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

**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:

Ex 1.1 Class 8 Maths Question 2.

Write the additive inverse of each of the following:

(i) \(\frac { 2 }{ 8 }\)

(ii) \(\frac { -5 }{ 9 }\)

(iii) \(\frac { -6 }{ -5 }\)

(iv) \(\frac { 2 }{ -9 }\)

(v) \(\frac { 19 }{ -6 }\)

Solution:

Ex 1.1 Class 8 Maths Question 3.

Verify that -(-x) = x for

(i) x = \(\frac { 11 }{ 5 }\)

(ii) x = \(\frac { -13 }{ 17 }\)

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

Solution:

Ex 1.1 Class 8 Maths Question 7.

Tell what property allows you to compute

Solution:

Since a × (b × c) = (a × b) × c shows the associative property of multiplications.

Ex 1.1 Class 8 Maths Question 8.

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

Solution:

Here -1\(\frac { 1 }{ 8 }\) = \(\frac { -9 }{ 8 }\).

Since multiplicative inverse of \(\frac { 8 }{ 9 }\) is \(\frac { 9 }{ 8 }\) but not \(\frac { -9 }{ 8 }\)

\(\frac { 8 }{ 9 }\) is not the multiplicative inverse of -1\(\frac { 1 }{ 8 }\)

Ex 1.1 Class 8 Maths Question 9.

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

Solution:

Multiplicative inverse of 0.3 or \(\frac { 3 }{ 10 }\) is \(\frac { 10 }{ 3 }\).

Thus, 0.3 is the multiplicative inverse of 3\(\frac { 1 }{ 3 }\).

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

[∵ \(\frac { 1 }{ 0 }\) is not defined]

(ii) Reciprocal of 1 = \(\frac { 1 }{ 1 }\) = 1

Reciprocal of -1 = \(\frac { 1 }{ -1 }\) = -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 \(\frac { 1 }{ x }\), 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) \(\frac { -1 }{ 5 }\)

(iv) x

(v) rational number

(vi) positive