NCERT Solutions | Class 8 Maths Chapter 1 | Rational Numbers

CBSE Solutions | Maths Class 8

Check the below NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Pdf free download. NCERT Solutions Class 8 Maths were prepared based on the latest exam pattern. We have Provided Rational Numbers Class 8 Maths NCERT Solutions to help students understand the concept very well.

NCERT | Class 8 Maths

NCERT Solutions Class 8 Maths
Book:	National Council of Educational Research and Training (NCERT)
Board:	Central Board of Secondary Education (CBSE)
Class:	8th
Subject:	Maths
Chapter:	1
Chapters Name:	Rational Numbers
Medium:	English

Rational Numbers | Class 8 Maths | NCERT Books Solutions

You can refer to MCQ Questions for Class 8 Maths Chapter 1 Rational Numbers to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Exercise 1.1

Ex 1.1 Class 8 Maths Question 1.
Using appropriate properties find. 5
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 1

Solution:

Ex 1.1 Class 8 Maths Question 2.

Write the additive inverse of each of the following:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 4

Solution:

Ex 1.1 Class 8 Maths Question 3.

Verify that – (-x) = x for:
(i) \(x=\frac { 11 }{ 15 } \)
(ii) \(x=-\frac { 13 }{ 17 } \).

Solution:

Ex 1.1 Class 8 Maths Question 4.

Find the multiplicative inverse of the following:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 8

Solution:

Ex 1.1 Class 8 Maths Question 5.

Name the property under multiplication used in each of the following:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 11

Solution:

(i) Existence of multiplicative identity.
(ii) Commutative property of multiplication.
(iii) Existence of multiplicative inverse.

Ex 1.1 Class 8 Maths Question 6.

Multiply \(\frac { 6 }{ 13 } \) by the reciprocal of \(\frac { -7 }{ 16 } \).

Solution:

Ex 1.1 Class 8 Maths Question 7.

Tell what property allows you to compute.
\(\frac { 1 }{ 3 } \times \left( 6\times \frac { 4 }{ 3 } \right) as\left( \frac { 1 }{ 3 } \times 6 \right) \times \frac { 4 }{ 3 } \)

Solution:

Associative property of multiplication over rational numbers allows us to compute :
\(\frac { 1 }{ 3 } \times \left( 6\times \frac { 4 }{ 3 } \right) as\left( \frac { 1 }{ 3 } \times 6 \right) \times \frac { 4 }{ 3 } \)

Ex 1.1 Class 8 Maths Question 8.

Is \(\frac { 9 }{ 8 } \) the multiplicative inverse of – 1 \(\frac { 1 }{ 8 } \)? Why or why not?

Solution:

No, \(\frac { 9 }{ 8 } \) is not the multiplicative inverse of -1 \(\frac { 1 }{ 8 } \).
Because \(\frac { 8 }{ 9 } \times -1\frac { 1 }{ 8 } =\frac { 8 }{ 9 } \times \frac { -9 }{ 8 } =-1\neq 1\).

Ex 1.1 Class 8 Maths Question 9.

Is 0.3 the multiplicative inverse of 3\(\frac { 1 }{ 3 } \)? Why or why not?

Solution:

Yes, 0.3 is multiplicative inverse of 3\(\frac { 1 }{ 3 } \).
Because \(0.3\times 3\frac { 1 }{ 3 } =\frac { 3 }{ 10 } \times \frac { 10 }{ 3 } =1\).

Ex 1.1 Class 8 Maths Question 10.

Write:
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.

Solution:

(i) We know that there is no rational number which when multiplied with 0, gives 1. Therefore, the rational number 0 has no reciprocal.
(ii) We know that the reciprocal of 1 is 1 and the reciprocal of -1 is -1. 1 and -1 are the only rational numbers which are their own reciprocals.
(iii) The rational number 0 is equal to its negative.

Ex 1.1 Class 8 Maths Question 11.

Fill in the blanks :
(i) Zero has ……………. reciprocal.
(ii) The numbers ……………. and ………. are their own reciprocals.
(iii) The reciprocal of – 5 is …………….
(iv) Reciprocal of \(\frac { 1 }{ x } \), where ≠0 is ………
(v) The product of two rational numbers is always a ………….
(vi) The reciprocal of a positive rational number is ………..

Solution:

(i) No,
(ii) 1, -1,
(iii) \(\frac { -1 }{ 5 } \)
(iv) x,
(v) rational number,
(vi) positive.

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

Ex 1.2 Class 8 Maths Question 1.

Represent these numbers on the number line.
(i) \(\frac { 7 }{ 4 } \)
(ii) \(\frac { -5 }{ 6 } \)

Solution:

(i) For \(\frac { 7 }{ 4 } \), we make 7 markings of distance each on the right of zero and starting from 0. The seven marking is \(\frac { 7 }{ 4 } \).
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 13

The point P represents the rational number —.
(ii) For \(\frac { -5 }{ 6 } \), we make 5 markings of distance \(\frac { 1 }{ 6 } \) each on the left of zero and starting from 0. The fifth marking \(\frac { -5 }{ 6 } \) The point P represents the 6 rational number \(\frac { -5 }{ 6 } \).
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 14

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 14

Ex 1.2 Class 8 Maths Question 2.

Represent \(\frac { -2 }{ 11 } ,\frac { -5 }{ 11 } ,\frac { -9 }{ 11 } \) on the number line.

Solution:

To represent \(\frac { -2 }{ 11 } ,\frac { -5 }{ 11 } ,\frac { -9 }{ 11 } \) on a number line, draw a number line and mark a point O on it to represent zero. Now, mark a point P representing integers -1 on the left side of O on the number line.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 15

Divide the segment OP into eleven equal parts. Let A, B, C, D, E, F, G, H, I, J be the points of division so that OA=AB =BC = … = JP. By construction, OB is two-eleventh of OP so B represents \(\frac { -2 }{ 11 } \) OE is five-eleventh of OP so E represents \(\frac { -5 }{ 11 } \) and OI is nine-eleventh of OP so I represents \(\frac { -9 }{ 11 } \).

Ex 1.2 Class 8 Maths Question 3.

Write five rational numbers, which are smaller than 2.

Solution:

Five rational numbers less than 2 may be taken
\(1,\frac { 1 }{ 2 } ,0,-1,\frac { -1 }{ 2 } \)
(There can be many more such rational numbers.)

Ex 1.2 Class 8 Maths Question 4.

Find ten rational numbers between \(\frac { -2 }{ 5 } \) and \(\frac { 1 }{ 2 } \).

Solution:

Converting the given rational numbers with the same denominators
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 16

Ex 1.2 Class 8 Maths Question 5.

Find five rational numbers between
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 17

Solution:

(i) Converting the given rational numbers with the same denominators
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 18

(ii) Converting the given rational numbers with the same denominators
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 19

(iii) Converting the given rational numbers with the same denominators
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 21

Ex 1.2 Class 8 Maths Question 6.

Write five rational numbers greater than – 2.

Solution:

Five rational numbers greater than -2 may be taken as
\(-\frac { 3 }{ 2 } ,-1,\frac { -1 }{ 2 } ,0,\frac { 1 }{ 2 } \)
There can be many more such rational numbers.