Class 8th Mathematics

Chapter :1 Rational Number

Rational Number:-

A Number That can be Represented As P/Q form where Q≠ 0

Example= 1/2, 3/4 , 0, 2, -1/3

• Rational Number contains Whole Number, Natural Number, Integers
• π is an Irrational Number

Irrational Number

Any real number that cannot be expressed as the P/Q form

Example :- π , √11, √21

Tpyes of Rational Number

There are different types of rational numbers. We shouldn’t assume that only fractions with integers are rational numbers. The different

types of rational numbers are:

• integers like -2, 0, 3 etc.
• fractions whose numerators and denominators are integers like 3/7, -6/5, etc.
• terminating decimals like 0.35, 0.7116, 0.9768, etc.
• non-terminating decimals with some repeating patterns (after the decimal point) such as 0.333…, 0.141414…, etc. These are popularly known as non-terminating repeating decimals

How to Identify Rational Number

In each of the above cases, the number can be expressed as a fraction of integers. Hence, each of these numbers is a rational number. To find whether a given number is a rational number, we can check whether it matches with any of these conditions:

• We can represent the given number as a fraction of integers
• We the decimal expansion of the number is terminating or non-terminating repeating.
• All whole numbers are rational numbers

Rational Number In Form Of Decimal

Decimal Numbers Also come under Rational Number For example 0.3 Because we can Write 0.3 as 3/10 which is A Rational Number

Is 0 a Rational Number…?

Yes 0 is a Rational Number Becuase it can be written As 0/1 which is A Rational Number

Properties Of Rational Number

General Properties of Rational Numbers Like

Closure property, Associative property, Commutative property, Distributive property, identity, Inverse etc.

Closure Property

Closure property with reference to Rational Numbers

Closure property states that if for any two numbers a and b, a∗b is also a rational number, then the set of rational numbers is closed under addition.
∗ represents +,−,× 

Associative Property

A set of numbers is said to be associative for a specific mathematical operation if the result obtained when changing grouping (parenthesizing) of the operands does not change the result.

Addition Associatice Property

For exg:- a+(b+c) = c+(a+b)

Subtraction Associative property

Does not Follow

Multiplicative Associative Property

For exg:- a×(b×c) = c×(a×b)

Divisional Associative Property

Does not follow

Commutative Property

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division. Let’s see

The above examples clearly show that the commutative property holds true for addition and multiplication but not for subtraction and division. So, if we swap the position of numbers in subtraction or division statements, it changes the entire problem. 

So, mathematically commutative property for addition and multiplication looks like this

Commutative Property of Addition:

a + b = b + a; where a and b are any 2 whole numbers

Commutative Property of Multiplication:

a × b = b × a; where a and b are any 2 nonzero whole numbers

Distributive property

If three numbers are a, b and c then a×(b+c)=ab+ac , a×(b-c) = ab-ac

Multiplicative Inverse

Multiplication Inverse Means A fraction and Multiply the Fraction By Reciprocal Of that Fraction So the Result Is 1. For exg

For Fraction a/b the Multiplicative will be b/a so that a/b ×b/a gives 1

Additive Inverse

Additive inverse means A fraction and Add the Same Fraction with opposite of that sign so the result is 0. For exg

a/b+(-a/b) =a/b-a/b =0

Additive Identity

0 is know as Additive Identity beacuse 7+0 =0+7 thus 7=7 No change in Value

Multiplicative Identity

1 is known as multiplicative Identity because 7×1 =1×7 =7=7 the Value Not change

Standard form of Rational Number

Standard form of rational number Means There is No Common Between Numerator and Denominator except 1. For exg

Standard form of 16/8 is 2/1