Rational Numbers - Solutions 1
CBSE Class –VIII Mathematics
NCERT Solutions
CHAPTER - 1
Rational Numbers (Ex. 1.1)
NCERT Solutions
CHAPTER - 1
Rational Numbers (Ex. 1.1)
Questions
1. Using appropriate properties to find:
(i)

(ii)

Ans. (i)

=
[Using Associative property]

=
[Using distributive property]

=
=

=

=
=
= 2


(ii)

=
[Using Associative property]

=
[Using distributive property]

=

=
=


=
=


2. Write the additive inverse of each of the following:
(i)
(ii)
(iii)
(iv)
(v)





Ans. We know that additive inverse of a rational number
is
such that



(i) Additive inverse of
is
(ii) Additive inverse of
is 




(iii) Additive inverse of
is
(iv) Additive inverse of
is 




(v) Additive inverse of
is 


3. Verify that
for:

(i)
(ii)


Ans. (i) Putting
in 






Hence, verified.
(ii) Putting
in 






Hence, verified.
4. Find the multiplicative inverse of the following:
(i)
(ii)
(iii)



(iv)
(v)
(vi)



Ans. We know that multiplicative inverse of a rational number
is
such that



(i) Multiplicative inverse of
is


(ii) Multiplicative inverse of
is


(iii) Multiplicative inverse of
is


(iv) Multiplicative inverse of
is


(v) Multiplicative inverse of
is


(vi) Multiplicative inverse of
is
= -1


5. Name the property under multiplication used in each of the following:
(i)

(ii)

(iii)

Ans. (i) 1 is the multiplicative identity.
(ii) commutativity property.
(iii) Multiplicative Inverse property.
6. Multiply
by the reciprocal of


Ans. The reciprocal of
is


According to the question,


7. Tell what property allows you to compute


Ans. By using associative property of multiplication,
we will compute as
.

8. Is
the multiplicative inverse of
Why or why not?


Ans. Since multiplicative inverse of a rational number
is
if



Therefore,
=
=



But its product must be positive 1.
Therefore,
is not the multiplicative inverse of


9. Is 0.3 the multiplicative inverse of
Why or why not?

Ans. Since multiplicative inverse of a rational number
is
if 



Therefore,
=
= 1


Therefore, Yes 0.3 is the multiplicative inverse of

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.
Ans.(i) 0
(ii) 1 and

(iii) 0
11. Fill in the blanks:
(i) Zero has ____________ reciprocal.
(ii) The numbers ___________ and __________ are their own reciprocals.
(iii) The reciprocal of
is _____________.

(iv) Reciprocal of
where
is _____________.


(v) The product of two rational numbers is always a ____________.
(vi) The reciprocal of a positive rational number is _______________
Ans. (i) No
(ii) 1,

(iii)

(iv)

(v) Rational Number
(vi) Positive