, 44/60, 45/60

(ii) Find five rational numbers between -3/2 and 5/3 

The LCM of both denominators i.e. 2 and 3 is 6.

So we shall multiply the numbers to get the denominator as a multiple of 6

Multiplying both the numerator and denominator of -3/2 by 3, we get

-3/2 = -3/2 × 3/3 = -9/6

Multiplying both the numerator and denominator of 5/3 by 2, we get

5/3 = 5/3 × 2/2 = 10/6

The five rational numbers between -3/2 and 5/3 can be taken as:

-8/6, -7/6, 1, 3/6, 5/6

(iii) Find five rational numbers between 1/4 and 1/2

The LCM of both denominators i.e. 4 and 2 is 8.

So we shall multiply the numbers to get the denominator as a multiple of 8

Multiplying both the numerator and denominator of 1/4 by 8, we get

1/4 = 1/4 × 8/8 = 8/32

Multiplying both the numerator and denominator of 1/2 by 16, we get

1/2 = 1/2 × 16/16 = 16/32

The five rational numbers between 1/4 and 1/2 can be taken as:

9/32, 10/32, 11/32, 12/32, 13/32