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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:

Let's convert the given fractions to like fractions by making their denominators equal.

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

(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 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 < -1/6 < 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

☛ Check: NCERT Solutions for Class 7 Maths Chapter 9

Video Solution:

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

Class 7 Maths NCERT Solutions Chapter 9 Exercise 9.1 Question 1

Summary:

(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.

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