Vikasana – Bridge Course 2012 - KEA · MULTIPLICATION – REPEATED ADDITION DIVISION SUCCESSIVE SUBTRACTION Vikasana – Bridge Course 2012 – SUCCESSIVE SUBTRACTION. THE PROPERTIES

Vikasana – Bridge Course 2012

COUNTING IS THE BASIC MATHEMATICAL ACTIVITYACTIVITY

EVERY HUMAN ACTIVITY DAY IN AND DAY EVERY HUMAN ACTIVITY, DAY IN AND DAY OUT INVOLVES THIS COUNTING, IN ONEWAY OR THE OTHER.House wife in the kitchen to A space scientistFarmer on the field to AN industrialistA petty hawker to A great economist

All of them play with numbers to achieve their Vikasana – Bridge Course 2012

o t e p ay w t u be s to ac eve t etargets.

As the human Endeavors advanced simple counting has become computation, calculations and estimationsestimations.

To make calculations computations and estimationsTo make calculations, computations and estimations, easier and quicker, operations on numbers are used.


An operation is said to be well defined i t if it i ibl t ff t thin a set, if it is possible to effect the

execution of the process of operation.


IT IS ABSOLUTELY NECESSARY TO HAVE THE SET OF ELEMENTS TO OPERATE WITHOF ELEMENTS TO OPERATE WITH

ANDAND

TO KNOW THE PROCESS OF EXECUTION OF THE O O OC SS O CU O OOPERATION


ALGEBRAALGEBRAAn ALGEBRA is a structure, consisting of “a non‐empty

( )set”, along with “well defined” operation (s) in it.Example: SET OF NATURAL NUMBERS WITH ADDITION OPERATIONS [N +]ADDITION OPERATIONS [N,+]

SET OF REAL NUMBERS WITH MUILTIPLICATION OPERATIONS [R ×]OPERATIONS [R, ]


ALGEBRE

REAL NUMBER ALGEBRAVECTOR ALGEBRAMATRIX ALGEBRACOMPLEX ALGEBRA

ALGEBRA OF FUNCTION etc


The fundamental operations on set of real numbersThe fundamental operations on set of real numbers widely accepted are

ADDITIONSUBTRACTION

MULTIPLICATIONDIVISION


ADDITION is the process of counting the elements of two sets taken ‘TOGETHER’

Eg: Adding the number of students of section A & B of l 10 f ti l h lclass 10 of aparticular school


SUBTRACTION is the process of counting the remaining elements of a given set, after ‘TAKING

AWAY’ a few elements from it.

fEg: How many students of class consisting 50 students are left, after 15 students leave the school.


MULTIPLICATION is a process of ‘REPEATED ADDITION OF THE SAME NUMBER’

Eg: 4+4+4+4+4+4 is same 6 times 46×4=24


DIVISION is the process of ‘SUCCESSIVEDIVISION is the process of ‘SUCCESSIVE SUBTRACTION’ of the same number.

Eg: 24-4-4-4-4-4-4 = 04 can be successively subtracted 6 times from 24 to4 can be successively subtracted 6 times from 24 to

get the reminder 024/4 = 6


All fundamental operations on Real numbersinvolve two facts at a timeinvolve two facts at a time.

Basic operations are denoted by symbols inmathematical sentencesmathematical sentences

The most basic operation on Real numbers isAdditiondd t o

Other operations are derived from additionSUBTRACTION NEGETIVE ADDITIONSUBTRACTION – NEGETIVE ADDITIONMULTIPLICATION – REPEATED ADDITIONDIVISION SUCCESSIVE SUBTRACTION

Vikasana – Bridge Course 2012DIVISION – SUCCESSIVE SUBTRACTION

THE PROPERTIES OF OPERATIONS ON REAL THE PROPERTIES OF OPERATIONS ON REAL NUMBERS

CLOSURE PROPERTY: If the result of the operations is a member of the set on which the operation is effected, the operations is said to have closure property.

Eg: Addition in the set, of Natural numbers has the closure property closure property

4+7 = 11


COMMUTATIVE PROPERTY: If the result of the COMMUTATIVE PROPERTY: If the result of the operations remain same, when the facts are inter change, the operations has commutative property

Eg: Multiplication of Real numbers is commutative 7×5 = 5×7 = 35


ASSOCIATIVE PROPERTY: if the result of the operations is independent of the association of facts the operation is said to have associative propertythe operation is said to have associative property.

Eg: Addition of Natural numbers is AssociativeEg: Addition of Natural numbers is Associative (4+5)+7 = 4+(5+7)


DISTRIBUTIVE PROPERTY: In this property twoDISTRIBUTIVE PROPERTY: In this property two operations are involved Addition and Multiplication.

Eg: 3×(7+5) = 36g ( )(3×7)+(3×5) = 36

Multiplication is distributive over Additionp

Note: Addition is not distributive over Multiplication in pthe set of Real numbers


UNARY OPERATIONSUNARY OPERATIONSThese operations involve only one fact at a time.For Eg: √81=9 √64=8 √6 25=2 5 √4=2For Eg: √81=9, √64=8, √6.25=2.5, √4=2

5² = 25, 10³ = 1000

Note: every positive Real number has a unique real square rootsqua e oo


Operations on Real numbers need not be basic Ope at o s o ea u be s eed ot be bas coperations only

We can define other operations with defined symbols

Eg: a*b = a/b + b/a a,b ≠ 0x▲y = √x + √y x,y > 0p♥q = p² ‐ q²


All operations on Real numbers essentially consist f d t l tifundamental operations

ADDITION

SUBTRACTION

MULTIPLICATION

DIVISIONVikasana – Bridge Course 2012

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Vikasana – Bridge Course 2012 - KEA · MULTIPLICATION – REPEATED ADDITION DIVISION SUCCESSIVE SUBTRACTION Vikasana – Bridge Course 2012 – SUCCESSIVE SUBTRACTION. THE PROPERTIES