# NCERT Solutions for Class 8 Math Chapter 1 – Rational Numbers

#### Question 1:

Using appropriate properties find:

(i)

(ii)

(i)

(ii)

(By commutativity)

#### Question 2:

Write the additive inverse of each of the following:

(i) (ii) (iii) (iv) (v)

(i)

(ii)

(iii)

(iv)

(v)

#### Question 3:

Verify that −(−x) = x for.

(i) (ii)

(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

#### Question 4:

Find the multiplicative inverse of the following.

(i) (ii) (iii)

(iv) (v) (vi) −1

(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)

(i)

1 is the multiplicative identity.

(ii) Commutativity

(iii) Multiplicative inverse

#### Question 6:

Multiply by the reciprocal of.

#### Question 7:

Tell what property allows you to compute.

Associativity

#### Question 8:

Is the multiplicative inverse of? Why or why not?

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?

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.

(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 __________.

(v) The product of two rational numbers is always a __________.

(vi) The reciprocal of a positive rational number is __________.

(i) No

(ii) 1, −1

(iii)

(iv) x

(v) Rational number

(vi) Positive rational number

#### Question 1:

Represent these numbers on the number line.

(i) (ii)

(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.

can be represented on the number line as follows.

#### Question 3:

Write five rational numbers which are smaller than 2.

2 can be represented as.

Therefore, five rational numbers smaller than 2 are

#### Question 4:

Find ten rational numbers between and.

and can be represented as respectively.

Therefore, ten rational numbers between andare

#### Question 5:

Find five rational numbers between

(i)

(ii)

(iii)

(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

#### Question 6:

Write five rational numbers greater than − 2.

−2 can be represented as −.

Therefore, five rational numbers greater than −2 are

#### Question 7:

Find ten rational numbers between and.

and can be represented as respectively.

Therefore, ten rational numbers between and are