NCERT Solutions for Class 8 Math Chapter 1 Rational Numbers are provided here with simple step-by-step explanations. These solutions for Rational Numbers are extremely popular among Class 8 students for Math Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the NCERT Book of Class 8 Math Chapter 1 are provided here for you for free.You will also love the ad-free experience on SOFT DATA SOLUTIONS NCERT Solutions. All NCERT Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

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**CLASS 8 CH 1 RATIONAL NUMBERS FREE PDF DOWNLOAD NCERT SOLUTIONS**

#### Page No 14:

#### Question 1:

Using appropriate properties find:

(i)

(ii)

#### ANSWER:

(i)

(ii)

(By commutativity)

#### Page No 14:

#### Question 2:

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

#### Page No 14:

#### Question 3:

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*

#### Page No 14:

#### Question 4:

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

#### Page No 14:

#### 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

#### Page No 14:

#### Question 6:

Multiply by the reciprocal of.

#### ANSWER:

#### Page No 14:

#### Question 7:

Tell what property allows you to compute.

#### ANSWER:

Associativity

#### Page No 14:

#### Question 8:

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

#### Page No 14:

#### Question 9:

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.

#### Page No 15:

#### 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.

#### Page No 15:

#### 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 __________.

#### ANSWER:

(i) No

(ii) 1, −1

(iii)

(iv) *x*

(v) Rational number

(vi) Positive rational number

#### Page No 20:

#### Question 1:

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.

#### Question 4:

Find ten rational numbers between and.

#### ANSWER:

and can be represented as respectively.

Therefore, ten rational numbers between andare

#### Page No 20:

#### Question 5:

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

#### Page No 20:

#### Question 6:

Write five rational numbers greater than − 2.

#### ANSWER:

−2 can be represented as −.

Therefore, five rational numbers greater than −2 are

#### Page No 20:

#### Question 7:

Find ten rational numbers between and.

#### ANSWER:

and can be represented as respectively.

Therefore, ten rational numbers between and are

#### Question 8:

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

NCERT Solution for Class 8 math – Rational Numbers 14 , Question 8

#### Page No 14:

#### Question 9:

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.

#### Page No 15:

#### 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.

#### Page No 15:

#### 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 __________.

#### ANSWER:

(i) No

(ii) 1, −1

(iii)

(iv) *x*

(v) Rational number

(vi) Positive rational number

**EXERCISE 1.2**

#### Page No 20:

#### Question 1:

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.

NCERT Solution for Class 8 math – Rational Numbers 20 , Question 1

#### Page No 20:

#### Question 2:

Represent on the number line.

#### ANSWER:

can be represented on the number line as follows.

#### Page No 20:

#### 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

#### Page No 20:

#### Question 4:

Find ten rational numbers between and.

#### ANSWER:

and can be represented as respectively.

Therefore, ten rational numbers between andare

#### Page No 20:

#### Question 5:

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

#### Page No 20:

#### Question 6:

Write five rational numbers greater than − 2.

#### ANSWER:

−2 can be represented as −.

Therefore, five rational numbers greater than −2 are

#### Page No 20:

#### Question 7:

Find ten rational numbers between and.

#### ANSWER:

and can be represented as respectively.

Therefore, ten rational numbers between and are

#### Question 8:

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

#### Page No 14:

#### Question 9:

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.

#### Page No 15:

#### 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.

#### Page No 15:

#### 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 __________.

#### ANSWER:

(i) No

(ii) 1, −1

(iii)

(iv) *x*

(v) Rational number

(vi) Positive rational number

#### Page No 20:

#### Question 1:

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.

NCERT Solution for Class 8 math – Rational Numbers 20 , Question 1

#### Page No 20:

#### Question 2:

Represent on the number line.

#### ANSWER:

can be represented on the number line as follows.

Page No 20:

#### 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

Page No 20:

#### Question 4:

Find ten rational numbers between and.

#### ANSWER:

and can be represented as respectively.

Therefore, ten rational numbers between andare

#### Page No 20:

#### Question 5:

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

#### Page No 20:

#### Question 6:

Write five rational numbers greater than − 2.

#### ANSWER:

−2 can be represented as −.

Therefore, five rational numbers greater than −2 are

#### Page No 20:

#### Question 7:

Find ten rational numbers between and.

#### ANSWER:

and can be represented as respectively.

Therefore, ten rational numbers between and are

#### Question 8:

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

##### Video Solution for Rational Numbers (Page: 14 , Q.No.: 8)

NCERT Solution for Class 8 math – Rational Numbers 14 , Question 8

#### Page No 14:

#### Question 9:

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.

#### Page No 15:

#### 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.

#### Page No 15:

#### 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 __________.

#### ANSWER:

(i) No

(ii) 1, −1

(iii)

(iv) *x*

(v) Rational number

(vi) Positive rational number

#### Page No 20:

#### Question 1:

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.

##### Video Solution for Rational Numbers (Page: 20 , Q.No.: 1)

NCERT Solution for Class 8 math – Rational Numbers 20 , Question 1

#### Page No 20:

#### Question 2:

Represent on the number line.

#### ANSWER:

can be represented on the number line as follows.

##### Video Solution for Rational Numbers (Page: 20 , Q.No.: 2)

NCERT Solution for Class 8 math – Rational Numbers 20 , Question 2

#### Page No 20:

#### 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

##### Video Solution for Rational Numbers (Page: 20 , Q.No.: 3)

NCERT Solution for Class 8 math – Rational Numbers 20 , Question 3

#### Page No 20:

#### Question 4:

Find ten rational numbers between and.

#### ANSWER:

and can be represented as respectively.

Therefore, ten rational numbers between andare

#### Page No 20:

#### Question 5:

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

#### Page No 20:

#### Question 6:

Write five rational numbers greater than − 2.

#### ANSWER:

−2 can be represented as −.

Therefore, five rational numbers greater than −2 are

#### Page No 20:

#### Question 7:

Find ten rational numbers between and.

#### ANSWER:

and can be represented as respectively.

Therefore, ten rational numbers between and are