Class 8 NCERT Solutions – Chapter 1 Rational Numbers – Exercise 1.2
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
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