Mathematics NCERT Grade 8, Chapter 1: Rational Numbers- Basic operations on rational numbers are already discussed.
In this chapter, students will try to explore some properties of operations on the different types of the number they have seen so far.
Section 1.2 explains the topic- Properties of Rational Numbers.
• The number which can be written in the form of p/q, where p and q are integers and q $\ne$ 0 is called rational number
• For any rational number a, a $÷$ 0 is not defined.
The operations for addition and multiplication are:
(i)  commutative for rational numbers.
(ii) associative for rational numbers.

Operations students will study on rational numbers include:
1. Addition
2. Subtraction
3. Multiplication
4. Division
The same operations will be studied while dealing with both the topics- Associativity and Commutativity.
Solved examples are given to make the students understand the topic.
After that, the role of zero (0) and the role of 1 is made clear by giving a short description of the same.
• 0 is Additive identity for rational numbers
• 1 is Multiplicative identity for rational numbers
Section 1.2.6 deals with the topic- Negative of a number or additive inverse. Further in this chapter reciprocal or multiplicative inversedistributivity of multiplication over addition for rational numbers are explained.
Exercise 1.1 has 11 questions.
Next exercise 1.2 is based on the topics- Representation of Rational Numbers on the Number Line and Rational Numbers between Two Rational Numbers.
• Any rational number can be represented on the number line. How to represent a rational number on the number line is explained in detail.
• Between any two given rational numbers, there are countless rational numbers.
Solved examples are given in the chapter. Following those examples students can solve the problems of exercises easily.
In the end key points of chapter are given for quick revision.

#### 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)

#### 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)

#### 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.

#### 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

#### Question 5:

Name the property under multiplication used in each of the following:

(i)

(ii)

(iii)

#### Answer:

(i)  i.e., the multiplicative identity.

(ii)  i.e., Commutativity identity.

(iii) i.e., 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?

#### Answer:

If it is the multiplicative inverse, then the product should be 1.

However, here, the product is not 1 as

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##### Video Solution for rational numbers (Page: 14 , Q.No.: 8)

NCERT Solution for Class 8 maths - rational numbers 14 , Question 8

#### 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.

#### 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 __________.

(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

#### Question 1:

Represent these numbers on the number line.

(i) (ii)

#### Answer:

(i) can be represented on the number line as follows.

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(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 maths - rational numbers 20 , Question 1

#### Question 2:

Represent on the number line.

#### Answer:

can be represented on the number line as follows.

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##### Video Solution for rational numbers (Page: 20 , Q.No.: 2)

NCERT Solution for Class 8 maths - rational numbers 20 , Question 2

#### 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

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##### Video Solution for rational numbers (Page: 20 , Q.No.: 3)

NCERT Solution for Class 8 maths - rational numbers 20 , Question 3

#### Question 4:

Find ten rational numbers between and.

#### Answer:

and can be represented as respectively.

Therefore, ten rational numbers between andare

#### 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

#### 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.

#### Answer:

and can be represented as respectively.

Therefore, ten rational numbers between and are

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##### Video Solution for rational numbers (Page: 20 , Q.No.: 7)

NCERT Solution for Class 8 maths - rational numbers 20 , Question 7

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