# Chapter 1 Rational Numbers

Exercise 1.1

Ex 1.1 Class 8 Maths Question 1.
Using appropriate properties find:

Solution:

Ex 1.1

Question 2.
Write the additive inverse of each of the following:

(i)
(ii)
(iii)
(iv)
(v)
Solution:

Question 3.
Verify that -(-x) = x for
(i) x =

(ii) x =

Solution:

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
by the reciprocal of .
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 the multiplicative inverse of -1 ? Why or Why not?
Solution:
Here -1
= .
Since multiplicative inverse of
is but not
is not the multiplicative inverse of -1

Ex 1.1 Class 8 Maths

Question 9.
If 0.3 the multiplicative inverse of 3
? Why or why not?
Solution:

Multiplicative inverse of 0.3 or is .
Thus, 0.3 is the multiplicative inverse of 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
[
is not defined]
(ii) Reciprocal of 1 = = 1
Reciprocal of -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 , 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)
(iv) x
(v) rational number
(vi) positive