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 Associative property]
= 
[Using distributive property]
[Using distributive property]
=
= 
= 
= 
= 
= 2
= = 2
(ii)
= 
[Using Associative property]
[Using Associative property]
= 
[Using distributive property]
[Using distributive property]
= 
= 
= 
=
= 
= 
=
2. Write the additive inverse of each of the following:
(i) 
(ii)
(iii)
(iv)
(v)
(ii) (iii) (iv) (v)
Ans. We know that additive inverse of a rational number 
is 
such that 
is such that
(i) Additive inverse of is 
(ii) Additive inverse of is 
is (ii) Additive inverse of is
(iii) Additive inverse of is 
(iv) Additive inverse of is 
is (iv) Additive inverse of is
(v) Additive inverse of is 
is
3. Verify that 
for:
for:
(i)
(ii)
(ii)
Ans. (i) Putting in 
in 
L.H.S. = R.H.S.
Hence, verified.
(ii) Putting 
in
in 
L.H.S. = R.H.S.
Hence, verified.
4. Find the multiplicative inverse of the following:
(i)
(ii)
(iii)
(ii) (iii)
(iv)
(v)
(vi)
(v) (vi)
Ans. We know that multiplicative inverse of a rational number 
is 
such that 
is such that
(i) Multiplicative inverse of is 
is
(ii) Multiplicative inverse of is 
is
(iii) Multiplicative inverse of is 
is
(iv) Multiplicative inverse of 
is 
is
(v) Multiplicative inverse of 
is 
is
(vi) Multiplicative inverse of is 
= -1
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 
by the reciprocal of
Ans. The reciprocal of 
is 
is
According to the question,
= 
7. Tell what property allows you to compute
as 
Ans. By using associative property of multiplication,
we will compute as 
.
.
8. Is 
the multiplicative inverse of 
Why or why not?
the multiplicative inverse of Why or why not?
Ans. Since multiplicative inverse of a rational number is if
is if
Therefore,
= 
=
= =
But its product must be positive 1.
Therefore, is not the multiplicative inverse of 
is not the multiplicative inverse of
9. Is 0.3 the multiplicative inverse of 
Why or why not?
Why or why not?
Ans. Since multiplicative inverse of a rational number is if
is if
Therefore,
= 
= 1
= = 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 _____________.
is _____________.
(iv) Reciprocal of 
where 
is _____________.
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
