1 / 7

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=.

rory
Download Presentation

INTEGERS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related