# Rational Numbers-NCERT Solutions

NCERT SOLUTIONS FOR RATIONAL NUMBERS
Exercise 1.1

Question 1:
Using appropriate properties Find:
(i)
(ii)
Solution:
(i)

(ii)

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

Question 3:
Verify that –(–x) = x for.
(i)
(ii)
Solution:
(i)

The equality
represents that the additive inverse of
or it can be said that

(ii)

This equality represents that
i.e., –(–x)=x

Question 4:
Find the multiplicative inverse of the following.
(i)       -13
(ii)
(iii)
(iv)
(v)
(vi)       -1
Solution:
(i)
(ii)
(iii)
(iv)
(v)
(vi)

Question 5:
Name the property under multiplication used in each of the following:
(i)
(ii)
(iii)
Solution:
(i)
1 is the multiplicative identity.
(ii)      Commutativity
(iii)    Multiplicative inverse

Question 6:
Multiply by the reciprocal of
Solution:

Question 7:
Tell what property allows you to compute

Solution:
Associativity

Question 8:
Is the multiplicative inverse of Why or why not?
Solution:
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?
Solution:

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.
Solution:
(i)       0 is a rational number but its reciprocal is not defined.
(ii)      1 and –1are 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 x ≠ 0 is _________.
(v)       The product of two rational numbers is always a _________.
(vi)       The reciprocal of a positive rational number is _________.
Solution:
(i)       Zero has no reciprocal.
(ii)      The numbers 1, and –1 are their own reciprocals.
(iii)    The reciprocal of –5 is
(iv)    The reciprocal of where x ≠ 0 is x.
(v)       Rational number
(vi)       Positive Rational number
Exercise 1.2

Question 1:
Represent these numbers on the number line:
(i)
(ii)
Solution:
(i)        can be represented on the number line as follows.
(ii)       can be represented on the number line as follows.

Question 2:
Represent on the number line.
Solution:
can be represented on the number line as follows.

Question 3:
Write five rational numbers which are smaller than 2.
Solution:
2 can be represented as
Therefore, five rational numbers smaller than 2 are:

Question 4:
Find ten rational numbers between
Solution:
can be represented as respectively.
Therefore, ten rational numbers between are

Question 5:
Find five rational numbers between
(i)
(ii)
(iii)
Solution:
(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 and

Question 6:
Write five rational numbers greater than –2.
Solution:
–2 can be represented as
Therefore, five rational numbers greater than –2 are

Question 7:
Find ten rational numbers between

Solution:
can be represented as
Therefore, ten rational numbers between are
NCERT SOLUTIONS FOR RATIONAL NUMBERS