Exercise 1.1 : Solutions of Questions on Page Number : 14
Q1 : Using appropriate properties find:
(i)
(ii)
Answer :
(i)
(ii)
(By commutativity)
Q2 : Write the additive inverse of each of the following:
(i) 
(ii) 
(iii)
(iv)
(v)
Answer :
(i)
Additive inverse =
(ii)
Additive inverse =
(iii)
Additive inverse =
(iv)
Additive inverse
(v)
Additive inverse
Q3 : Verify that – ( – x) = x for.
(i)
(ii)
Answer :
(i)
The additive inverse of is 
as
This equality
represents that the additive inverse of 
is 
or it can be said that
i.e., – ( – x) = x
(ii)
The additive inverse of is 
as
This equality 
represents that the additive inverse of 
is-
i.e., – ( – x) = x
Q4 : Find the multiplicative inverse of the following.
(i)
(ii) 
(iii)
(iv)
(v)
(vi) – 1
Answer :
(i) – 13
Multiplicative inverse = –
(ii)
Multiplicative inverse =
(iii)
Multiplicative inverse = 5
(iv)
Multiplicative inverse
(v)
Multiplicative inverse
(vi) – 1
Multiplicative inverse = – 1
Q5 : Name the property under multiplication used in each of the following:
(i)
(ii)
(iii)
Answer :
(i)
1 is the multiplicative identity.
(ii) Commutativity
(iii) Multiplicative inverse
Q6 : Multiply 
by the reciprocal of
.
Answer :
Q7 : Tell what property allows you to compute
.
Answer :
Associativity
Q8 : Is 
the multiplicative inverse of
? Why or why not?
Answer :
If it is the multiplicative inverse, then the product should be 1.
However, here, the product is not 1 as
Q9 : Is 0.3 the multiplicative inverse of
? Why or why not?
Answer :
0.3 × = 0.3 ×
Here, the product is 1. Hence, 0.3 is the multiplicative inverse of.
Q10 : 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.
Answer :
(i) 0 is a rational number but its reciprocal is not defined.
(ii) 1 and -1 are the rational numbers that are equal to their reciprocals.
(iii) 0 is the rational number that is equal to its negative.
Q11 : 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
is __________.
(v) The product of two rational numbers is always a __________.
(vi) The reciprocal of a positive rational number is __________.
Answer :
(i) No
(ii) 1, – 1
(iii)
(iv) x
(v) Rational number
(vi) Positive rational number
Exercise 1.2 : Solutions of Questions on Page Number : 20
Q1 : Represent these numbers on the number line.
(i)
(ii)
Answer :
(i) can be represented on the number line as follows.
(ii) can be represented on the number line as follows.
Q2 : Represent
on the number line.
Answer :
can be represented on the number line as follows.
Q3 : Write five rational numbers which are smaller than 2.
Answer :
2 can be represented as
.
Therefore, five rational numbers smaller than 2 are
Q4 : Find ten rational numbers between 
and
.
Answer :
and can be represented as
respectively.
Therefore, ten rational numbers between and are
Q5 : Find five rational numbers between
(i)
(ii)
(iii)
Answer :
(i) can be represented as
respectively.
Therefore, five rational numbers between are
(ii) can be represented as 
respectively.
Therefore, five rational numbers between are
(iii) can be represented as 
respectively.
Therefore, five rational numbers between are
Q6 : Write five rational numbers greater than – 2.
Answer :
– 2 can be represented as –
.
Therefore, five rational numbers greater than – 2 are
Q7 : Find ten rational numbers between
and
.
Answer :
and can be represented as
respectively.
Therefore, ten rational numbers between and are