Integers Lesson 5

GOOD MORNING BOYS.....
I HOPE YOU ALL ARE READY FOR ANOTHER INTERESTING TOPIC IN MATHS SO TODAY LET'S START WITH.....

                      MULTIPLICATION OF INTEGERS

TODAY BY THE END OF THIS LESSON (LEARNING OBJECTIVES)

(1)YOU WILL BE ABLE TO UNDERSTAND HOW MULTIPLY A POSITIVE 

& NEGATIVE INTEGER and hence apply it to more than two integers

(2) YOU WILL BE ABLE TO UNDERSTAND HOW MULTIPLY A NEGATIVE

 & NEGATIVE INTEGER and hence apply to more than two integers.

            

  ### SIMPLE RULES TO REMEMBER.(kindly copy them in your notebook)

(1)The product of any two positive integers is POSITIVE .E.g.    4 x 3 = 12

(2)The product  of any two negative integers is POSITIVE .E.g.   (-4) x (-2) = 8

(3)The product of a positive integer and a negative integer is NEGATIVE               E.g.(4) x(-5)= (-20)

Thus

(1)              (+)     X   (+)     =   (+)   

(2)              ( - )     X   ( - )     =   (+)             

(3)             (+)     X   ( - )     =   ( - )   

SAMPLE QUESTIONS

 (i)       (- 100)  x   (-2) = ( -)  x   (-)   x 100  x  2 = (+)  200 =  200

(ii)          ( +100) x ( - 5) = (+)x(-) x 100x 5 = (-)  500 =  -       500

TRY IT YOURSELF                                       NCERT Ex1.3                                        

Q.1 Find each of the following  products (write  the question and TRY  

ANSWERING in your notebooks )

(a)   3x (-1) =  ……….

(b)   (-1) x 225 =  ……….

(c)    (-21)X (-   30)  =…………

(d)   (-316 integer) x (-1) =…………

( Answers       (a) (-3)   (b)    -225    (c)   630  (d)  316 )

We just observed that on multiplying two negative integers we get a positive, If 

to that positive integer we multiply another negative integer………..

(-2) x (-2) = (+4)                                                 result (+)      (  2 negative integers)

(-2) x (-2) x (-2) = (+4) x(-2) = (-8)                   result (-)         ( 3 negative integers)

(-2) x (-2) x (-2) x (-2) = (+4) x (+4) = ( + 16)     result (+)        ( 4 negative integers)

USING THE ABOVE OBSERVATION WE CAN CONCLUDE……….

 ###   SOME MORE RULES IN MULTIPLICATION  (KINDLY NOTE DOWN THE RULES IN YOUR NOTEBOOK)

WHILE WE MULTIPLY MORE THAN TWO INTEGERS,,,,

(1)The product of EVEN number of negative integers is POSITIVE  

(2)The product of ODD number of negative integers is NEGATIVE

NCERT QUESTIONS    E x 1.3   { ALL ANSWERS TO BE NOTED IN THE NOTEBOOKS }

Q.1       (e) (-15) x 0 x (-18)  =    0 x {anything}   = 0      ( ANS)

 (f)    (-12) x (-11) x ( 10)   = {(-12)x (-11)}  x 10

                                              =  {   132  }   x 10  =  +  1320    (ans)

(h) (-18)  x  ( -5)  x ( -4)  = (-18) x {(-5) x (-4)}

                                           =(-18)  x {  20}  = ( -360 )   (ans)

Question for practice (H.W) (TAKE A SCREEN SHOT OF IT TO DO IT LATER)

Q.1 What will be the sign of the product if we multiply together ;
 (a)   9 negative integers and 4 positive integers ?
 (b)   6  negative integers and 3 positive integers ?
 (c)  (-1)  x ( -1) x (-1) ...........200 times ?
 (d)   (-1)  x ( -1)  x ( -1).........301 times ?      [ ans (a) Neg.  (b) Pos.  (c) Pos. (d) Neg.  ]

Q.2. Find the product of the following
(a)    (-100) x (-1)
(b) (-20) x (-30) x ( 10)
(c)  1x (-125) x 8 x (-100)
(d) (-1) x (-2)x (-3)x (-4) x (-5)      

  [ ans (a)   100   (b)6000  (c)100000 (d) (-120)   ]

THAT  ' S ALL FOR TODAY.............