# 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) 65
(iv) 29
(v) 196
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 = 11 = -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

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