NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 , has been designed by the NCERT to test the knowledge of the student on the following topics :  

  • Representation of Rational Numbers on the Number Line
  • Rational Numbers between Two Rational Numbers




NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 image 1 NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 image 2




NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 image 3 NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 image 4

NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 Rational Numbers

1.1 Introduction

Q.1 Represent these numbers on the number line.
(i) \cfrac { 7 }{ 4 }

(ii) \cfrac { -5 }{ 6 }

Solution:

(i)  Representing  \cfrac { 7 }{ 4 } on number line : – 

We take 7 markings at a distance \cfrac { 1 }{ 4 } each on the right of zero and starting from zero (The number of markings required to be taken are equal to the value of the numerator, , i.e, 7  in this case) . The seventh marking is \cfrac { 7 }{ 4 }

NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 Question 1i

(ii) Representing  \cfrac { -5 }{ 6 } on number line:

We make 5 markings at a distance \cfrac { 1 }{ 6 } each on the left of zero and starting from zero (The number of markings required to be taken are equal to the value of the numerator, i.e, 5 in this case ). The fifth marking is \cfrac { -5 }{ 6 }

NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 Question 1ii




Q.2 Represent \cfrac { -2 }{ 11 } , \cfrac { -5 }{ 11 } , \cfrac { -9 }{ 11 }  on the number line.

Solution:

We make 11 markings at a distance \cfrac { 1 }{ 11 } each on the left of zero and starting from zero. The second marking is \cfrac { -2 }{ 11 } the fifth marking is \cfrac { -5 }{ 11 } and the ninth marking is \cfrac { -9 }{ 11 }

NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2 Question 2

Q.3 Write five rational numbers which are smaller than 2.

Solution:

2 can be represented as \cfrac { 10 }{ 5 }
Five rational numbers smaller than 2 are \cfrac { 9}{ 5 } , \cfrac { 8 }{ 5 } , \cfrac { 7 }{ 5 } , \cfrac { 6 }{ 5 } , \cfrac { 5 }{ 5 }

Q.4 Find ten rational numbers between \cfrac { -2 }{ 5 } and \cfrac { 1 }{ 2 }

Solution:

\cfrac { -2 }{ 5 } can also be written as \cfrac { -8 }{ 20 } and \cfrac { 1 }{ 2 } can also be written as\cfrac { 10 }{ 20 }
So, any ten rational numbers lying between \cfrac { -8 }{ 10 } , \cfrac { 10 }{ 20 } are ten rational numbers between \cfrac { -2 }{ 5 } and \cfrac { 1 }{ 2 }
Therefore, ten rational numbers between \cfrac { -2 }{ 5 } and \cfrac { 1 }{ 2 }
\cfrac { -7 }{ 20 } , \cfrac { -6 }{ 20 } , \cfrac { -5 }{ 20 } , \cfrac { -4 }{ 20 } , \cfrac { -3 }{ 20 } , \cfrac { -2 }{ 20 } , \cfrac { -1 }{ 20 } , 0, \cfrac { 1 }{ 20 } , \cfrac { 2 }{ 20 }
(There can be many more such rational numbers)

Q.5 Find five rational numbers between
(i)  \cfrac { 2 }{ 3 } and \cfrac { 4 }{ 5 }
(ii) \cfrac { -3 }{ 2 } and \cfrac { 5 }{ 3 }
(iii) \cfrac { 1 }{ 4 } and \cfrac { 1 }{ 2 }

Solution:

(i) \cfrac { 2 }{ 3 } can be written as \cfrac { 40 }{ 60 } and \cfrac { 4 }{ 5 } can be written as \cfrac { 48 }{ 60 }
Therefore, five rational numbers between \cfrac { 2 }{ 3 } and \cfrac { 4 }{ 5 }
\cfrac { 41 }{ 60 } , \cfrac { 42 }{ 60 } , \cfrac { 43 }{ 60 } , \cfrac { 44 }{ 60 } , \cfrac { 45 }{ 60 }
(There can be many more such rational numbers)

(ii) \cfrac { -3 }{ 2 } can be written as \cfrac { -9 }{ 6 } and \cfrac { 5 }{ 3 } can be written as \cfrac { 10 }{ 6 }
Therefore, five rational numbers between \cfrac { -3 }{ 2 } and \cfrac { 5 }{ 3 }
\cfrac { -8 }{ 6 } , \cfrac { -7 }{ 6 } , 0, \cfrac { 1 }{ 6 } , \cfrac { 2 }{ 6 }
(There can be many more such rational numbers)

(iii) \cfrac { 1 }{ 4 } can be written as \cfrac { 8 }{ 32 } and \cfrac { 1 }{ 2 } can be written as \cfrac { 1 }{ 6 }
Therefore, five rational numbers between \cfrac { 1 }{ 4 } and \cfrac { 1 }{ 2 }
\cfrac { 9 }{ 32 } , \cfrac { 10 }{ 32 } , \cfrac { 11 }{ 32 } , \cfrac { 12 }{ 32 } , \cfrac { 13 }{ 32 }
(There can be many more such rational numbers)

Q.6 Write five rational numbers greater than -2

Solution:

-2 can also be written as \cfrac { -10 }{ 5 }
Therefore, five rational numbers greater than -2 are
\cfrac { -9 }{ 5 } , \cfrac { -8 }{ 5 } , \cfrac { -7 }{ 5 } , \cfrac { -6 }{ 5 } , \cfrac { -5 }{ 5 }
(There can be many more such rational numbers)

Q.7 Find ten rational numbers between \cfrac { 3 }{ 5 } and \cfrac { 3 }{ 4 }

Solution:
\cfrac { 3 }{ 4 } can also be written as \cfrac { 60 }{ 80 } and \cfrac { 3 }{ 5 } can also be written as \cfrac { 48 }{ 80 }
Therefore, ten rational numbers between \cfrac { 3 }{ 5 } and \cfrac { 3 }{ 4 }
\cfrac { 49 }{ 80 } , \cfrac { 50 }{ 80 } , \cfrac { 51 }{ 80 } , \cfrac { 52 }{ 80 } , \cfrac { 53 }{ 80 } , \cfrac { 54 }{ 80 } , \cfrac { 55 }{ 80 } , \cfrac { 56 }{ 80 } , \cfrac { 57 }{ 80 } , \cfrac { 58 }{ 80 }
(There can be many more such rational numbers)




The next Exercise for NCERT Solutions for Class 8 Maths Chapter 2 Exercise 2.1 – Linear Equation in two Variables can be accessed by clicking here .

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

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