Exercise 1.1
Question 1- Using appropriate properties find:
(By commutativity)
Question 1- Using appropriate properties find:
(i) 
(ii) 
Answer - (i)
(ii)
(By commutativity)
Question 2- Write the additive inverse of each of the following:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(ii) (iii) (iv) (v)
Answer - (i)
Additive inverse = 
(ii) 
Additive inverse = 
(iii) 
Additive inverse = 
(iv) 
Additive inverse 
(v) 
Additive inverse 
Question 3- Verify that −(−x) = x for.
(i) 
(ii) 
(ii)
Answer - (i)
The additive inverse of is 
as 
is as
This equality represents that the additive inverse of 
is 
or it can be said that 
i.e., −(−x) = x
represents that the additive inverse of is or it can be said that i.e., −(−x) = x
(ii)
The additive inverse of is 
as 
is as
This equality represents that the additive inverse of 
is − i.e., −(−x) = x
represents that the additive inverse of is − i.e., −(−x) = x
Question 4- Find the multiplicative inverse of the following.
(i) 
(ii) 
(iii) 
(ii) (iii)
(iv) 
(v) 
(vi) −1
(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
Question 5- 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
Question 6- Multiply 
by the reciprocal of
.
by the reciprocal of.
Answer - 
Question 7- Tell what property allows you to compute
Answer - Associativity
Question 8- Is 
the multiplicative inverse of
? Why or why not?
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
Question 9- Is 0.3 the multiplicative inverse of
? Why or why not?
? Why or why not?
Answer - 
0.3 × = 0.3 × 
= 0.3 ×
Here, the product is 1. Hence, 0.3 is the multiplicative inverse of.
.
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.
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.
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 
is __________.
, 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
Question 1- Represent these numbers on the number line.
(i) 
(ii) 
(ii)
Answer - (i) can be represented on the number line as follows.
can be represented on the number line as follows.
(ii) 
can be represented on the number line as follows.
can be represented on the number line as follows.
Question 2- Represent 
on the number line.
on the number line.
Answer - can be represented on the number line as follows.
can be represented on the number line as follows.
Question 3- Write five rational numbers which are smaller than 2.
Answer - 2 can be represented as
.
.
Therefore, five rational numbers smaller than 2 are
Question 4- Find ten rational numbers between 
and
.
and.
Answer - and can be represented as 
respectively.
and can be represented as respectively.
Therefore, ten rational numbers between andare
andare
Question 5- Find five rational numbers between
(i) 
(ii) 
(iii) 
Answer - (i) can be represented as
respectively.
can be represented as respectively.
Therefore, five rational numbers between are
are
(ii) 
can be represented as 
respectively.
can be represented as respectively.
Therefore, five rational numbers between are
are
(iii) can be represented as 
respectively.
can be represented as respectively.
Therefore, five rational numbers between are
are
Question 6- Write five rational numbers greater than − 2.
Answer - −2 can be represented as −
.
.
Therefore, five rational numbers greater than −2 are
Question 7- Find ten rational numbers between 
and
.
and.
Answer - and can be represented as 
respectively.
and can be represented as respectively.
Therefore, ten rational numbers between and are
and are