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UNIVERSAL CONVENT SENIOR SECONDARY SCHOOL SESSION : 2023-2024 SUBJECT : MATHEMATICS CLASS : VIII ‘A’ SUBMITTED TO : MR. L. M. JOSHI SUBMITTED BY : BHAVYA PANDEY.

TOPIC. RATIONAL NUMBERS. 46 Cool Math Wallpaper WallpaperSafari.

What are Rational Numbers ?. All number including natural numbers whole number and integers are rational number. A number of the form p/q , where q is not equal to 0 is called a Rational number. Here, p and q both are integers. For example, (-5)/6. 11/5, 2/15 etc..

Properties of rational number. Properties of regional number lie under the 4 operation of arithmetic : Addition of rational number Subtraction of rational number Multiplication of rational number. Division of rational number..

Addition of Rational number. Closure property : Sum of two rational number is always a rational number. For example, 1/2 + 3/4 = 5/4 Commutative property : The sum of two rational number does not depend on the order in which they are added. ( a + b = b + a ) For example, 1/2 + 3/4 = 3/4 + 1/2 = 4/6 Identity property (Property of 0): 0 added to any rational numbers the number does not change, so zero is called Identity Element for addition of rational numbers. (0 + a = a). Additive inverse : If the sum of two rational numbers is 0 , then the two rational numbers are called additive inverse of each other. For example, 2/3 + (-2)/3 = 0.

Subtraction of rational numbers. Closure property : The difference of two rational number is also a rational number. Commutative and associative property : Rational numbers do not hold commutative and associative property under Subtraction. Property of Zero : Zero Subtracted from any rational number leaves it unchanged and any rational number subtracted from 0 gives it's additive inverse..

Multiplication of rational numbers. Closure property : The product of two rational number is also a rational number. Commutative property : Two rational numbers can be multiplied in any order . Associative property : The product of three or more numbers does not depend on the order they are multiplied in or they are in grouped as. Zero property, the product. Of any rational number and 0 is 0. For example, 9874561253 X 0 = 0. Distributive property of multiplication over addition and Subtraction: [a x (b + c) = a x b = a x c] [a x (b – c) = a x b – a x c].

Division of Rational Numbers. Closure property: A rational number divided by a rational number may or may not be a rational number. Commutative and Associative Property: Rational numbers do not hold these properties under division..

Representation of numbers on the number line. Numbers can be represented on the number line according to their types. The most ways of representing the numbers on the number line are as follows: Natural number. Whole number. Integers. Rational numbers..

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