OPER ATION S ON RATIO NUMB NAL ERS

OPER ATION S ON RATIO NUMB NAL ERS SL. NO SUB-TOPIC SLIDE NO 1 INTRODUCTION 3 2 ADDITION OF RATIONAL NUMBERS AND ITS PROPERTIES 5 3 SUBTRACTION OF RATIONAL NUMBERS AND ITS PROPERTIES 8 4 MULTIPLICATION OF RATIONAL NUMBERS AND ITS PROPERTIES 12 5 DIVISION OF RATIONAL NUMBERS AND ITS PROPERTIES 18 6 RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS 24

INTRODUCTION One day two children of Real number, Whole number and Rational number have a talk with each other; Whole number: Do you know rational , different operations like Addition, Subtraction , MULTIPLICATION and DIVISION can act on me and they also satisfies different properties. Rational number: But brother I do not have any knowledge that how these operations act on me. Let’s ask our teacher about this… before v v v Teacher- I will definitely clear your doubts but that answer my questions… What is the additive identity for whole numbers ? Does whole number obeys commutative law under Subtraction ? What is the multiplicative inverse of 5 ? Define distributive property of Multiplication over Addition ? Say two whole numbers between 5 and 12 ? Tell whether division obeys closure property or not ? ng tti ers e r g nsw eed e t a Af ect proc r rr. . co che er a h rt te fu

Rational Numbers Can yo u say w hy ‘ 0’ i Rationa l numbe s a r? As that of Whole numbers for rational numbers, also there are four operations they are as following. Let’s discuss one after another… v ADDITION v SUBTRACTION v MULTIPLICATION v DIVISION r re fo. . e h k k Clic AE Boo C DAV

ADDITION ON RATIONAL NUMBERS CASE-1 WHEN RATIONAL NUMBER HAVING SAME DENOMINATOR CASE-2 WHEN RATIONAL NUMBER DO NOT HAVE SAME DENOMINATOR

PROPERTIES OF ADDITION OF RATIONAL NUMBERS of tion i d d r e. A Henc al numbe ve ti n ratio Associa fy satis rty. e prop

SUBTRACTION ON RATIONAL NUMBERS CASE-1 WHEN RATIONAL NUMBER HAVING SAME DENOMINATOR CASE-2 WHEN RATIONAL NUMBER DO NOT HAVE SAME DENOMINATOR

PROPERTIES OF SUBTRACTION OF RATIONAL NUMBERS f on o i t c a r Subt ber does e c n m He al nu n o i t ra tisfy roperty. a s t p no ative i c o s As

MULTIPLICATION OF RATIONAL NUMBERS

PROPERTIES OF MULTIPLICATION OF RATIONAL NUMBERS Commutative property holds TRUE in multiplication of rational number.

LHS=RHS al tion a r ce ys Hen er obe b num ciative asso der un ion. t a c tipli mul

1 is the identity element under the multiplication v PRODUCT OF A RATIONAL NUMBER AND ZERO IS ALWAYS ZERO

v. Distributive property: LHS=RHS Hence verified… So Rational numbers obeys Distributive property of multiplication over Addition and Subtraction.

v Reciprocal of a rational number(Multiplicative Inverse )

DIVISION OF RATIONAL NUMBERS

PROPORTIES OF DIVISION OF RATIONAL NUMBER

• • Associative property does not holds true for division

• • LHS = RHS

• • Distributive property does not hold true for division

RATIONALS BETWEEN TWO RATIONAL NUMBERS

KEY POINTS v. Introduction of Rational number v. Operation of rational number v. Properties of addition of rational number v. Properties of subtraction of rational number v. Properties of Multiplication of rational number v. Properties of division of rational number v. Insert rational numbers between two given rational number