This document contains NCERT solutions for Class 8 Maths Chapter 1 on Rational Numbers. It includes solutions to 11 questions from Exercise 1.1 that involve finding additive and multiplicative inverses of rational numbers, identifying properties used in multiplication, determining if a number is its own reciprocal, and filling in blanks about rational numbers and their reciprocals. The questions cover key concepts about rational numbers such as their properties and operations involving addition, subtraction, multiplication and division.

1. NCERT Solutions for Class 8 Maths
Chapter 1 Rational Numbers
October 28, 2020 by Sastry CBSE
NCERT Solutions for Class 8 Maths Chapter
1 Rational Numbers
 Class 8 Maths Rational Numbers Exercise 1.1
 Class 8 Maths Rational Numbers Exercise 1.2
 Rational Numbers Class 8 Extra Questions
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:
Solution:

2. Ex 1.1 Class 8 Maths Question 2.
Write the additive inverse of each of the following:
(i) 28
(ii) −59
(iii) −6−5
(iv) 2−9
(v) 19−6

3. Solution:
Ex 1.1 Class 8 Maths Question 3.
Verify that -(-x) = x for
(i) x = 115
(ii) x = −1317
Solution:
Ex 1.1 Class 8 Maths Question 4.
Find the multiplicative inverse of the following:

4. Solution:

5. Ex 1.1 Class 8 Maths Question 5.
Name the property under multiplication used in each of the following:
Solution:
(i) Commutative property of multiplication
(ii) Commutative property of multiplication
(iii) Multiplicative inverse property
Ex 1.1 Class 8 Maths Question 6.
Multiply 613 by the reciprocal of −716.

6. Solution:
Ex 1.1 Class 8 Maths Question 7.
Tell what property allows you to compute
Solution:
Since a × (b × c) = (a × b) × c shows the associative property of multiplications.
Ex 1.1 Class 8 Maths Question 8.
Is 89 the multiplicative inverse of -118? Why or Why not?
Solution:
Here -118 = −98.
Since multiplicative inverse of 89 is 98 but not −98
89 is not the multiplicative inverse of -118
Ex 1.1 Class 8 Maths Question 9.
If 0.3 the multiplicative inverse of 313? Why or why not?
Solution:
Multiplicative inverse of 0.3 or 310 is 103.
Thus, 0.3 is the multiplicative inverse of 313.
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) 0 is the rational number which does not have its reciprocal
[∵ 10 is not defined]
(ii) Reciprocal of 1 = 11 = 1
Reciprocal of -1 = 1−1 = -1
Thus, 1 and -1 are the required rational numbers.
(iii) 0 is the rational number which is equal to its negative.
Ex 1.1 Class 8 Maths Question 11.
Fill in the blanks.

7. (i) Zero has ……….. reciprocal.
(ii) The numbers ……….. and ……….. are their own reciprocals.
(iii) The reciprocal of -5 is ………
(iv) Reciprocal of 1x, where x ≠ 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 and 1
(iii) −15
(iv) x
(v) rational number
(vi) positive