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INTEGERS

INTEGERS. MULTIPLICATION OF INTEGERS. Multiplication is also defined is REPEATED ADDITION . Eg :- 5 x 3= 5+5+5=15 Similarly using a no. line we can represent the mutiplication of integers. Taking an example: (-7)x2=.

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INTEGERS

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  1. INTEGERS

  2. MULTIPLICATION OF INTEGERS Multiplication is also defined is REPEATED ADDITION . Eg:- 5 x 3= 5+5+5=15 Similarly using a no. line we can represent the mutiplicationof integers. Taking an example: (-7)x2= -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -09 -08 -07 -06 -05 -04 -03 -02 -01 0 Now let us do it in a different way. First multiply 7 and 2, then put a minus sign. Therefore; (-7)x2=(-14). Similarly; (-15)x4=(-60) IN GENERAL: (-a)xb=-(axb) Q: TRY THEM- 13X(-2)= 3)7x(-13)= 2) (-5)x6= 4)35x(-2)=

  3. MULTIPLICATION OF TWO NEGATIVE INTEGERS So, what is (-3)x(-2)=? We can see using repeated addition that (-3)x(-2)= (3)-(-3)=6 So we can say that product of two negative integers is positive. Similarly we have- (-10)x(-12)=120 (-15)x(-2)=30 IN GENERAL: (-a)x(-b)=(axb) Q: TRY THEM- 13X(-2)= 3)7x(-13)= 2) (-5)x6= 4)35x(-2)= PRODUCT OF THREE OR MORE INTEGERS IF THE NUMBER OF NEGATIVE INTEGER IS EVEN THEN THE PRODUCT IS A POSITIVE, ELSE THE PRODUCT IS A NEGATIVE INTEGER.

  4. PROPRTIES OF MULTIPLIACATION OF INTEGERS • CLOSURE UNDER MULTIPLICATION • axb is an integer for all integers a and b. • 2) COMMUTATIVITY UNDER MULTIPLICATION • axb = bxa • 3) MULTIPLICATION BY ZERO • ax0=0xa=0 • 4) MULTIPLICATIVE INDENTITY • ax1=1xa=a • 5) ASSOCIATIVITY FOR MULTIPLICATION • (axb)xc=ax(bxc) • 6) DISTRIBUTIVE PROPERTY • (axb)+c=(axb)+(axc) & (axb)-c=(axb)-(axc)

  5. DIVISION OF INTEGERS We all know that division is just the inverse of multiplication. Have a look at these operations:- (-12)/(2)=(-6) (-20)/(5)=(-5) (-32)/(4)=(-8) (-45)/(5)=(-9) From here we observe that WHEN WE DIVIDE A NEGATIVE INTEGER BY A POSITIVE INTEGER WE ACTUALLY DIVIDE THEM AS WHOLE NUMBERS AND THEM PUT A MINUS SIGN. IN GENERAL: (-a)/b = a/(-b) IN GENERAL: (-a)/(-b) = a/b

  6. PROPRTIES OF DIVISION OF INTEGERS • 1) Division is not commutative for integers. • 2) Any integer divided by zero is undefined and 0/a=0 for any integer a. • 3) a/1=a for any integer a.

  7. THANK YOU Mrs J Subramanyan TGT Maths

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