**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****/**where**q,***p*and*q*are integers and*q*$\ne $ 0 is called**rational number**. - For any
**rational number**,*a*is*a*$\xf7$ 0**not defined**.

**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**

**Negative of a number**or

**additive inverse**. Further in this chapter

**reciprocal**or

**multiplicative inverse**,

**distributivity 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.**

In the end key points of chapter are given for quick revision.

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

(ii) i.e., Commutativity identity.

(iii) i.e., 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

##### 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

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

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

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