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:
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+aca(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.
Using appropriate properties find:-
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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