# NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Ex 1.1 Class 8 Maths Question 1.

Using appropriate properties find:

Solution:

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

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:

Solution:

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.

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.

(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