Integers

Integers By- Rishabh Singla

Introduction

IntegersThe collection of whole numbers

together withthe numbers -1, -2, -3… is called

integers.

Absolute Value

Absolute Value of an integer is its numerical

value with no regard to sign.Example- |-2|= 2 |21|= 21The vertical bars || indicates the

absolute value.

Ordering Integers

Any integer, say a is greater than any other

integer b if it lies on right of the number line.

a= 5b= -1

Adding And Subtracting Integers

Adding Integers

Case- 1When the integers are of like

signs.

To add two integers of like signs, first add their

absolute value and then put the common signs

before the sum.

Adding Integers

Case- 2When the integers are of unlike

signs.

To add two integers of unlike signs, first we find

the difference of two integers and then put the

sign of greater value before the difference.

Rules for Addition And Subtraction

Sign How to Operate Sign in Answer

+ + + + - - + - + - - Sign of

Greater Value

- + - Sign of Greater Value

Rules Multiplication And Division

Sign How to Operate Sign In Answer

+ + X or / +

- - X or / +

+ - X or / - - + X or / -

Properties Of Addition, Subtraction, And

Multiplication1. Closure Property:-If a and b are integers then a+b

will also be aninteger.If a and b are integers then a-b

will also be anInteger.If a and b are integers then aXb

will also be anInteger.

Properties Of Addition, Subtraction, And

Multiplication2. Commutative Property:-If a and b are integers then a+b =

b+aIf a and b are integers then aXb =

bXa

Properties Of Addition, Subtraction, And

Multiplication3. Associative Property:-If a, b, and c are integers, then

(a+b)+c = a+(b+c).If a, b, and c are integers, then

(aXb)Xc= aX(bXc)

Properties Of Addition, Subtraction, And

MultiplicationAdditive Identity:-0 is the Additive Identity. If a is

any integer, thena+0=a.

Multiplicative Identity:-1 is the Multiplicative Identity. If a

is anyinteger, then aX1=a.

Properties Of Addition, Subtraction, And

MultiplicationProperty of Zero(0):-If a is any integer, then aX0= 0.

Properties Of Addition, Subtraction, And

MultiplicationAdditive Inverse:-The opposite of any number is called

its AdditiveInverse. Example- Additive Inverse of -5=5.Sum of any number and its additive

inverse isalways zero(0). Example- -5 + 5= 0.

Properties Of Addition, Subtraction, And

MultiplicationDistributive Property Of

Multiplication OverAddition:-If a, b, and c are integers, then

aX(b+c)=(aXb)+(aXc).

Properties Of Division

1.a/1 = a2.a/a = 13.a/(-a)= -14.a/(-1)= -a5.0/a = 06.a/0 = Not Defined(only True if a = 0).

Brackets

1. [ ] is known as rectangular or big brackets.

2. { } is known as curly brackets.3. ( ) is known as round or small

brackets.4. -- is generally known as bar

brackets or vinculum.

BODMAS

B - Bracket O - OfD - DivisionM - MultiplicationA - AdditionS - Subtraction

Thank You

Submitted To- Mrs. Dolly Tandon MamMade By - Rishabh Singla VII- J Roll No- 09