Rational Numbers: Exercise 2

Question 1. Represent these numbers on the number line?

(i) 7/4 (ii) -5/6

Solution:

(i) In number line we have to cover zero to positive integer 1 which signifies the whole no 1, after that we have to divide 1 and 2 into 4 parts and we have to cover 3 places away from 0, which denotes 3/4. And the total of seven places away from 0 represents 7/4. P represents 7/4.

(ii) For representing – 5/6 we have to divide 0 to – 1 integer into 6 parts and we have to go 5 places away from 0 for – 5/6.

Question 2. Represent – 2/11, -5/11, -9/11 on the number line?

Solution:

We have to divide 0 to – 1 integer into 11 parts and the distance of 2, 5, 9 from 0 towards the left of it represents – 2/11, -5/11, -9/11 marked A,  B, C,  respectively. 

Question 3. Write five rational numbers that are smaller than 2?

Solution:

We can write the number 2 as 6 / 3

Hence, we can write, the five rational numbers which are smaller than 2 are:

1 / 3 , 2 / 3 , 3 / 3 , 4/ 3 , 5 / 3

Question 4. Find ten rational numbers between – 2/5 and 1/2?

Solution:

For finding rational numbers between fractions we have to take L. C. M. of their denominators or its multiples. Here L. C. M. Of 5 and 2 is 10 and for finding fractions between them we have to take multiple of 10. Let us take 20 as denominator. 

So,

-2 / 5 = (- 2 / 5) × (4 / 4) = -8 / 20

Also,

1 / 2 = (1 / 2)  × (10 / 10) = 10 / 20

Hence ten rational numbers between – 2 / 5 to 1 / 2 are same as rational numbers between – 8 / 20 and 10 / 20. And those are as follows

-7 / 20, -6 / 20, -5 / 20, -4 / 20, -3 / 20, -2 / 20, -1 / 20, 0, 1 / 20, 2 / 20 

Question 5. Find five rational numbers between

(i) 2/3 and 4/5   (ii) – 3/2 and 5/3  (iii)1/4 and 1/2

Solution:

(i) 2 / 3 and 4 / 5

For finding rational numbers between fractions we have to take L. C. M. of their denominators or its multiples.

Here L. C. M. Of 3 and 5 is 15

And we take the denominators as multiple of 15, as 60

Hence

2 / 3 = ( 2 / 3 ) × ( 20 / 20 ) = 40 / 60

4 / 5 = ( 4 / 5 ) × ( 12 / 12 ) = 48 / 60

Five rational numbers between 2 / 3 and 4 / 5 same as five rational numbers between

40 / 60 and 48 / 60

Therefore, Five rational numbers between 40 / 60 and 48 / 60 are as follows

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

(ii) -3 / 2 and 5 / 3

Similarly, 

L. C. M. of 2 and 3 is 6.

Here we take denominators same as 6. 

-3 / 2 = ( -3 / 2 ) × ( 3 / 3 ) = -9 / 6

5 / 3 = ( 5 / 3 ) × ( 2 / 2 ) = 10 / 6

Hence five rational numbers between -3 / 2 and 5 / 3 are same as five rational numbers between -9 / 6 and 10 / 6 and those are  as follows

-8 / 6, -7 / 6, -1, -5 / 6, -4 / 6

(iii) 1 / 4 and 1 / 2

Here L. C. M. of 4 and 2 is 8.

Here we take denominator as multiple of 8 say 32.

Hence

1 / 4 = ( 1 / 4 ) × (8 / 8) = 8 / 32

1 / 2 = ( 1 / 2 ) × ( 16 / 16 ) = 16 / 32

Hence five rational numbers between 1 / 4 and 1 / 2 are same as five rational numbers between 8/32 and 16/32 and those are as follows

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

Question 6. Write five rational numbers greater than –2?

Solution:

We can write -2 as  -10 / 5 

Hence  five rational numbers greater than -2 are as follows

-1 / 5, -2 / 5, -3 / 5, -4 / 5 ,-1

Question 7. Find ten rational numbers between 3/5 and 3/4?

Solution:

L .C. M. of 4 and 5 is 20. For finding rational number between them we should make denominator same or multiple of L .C.M. 

Here we take 80.

3 / 5 = ( 3 / 5) × ( 16 / 16 ) = 48 / 80

3 / 4 = ( 3 / 4 ) × ( 20 / 20 ) = 60 / 80

Ten rational numbers between 3 / 5 and 3 / 4 are same as ten rational numbers between 48 / 80 and 60 / 80

Ten rational numbers between 48 / 80 and 60 / 80 are as follows 

49 / 80, 50 / 80, 51 / 80, 52 / 80, 54 / 80, 55 / 80, 56 / 80, 57 / 80, 58 / 80, 59 / 80

NCERT Solutions for Class 8 Maths Chapter 1- Rational Numbers is a resourceful article which was developed by GFG experts to aid students in answering questions they may have as they go through problems from the NCERT textbook.

This chapter contains the following topics:

• Rational Number
• Operations on Rational Numbers
  • Addition and subtraction of Rational Numbers
  • Multiplication and division of Rational Numbers
• Properties of Rational Numbers
  • Closure Property
  • Commutative Property
  • Associative Property
  • Distributive Property
  • Identity Property
  • Inverse Property
• Properties of Whole Numbers
• Properties of Integers
• Negative of a Number
• Reciprocal
• Representation of Rational Numbers on the Number Line
• Rational Numbers between Two Rational Numbers