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 additive inverse of

The equality

represents that the additive inverse of

or it can be said that

(ii)

The additive inverse of

This equality

represents that
the additive inverse of

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

CUET previous year paper