Intergers Blog 6

 THE    IDENTITY    AND THE INVERSE 

BEFORE I START THIS LESSON LET ME REMIND THAT 
(1)EACH AND EVERY WORD THAT HAS BEEN ASKED TO BE COPIED IN THE NOTEBOOKS SHOULD BE DONE PROPERLY IN FAIR AND
(2) SUBMITTED AS SOON AS THE SCHOOL REOPENS....
KINDLY KEEP THE SHEETS / OLD COPIES CAREFULLY TO COPY THE WORK IN YOUR FAIR NOTE BOOKS LATER
(3)INDEX TO BE DRAWN NEATLY
  
(4)DATE SHOULD BE WRITTEN ON THE LEFT SIDE TOP OF EACH PAGE.
(5)ROUGH COLUMN TO BE MADE ON THE RIGHT TO SHOW THE ROUGH WORK AGAINST EACH QUESTION.
(6) ONLY ONE REGISTER PER TERM  TO BE USED FOR BOTH C.W & H.W

TODAY BY THE END OF THIS LESSON (LEARNING OBJECTIVES)

(1)YOU WILL BE ABLE TO DEFINE   ADDITIVE IDENTITY  & INVERSE FOR INTEGERS and apply the knowledge to do simple sums based on them

(2) YOU WILL BE ABLE TO DEFINE ADDITIVE IDENTITY  & INVERSE FOR INTEGERS and apply the knowledge to do simple sums based on them.


BUT BEFORE WE START SOMETHING NEW LET'S REVISE 
Q9. NCERT ( kindly copy the answers in your notebook)
Q9 (a)  (-3)   x _______=  27  ( any guesses???)   yes it should be a negative number  because the final answer is positive. hence the integer is  (-9)
(b)   5   x _______= (-35)  ..guess the answer ...again it should  be negative because the final answer is negative.Hence the integer is (-7)
Do Q9 (c), (d ) as H.W 
DO Q.3 & Q.4 (NCERT ) as H.W ( CLASS 7 E has already done  yesterday!!!)

 KINDLY CLICK THE FOLLOWING FOR ADDITIVE IDENTITY 

                                             ADDITIVE IDENTITY

KINDLY NOTE DOWN THE PINK INK WORK  IN YOUR NOTEBOOKS  (INCLUDING Q.1 )

When  we add zero to any whole number ,we get the same whole number.

ZERO is an ADDITIVE IDENTITY for the whole number.

Is zero an additive identity for the Integers also  ??

Observe the following and fill in the blanks.

(i)   (-8)    +  0 =  (-8)          (ii)     0   +    (-8)   =    ( -8)

(iii)  (-25) + 0 =…………       (iv)    0   +    (-31)  =    (-31)

(v)    0  + (-59)  =………….     (v)     0  +    ( -45)  =…………

(ans …(-25)  ,  (-59) ,  (-45))

HENCE “ ZERO ” IS THE ADDITIVE INVERSE FOR THE INTEGERS

WORK TO BE DONE IN THE NOEBOOKS

 Q.1 TAKE ANY FIVE INTEGERS AND VERIFY THE FOLLOWING

                                                                             a   +     0     =  a  = 0   +    a

For Example. Integer(-2)                                (-2)  + 0 = (-2) = 0  +  (-2) 

                                             ADDITIVE INVERSE

SO, WHAT DO WE UNDERSTAND BY ADDITIVE INVERSE of integers  ???

YOU  ARE AWARE OF THE NEGATIVE INTEGERS

                           KINDLY CLICK HERE FOR  ADDITIVE INVERSE

Is -1    the   negative    of    1   ?????

Yes because -1 + 1 = 0

Now , Inverse means “ opposite of “ and   additive inverse means the “opposite of” number when added to the given number  gives a ZERO.

Thus, What should I add to 3 to get 0 ?

Or   3 + …….. = 0

The quess is “-3”  .Yes “-3 “ is the “ADDITIVE INVERSE” or “OPPOSITE OF “ or “NEGATIVE OF “  3

Thus what is the additive inverse of -7

        -7 + …….= 0                        

yes

 you are right 7 is the additive inverse of -7

                                                        MULTIPLICATIVE IDENTITY

KINDLY  CLICK HERE FOR      MULTIPLICATIVE IDENTITY
MULTIPLICATIVE IDENTITY REFERS TO THAT NUMBER WHICH WHEN MULTIPLIED TO

 THE WHOLE NUMBER OR THE INTEGER DOES NOT CHANGE THE VALUE OF THE 
WHOLE NUMEBER OR THE INTEGER
ANY GUESSES.....
FOR EXAMPLE .
   WHOLE NUMBER 5 X 1= 5  ( WHOLE NUMBER 5 REMAINS THE SAME)
INTEGER  (-9) X 1 = (-9)

THUS NUMBER 1 is the multiplicative identity for all the integers.

                                                        MULTIPLICATIVE INVERSE
 KINDLY CLICK HERE FOR MULTIPLICATION INVERSE

IN SIMPLE WORDS ,,
                                         MULTIPLICATIVE INVERSE MEANS " RECIPROCAL"

PLEASE REMEMBER...WHILE GIVING THE MULTIPLICATIVE INVERSE OF ANY NUMBER " BE  CAREFUL  THAT YOU DO NOT CHANGE THE SIGN OF THE NUMBER
 copy this example 
FOR EXAMPLE       MULTIPLICATIVE INVERSE OF (-5) is     1/ (-5)  or (-1) /5
similarly multiplicative inverse of   4 is   1/4 


QUESTIONS FOR PRACTICE (HW) (TAKE A SCREEN SHOT OF IT)
Q.1 Multiply the additive inverse of 5 to additive inverse of (-8)
Q.2 Add the additive inverse of 8 to additive inverse of (-2)
Q.3 From the the additive inverse of 9 SUBTRACT additive inverse of (11)
Q.4. Multiply the additive inverse of (-11) to multiplicative inverse of  fraction  1/7
Q.5 Add the multplicative  inverse of 1/(-5 )to additive inverse of (4)
Q.6 From the the additive inverse of (-6) SUBTRACT additive inverse of (-2)
Q.7 Multiply the additive inverse of 5 to additive inverse of (-2)

answers  1. (-40)       2.(-6 )      3 (.+2)       4  .77    5. (-9)    (6)    4   (7) (-10)

THAT'S ALL FOR TODAY..........