Syllabus of Class 8 Mathematics
1.Rational Numbers
2.Linear Equations in one variable
3.Understanding Quadrilaterals
4.Practical Geometry
5.Data Handling
6.Squares Square Roots
7.Cube and Cube Roots
8.Comparing Quantities
9.Algebraic Expressions and Identities
10.Visualising Solid Shapes
11.Mensuration
12.Exponents and Powers
13.Direct and Inverse Properties
14.Factorisation
15.Introduction to Graph
16.Playing with Numbers
Class 8 Maths Chapter 1 Notes - Rational Numbers
Introduction to Rational Numbers
A rational number is a number that can be written as a fraction, where, the numerator and denominator are integers and the denominator is non-zero. If the denominator of a rational number is greater than 0 and the common divisor of the numerator and the denominator is 1 only, then the rational number is said to be in its standard form.
A rational number is positive if the numerator and the denominator are of the same sign. A rational number is negative if the numerator and the denominator are of opposite signs.
Properties of Rational Numbers
1. Closure Property
For two rational numbers, if an operation performed (like addition, subtraction, multiplication), gives a rational number as the result, then the set of rational numbers is closed under that operation. The result of adding, subtracting and multiplying two rational numbers is always a rational number.
2. Commutative Property
If we swap the order of operation for any two rational numbers and the result does not change, then the rational numbers follow commutative property for that operation. Rational numbers follow this property for addition and multiplication, but not for subtraction and division.
3. Associative Property
If we rearrange a set of rational numbers among two or more same operations and their result does not change, rational numbers follow the associative property for that operation. Rational numbers follow this property for addition and multiplication only.
4. Distributive Property
When we multiply a sum of variables by a number, we get the same result as when we multiply each variable by the number and then add their products together, that is, if a, b and c are three rational numbers, then a × (b + c) = (a × b) + (a × c).
Similarly, if we multiply a difference of variables by a number, we get the same result as when we multiply each variable by the number and then find the difference between the products, that is, if a, b, and c are three rational numbers, then a × (b − c) = (a × b) − (a × c).
5. Identity Property
0 is the additive identity for the rational numbers because adding 0 to a rational number does not change it.
1 is the multiplicative identity for the rational numbers because multiplying a rational number with 1 does not change the value.
6. Inverse Property
The additive inverse is what we add to a number to get 0. For any rational number x/y, the additive inverse is –x/y.
The additive inverse of 3/4 is -3/4.
The multiplicative inverse is what we multiply to a number to get 1. It is the reciprocal of the number.
For any rational number x/y, y/x is the multiplicative inverse.
The multiplicative inverse of 3/4 is 4/3.
Representation on Number Line
We can represent rational numbers on a number line. A number line is a straight line with three parts: negative side, zero (origin), and positive side. Negative rational numbers lie on the negative side, that is to the left of 0, whereas, positive rational numbers lie on the positive side, that is to the right of 0. Let us see how to represent 3/4 on a number line.
3/4 is greater than 0 and less than 1. So, it will lie in between 0 and 1. Draw a number line and mark 0 and 1. Divide the gap between 0 and 1 into four equal parts and mark the third point from 0 towards the right as 3/4.
Finding Rational Numbers
There are infinite rational numbers between two rational numbers. We can use the methods given below to find rational numbers between two rational numbers.
Mid-point method:
If a and b are two rational numbers, a rational number between a and b is their mid-point.
When denominators are the same:
If the denominators are same, we can easily find the rational numbers between the given rational numbers.
3/7, 4/7, 5/7are rational numbers between 2/7 and 6/7.
When denominators are not the same:
If the denominators are not the same, we have to use the LCM method to find the rational numbers between the given rational numbers. Let us see an example.
Example: Find rational numbers between 3/11 and 5/9.
LCM of 11 and 9 = 99
So, LCM of 11 and 9 are rational numbers in between 3/11 and 5/9.
If you like my article, please comment me and if you have any valuable suggestions regarding my article please share with me,it will be highly welcomed.Thanks once again for being with me till now.Contact Us
Mid-point method:
If a and b are two rational numbers, a rational number between a and b is their mid-point.
When denominators are the same:
3/7, 4/7, 5/7are rational numbers between 2/7 and 6/7.
When denominators are not the same:
If the denominators are not the same, we have to use the LCM method to find the rational numbers between the given rational numbers. Let us see an example.
Example: Find rational numbers between 3/11 and 5/9.
LCM of 11 and 9 = 99
So, LCM of 11 and 9
Welcome to www.fuzymail.co.in
Please email us if you have any queries about the site, advertising, or anything else.
Contact Us
Welcome to www.fuzymail.co.in
Please email us if you have any queries about the site, advertising, or anything else.
We will revert you as soon as possible...
Thank you for contacting us!
Have a great day
.png)
I regular read your article,I like your article.
ReplyDeleteVery good
ReplyDeleteNice explained sir
ReplyDelete