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Integers
 

Integers

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    Integers Integers Presentation Transcript

    • INTEGERSIntegers form a bigger collection of numberswhich contains whole numbers andnegative numbers. For example-…-4, -3, -2,-1, 0, 1, 2, 3….
    • TYPES OF INTEGERSPOSITIVEINTEGERS- 1, 2, 3,4…i.e. the natural numbersare called positive integers.NEGATIVEINTEGERS- -1, -2, -3,-4… are called negativeintegers.On a number line points tothe right of zero arepositive integers and thepoints to the left of zeroare negative.
    • ZEROZero is neithernegative norpositive. It isgreater thanevery negativeinteger andsmaller thanevery positiveinteger.
    • MATHEMATICAL APPLICATIONS OF INTEGERSThe sum of two integers is also an integer.Example: -5 +7=+2The difference of two integers is also an integer.Example: +8-(-4)=8+4=12The product of two positive integers is alwayspositive. Example:+8 x +4 =32The product of two negative integer is alwayspositive. Example: -3 x -4 =+12The product of a positive integer with a negativeinteger is negative. example: +3 x -2=-6.The product of zero and an integer is alwayszero. Example: 0x 2=0
    • ADDITION AND SUBTRACTION
    • MATHEMATICAL APPLICATIONS OF INTEGERS (contd.)If the dividend and divisorare of the same sign thenthe quotient is a positiveinteger. Example: -4/-2=+2If dividend and divisor areintegers of opposite signthen the quotient is anegative integer.Example:4/-2=-2Any integer divided by 1gives the same integer.Zero divided by anyinteger is equal to zero.Division by zero is notpossible.
    • MULTIPLICATION AND DIVISION
    • COMMUTATIVE PROPERTYThe whole number can be added inany order. example: 5+(-6)=(-6)+5.Addition and multiplication iscommutative for integers.Whole numbers cannot be subtractedin any order. Example:5-6 is notequal to 6-5. Subtraction anddivision is not commutative forintegers.
    • ASSOCIATIVE PROPERTYFor all integers a, b and c,(a+b)+c=a+(b+c) i.e. addition isassociative for integers.For any three integers a, b and c,(a*b)*c=a*(b*c) i.e. for integers themultiplication is associative.
    • DISTRIBUTIVE PROPERTYFor any three integers a, b and c,a*(b+c)=a*b+a*c i.e. integers showdistributive property under additionand multiplication.
    • ADDITIVE IDENTITYWhen we add zero to any wholenumber, we get the same wholenumber.Zero is an additive identity for wholenumbers.
    • MULTIPLICATIVE IDENTITYOne is themultiplicativeidentity forwhole numbersas well as forintegers.Thusa*1=1*a=a.
    • ADDITIVE INVERSEThe additive inverse of any integer a is –aand the additive inverse of –a is a.The number zero is its own additiveinverse. INTEGERS ADDITIVE INVERSE 10 -10 -10 10
    • IMPORTANT POINTS Integers are closed for addition and subtraction both i.e. if a and b are integers then a+b and a-b are also integers. For any two integers a and b, a*b is an integer i.e. integers are closed under multiplication. For any integer a, we have:i. a/0 is not definedii. a/1 is equal to a Absolute value of an integer is its numerical value regardless of its sign.
    • THANK YOUBy:- Shivika And Aarushi 7th - b