# List five rational numbers between

(i) -1 and 0

(ii) -2 and -1

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

(iv) -1/2 and 2/3

**Solution:**

These questions can be solved easily with the concept of like fractions. First, make the fractions like by making their denominators equal.

You can make the denominator equal either by taking LCM of the denominator or by multiplying both numerator and denominator by the same integer.

Steps:

(i) -1 and 0

Multiplying both denominator and numerator by 6, we get:

(-1 × 6)/(1 × 6) = -6/6,

(0 × 6)/(1 × 6) = 0/6

Five rational numbers between -1 and 0 are

-6/6 < -5/6 < -4/6 < -3/6 < -2/6 < -1/6 < 0/6

-1 < -5/6 < -4/6 < -3/6 < -2/6 < -1/6 < 0

Thus five rational numbers between -1 and 0 are

-5/6 , -2/3 , -1/2 , -1/3 , -1/6

(ii) -2 and -1 Multiplying both numerator and denominator by 6 , we get

(-2 × 6)/(1 × 6) = (-12/6) , (-1 × 6)/(1 × 6) = -(6/6)

Five rational numbers between -2 -2 and -1 -1 are,

-12/6 < -11/6 < -10/6 < -9/6 < -8/6 < -7/6 < -6/6

-2 < -11/6 < -10/6 < -9/6 < -8/6 < -7/6 < -1

Thus, the five rational numbers between -2 and -1 are -11/6, -5/3, -3/2, -4/3, -7/6

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

Converting -4/5 and -2/3 into like fractions, we get

-4/5 = (-4 × 9)/(5 × 9) = (-36/45)

-2/3 = (-2 × 15)/(3 × 15) = -30/45

Five rational numbers between -4/5 and -2/3 are,

-36/45 < -35/45 < -34/45 < -33/45 < -32/45 < -31/45 < -30/45

-4/5 < -35/45 < -34/45 < -33/45 < -32/45 < -31/45 < -2/3

Thus, the five rational numbers between -4/5 and -2/3 are, -7/9 , -34/45 , -11/15 , -32/45 , -31/45

(iv) -1/2 and 2/3

Converting -1/2 and 2/3 into like fractions, we get

-1/2 = (-1 × 3)/(2 × 3)

= (-3/6)

2/3 = (2 × 2)/(3 × 2)

= (4/6)

Five rational numbers between -1/2 and 2/3 are,

-3/6 < -2/6 < -/6 < 0 < 2/6 < 3/6 < 4/6

Therefore, the five rational numbers between -1/2 and 2/3 are, -1/3, -1/6, 0, 1/3, 1/2

**Video Solution:**

### Class 7 Maths NCERT Solutions -Chapter 9 Exercise 9.1 Question 1

List five rational numbers between (i) -1 and 0 (ii) -2 and -1 (iii) -4/5 and -2/5 (iv) -1/2 and 2/3

(i) The five rational numbers between -1 and 0 are -5/6 , -2/3 , -1/2 , -1/3 , -1/6 (ii) The five rational numbers between -2 and -1 are -11/6 , -5/3 , -3/2 , -4/3 , -7/6 (iii) The five rational numbers between -4/5 and -2/3 are, -7/9 , -34/45 , -11/15 , -32/45 , -31/45 (iv) The five rational numbers between -1/2 and 2/3 are, -1/3, -1/6, 0, 1/3, 1/2