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

(ii) -3/2 and 5/3 (iii) 1/4 and 1/2

**Solution:**

We can find infinitely many rational numbers between any two given rational numbers by taking the mean of the two rational numbers.

Alternative method: We can make the denominator same for the two given rational numbers.

(i) 2/3 and 4/5

The LCM of both denominators 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) -3/2 and 5/3

The LCM of both denominators 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) 1/4 and 1/2

The LCM of both numbers 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

**Video Solution:**

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

### NCERT Solutions Class 8 Maths - Chapter 1 Exercise 1.2 Question 5

**Summary:**

Find five rational numbers between (i) 2/3 and 4/5 (ii) -3/2 and 5/3 (iii) 1/4 and 1/2 are: (i) 41/60, 42/60, 43/60, 44/60, 45/60, (ii) -8/6, -7/6, 1, 3/6, 5/6, (iii) 9/32, 10/32, 11/32, 12/32, 13/32