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CLASS 8 MATHS CHAPTER 1 SOLUTION

 

CHAPTER 1

RATIONAL NUMBER


Here is provided explaination of properties and  Solution  of Chapter 1 Rational Number of Class 8 maths according to latest syllabus of CBSE 2020-21.Student are able to solve the question related to CHAAPTER 1 RATIONAL  NUMBER  and easily understand the properties related to CHAPTER 1 RATIONAL NUMER CLASS 8 MATHS

INTRODUCTION:

RATIONAL NUMBER:- A  number which can be written in the form of P/Q , where p and q  are integers and q does not equal to 0, is called rational number.

For example:- 1/2,-1/2,0, 3/4 etc.

Properties of CHAPTER 1 RATIONAL NUMBER ARE GIVEN BELOW:

1.CLOSURE:-According to this property , sum of two rational numbers is also rational number.
This property is followed in Addition, subtraction, multiplication  and division  but if denominator is 0 it doesn't defined in division.
  
2.COMMUTATIVE:- According to this property, Two rational numbers can be added in any order without effect. It's result will be same. If we take  two rational number.[ a+b ].
Then [a+b] = [b+a]  [any order]. This property is followed in addition and multiplication but it doesn't followed in subtraction and division. 

3.ASSOCIATIVE:- According to this property, if we add three  rational number in  {a[b+c]} or {[a+b]+c}  order the answer will be same.
This property is followed in addition and multiplication but not in division and subtraction.

4.DISTRIBUTIVE:- For all rational numbers a,b and c 
a(b+c)=ab+ac
a(b-c) =ab-ac

Example: 7/5 ×(-3/12) + (7/5×5/12)
When you use distributivity,you split a product as a sum or difference of two products.

•Negative of a number or Additive inverse :-It means opposite nature of a number is called negative of a number or Additive inverse.

Ex:- Additive inverse of 8 is -8
 

 •Reciprocal of a number  or Multiplicative inverse :- The product of number and its reciprocal is always 1.

Example . If we multiply 3/4 by 4/3 then we get 1
 
Then 4/3 is reciprocal or Multiplicative inverse.

Ex 1.1 class 8 maths  QUESTION 1.

Using  appropriate properties find:-


(i) 

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) 

1 is the multiplicative identity.

(ii) Commutativity

(iii) Multiplicative inverse

Question 6:

Multiply by the reciprocal of.

ANSWER:


Question 7:

Tell what property allows you to compute.

ANSWER:

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

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


Solution of Exercise  1.2 of Chap 1   Rational Number



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 2:

Represent on the number line.

ANSWER:

 can be represented on the number line as follows.


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


​​​​​​​​​​​​​​​​​​​

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


​​​​​​​​​​​​​​​​​  

By this  article student can better understand the properties related to CHAPTER 1 RATIONAL NUMBER O CLASS 9 MATS.Students are able to solve the questions of CHAPTER 1 RATIONAL NUMER 

 

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