In this Rational Numbers Class 8 Notes Page we will explain the topics for the chapter 1 of Rational numbers Class 8 Maths.We have given quality notes and video to explain various things so that students can benefits from it and learn maths in a fun and easy manner, Hope you like them and do not forget to like , social share
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- Introduction to Rational Numbers
- Properties of Rational Numbers
- Additive Identity/Role of Zero
- Multiplicative identity/Role of one
- Additive Inverse
- Reciprocal or multiplicative inverse
- How to Represent Rational Number on the Number Line
- Rational Numbers between Two Rational Numbers

The numbers 1,2,3,… are called natural numbers or counting numbers.

Let us add one more number i.e. ,zero(0), to the collection of natural numbers.

Now the numbers are 0,1,2,… These numbers are called

We can say that whole numbers. consist of zero and the natural numbers. Therefore, except zero all the whole numbers. are natural numbers.

So all natural Number are whole number but all whole numbers are not natural numbers

Z={…-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6…..}

A number is called rational if it can be expressed in the form p/q where p and q are integers ( q> 0).

Example : ½ , 4/3 ,5/7 ,1 etc.

Here is the summary for the closure property on various mathematical operations on various numbers

Here is the summary for the commutative property on various mathematical operations on various numbers

Here is the summary for the Associative property on various mathematical operations on various numbers

Zero is called the identity for the addition of rational numbers. It is the additive identity for integers and whole numbers as well

1

So we say that (-a/b) is the additive inverse of a/b and a/b is the additive inverse for (-a/b)

What is the additive inverse of following numbers

a) 1/6

b) -8/9

Additive Inverse of any rational number a/b is defined as -a/b so that (a/b) +(-a/b)=0

So for 1/6, additive inverse will be -1/6

Similarly for -8/9 ,it will be 8/9

Zero does not have any reciprocal or multiplicative inverse

Find the multiplicative inverse of the following.

-54

-11/12

The multiplicative inverse of any rational number a/b is defined as b/a so that (a/b) x (b/a) =1

So answer would be

-54=-54/1 multiplicative inverse will 1/-54 =-1/54

Similarly for -11/12, the multiplicative inverse will be -12/11

a (b + c) = ab + ac

a (b – c) = ab – ac

Natural Numbers

Whole Numbers

Integers

Rational numbers can also be represented on the Number line

Lets take an example of 4/9

Step (1) In a rational number, the numeral below the bar, i.e., the denominator, tells the number of equal parts into which the first unit has been divided. The numeral above the bar i.e., the

numerator, tells ‘how many’ of these parts are considered

So in this particular example, we need to divide the first unit into 9 parts and we need to move to the 4

Step (2) Draw the straight line. Divide the first unit into equal parts equal to the denominator of the rational number. And then mark each equal part to the right of the line and reach the desired number

Now we will see some example to find the rational number between the rational numbers

Find the 3 rational number between 1 and 2

We know the average of two rational number lies between them and it is a rational number

Step 1: First average =(1+2)/2=3/2

So 3/2 lies between 1 and 2

Step 2: Average of 1 and 3/2 will also lie between 1 and 3/2 and hence 1 and 2,

So =1/2 (1+3/2 )=5/4

Step 3.: Again Average of 3/2 and 2 will also lie between 1 and 2. So 1/2 (3/2+2)=7/4

So 3/2,5/4 and 7.4 are rational Number

In General If a and b are two rational numbers, then (a+b)/2 is a rational number between a and b such that a < (a+b)/2< b.

We can write the number like 10/10 , 20/10

So the rational number would 11/10, 12/10, 13/10,14/10,15/10

Find the 3 rational number between 1/3 and 7/2

We know the average of two rational number lies between them and it is a rational number

So step 1: First average =(1/3+7/2)/2=23/24

So 23/24 lies between 1/3 and 7/2

Step 2: Average of 1/3 and 23/24 will also lie between 1/3 and 23/24 and hence 1/3 and 7/2

So = ½(1/3+23/24)=31/48

Step 3.: Again Average of 23/24 and 7/2 will also lie between 1/3 and 7/2. So=1/2(23/24+7/2)=107/48

1/3 =2/6

7/2=21/6

Now 2/6 <3/6 < 4/6< 5/6 …..< 20/6 < 21/6

So This way we can easy find the rational numbers

Yes 0 is a rational number as it ca expressed in the form p/q i.e 0/1

Rational numbers includes fractions,Integers, whole numbers, Natural numbers, terminating decimals numbers, Non terminating repeating decimals

Ratonal numbers are infinite.

Any number which can be expressed in the form p/q where p and q are integers is a Rational number. So when numbers with out decimals are given, you can easily identify using this definition Example 1/2. $\sqrt 3$ . 1/2 is Rational number as it can expressed as p/q , while $\sqrt 3$ is not rational as it cannot be expressed as p/q For decimals Numbers, If the number is terminating, then it is Rational number. If it is non terminating and repeating, then it is Rational Number. If it is non terminating and no repeating, then it is not Rational Number

1 is the identifty

Properties of Rational Number (i) Closure Property (ii) Commutative Property (iii) Associative Property (iv) Additive identity (v)Multiplicative Identity (vi)Additive Inverse (vii) Multipicative Inverse

- Rational number are closed under the operations of addition, subtraction and multiplication.
- The rational number 0 is the additive identity for rational numbers while The rational number 1 is the multiplicative identity for rational number
- The additive inverse and Multiplicative inverse of a/b is -a/b and b/a respectively
- There are infinite Rational number between two rational numbers

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Class 8 Maths Class 8 Science