8th Maths 1.2

Chapter 1

Rational Numbers

NCERT Class 10th solution of Exercise 1.1

Exercise 1.2

Q1. Represent these numbers on the number line. (i) `7/4` (ii) `-5/6`

Q3. Write five rational numbers which are smaller than `2`.

Solution :

Five rational numbers which are smaller than `2`

`-1, -1/2, 0, 1/2, 1`

Answer :

`-1, -1/2, 0, 1/2, 1`

Q4. Find ten rational numbers between `-2/5` and `1/2`.

Solution :

`LCM` of `5` and `2` is `10`.

`-2/5=(-2times4)/(5times4)=-8/20`

`1/2=(1times10)/(2times10)=10/20`

`-8/20, -7/20, -6/20, -5/20, -4/20, -3/20, -2/20, -1/20, 0/20, 1/20, 2/20,..10/20.`

Answer :

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

Q5. 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`

`LCM` of `3` and `5` is `15`

`2/3=(2times5)/(3times5)=10/15=(10times3)/(15times3)=30/45`

`4/5=(4times3)/(5times3)=12/15=(12times3)/(15times3)=36/45`

`30/45, 31/45, 32/45, 33/45, 34/45, 35/45, 36/45`

Answer :

`31/45, 32/45, 33/45, 34/45, 35/45`

ii) `-3/2` and `5/3`

`LCM` of `2` and `3` is `6`.

`-3/2=(-3times3)/(2times3)=-9/6`

`5/3=(5times2)/(3times2)=10/6`

`-9/6, -8/6, -7/6, -6/6, -5/6, -4/6,....10/6`

Answer :

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

iii) `1/4` and `1/2`

`LCM` of `4` and `2` is `4`.

`1/4=(1times1)/(4times1)=1/4=(1times8)/(4times8)=8/32`

`1/2=(1times2)/(2times2)=2/4=(2times8)/(4times8)=16/32`

`8/32, 9/32, 10/32, 11/32, 12/32, 13/32,...16/32`

Answer :

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

Q6. Write five rational numbers greater than `-2`.

Solution :

Five rational numbers greater than `-2`,

`-1, -1/2, 0, 1/2, 1`

Answer :

`-1, -1/2, 0, 1/2, 1`

Q7. Find ten rational numbers between `3/5` and `3/4`.

Solution :

`LCM` of `5` and `4` is `20`

`3/5=(3times4)/(5times4)=12/20=(12times8)/(20times8)=96/160`

`3/4=(3times5)/(4times5)=15/20=(15times8)/(20times8)=120/160`

`96/160, 97/160, 98/160, 99/160, 100/100, 101/160, 102/160, 103/160, 104/160, 105/160,` 

`106/160,...120/160`

Answer :

`97/160, 98/160, 99/160, 100/100, 101/160, 102/160, 103/160, 104/160, 105/160, 106/160`