Multiplication in Mathematics

                The beauty of Mathematics depends on basic four arithmetic Operations along with some functional operation:-

1. Addition  ( + )
2. Subtraction ( - )
3. Multiplication  ( x )
4. Division (÷)                                                                                                                                                    so we shall discuss the third operation multiplication.

MULTIPLICATION

                           Generally, "X " ( Popularly Read as a cross) OR  'Dot ' . ' symbol is used from ancient times. The subtraction is written using anyone from X OR. OR *  between the terms; that is, in symbolically. The result is expressed with equals " = " symbols.

                          it is a basic arithmetic operation that represents the operation of repeated addition of objects from a given collection. The result of the multiplication is also called a  Repeated addition.

                       multiplication can be learned as follows:-  

 The multiplication of numbers is another way of   REPEATED ADDITION; that is, the multiplication of two numbers is equivalent to adding as many times one of them, the multiplicand, as the value of the other one, is known as the multiplier. 
The multiplier can be written first traditionally and multiplicand second These are called factors.

For example, 2 multiplied by 3 (often written as 3 X 2 OR 2 X 3 and spoken as "3 times 2" OR 

" 2 times 3")  can be calculated by adding 3 copies of 2 together:

 3  +  3  =  Think about result ( 2 x 3  = 6 )

OR 

 adding 2 copies of 3 together:

2 X 3 = 2 + 2 + 2 = 6

For example, 4 multiplied by 3 (often written as ${\displaystyle 3\times 4}$ and spoken as "3 times 4") can be calculated by adding 3 copies of 4 together:

${\displaystyle 3\times 4=4+4+4=12}$

Therefore  3 and 4 are known as factors of 12.

•                                       If in ANOTHER way that we have four  fruits  and we have got four more  then Total fruits are such as 

                                       4 x 2 = 4 + 4 = 8 
OR
                                       2 X 4 = 2  +  2 + 2 +  2 = 8

BOTH results are the same it is an important property of multiplication. 

• BY MULTIPLYING SAME NUMBERS ZERO ( 0) 

 Zero MULTIPLIED by  ZERO  always equals  to ZERO 
  0 X 0 = 0 
 0 X 1 = 0 

   0 X 2= 0 + 0 = 0

     0 X 4 = .... Think and Write as addition as four zeroes together

  0 X 5= 0 + 0 + 0 + 0 + 0 = 0 

0 X 6 = .... Think and Write as addition as six zeroes together

 ...

If we multiply zero to any number result is always Zero. ( Important Fact of Mathematics)

•   BY MULTIPLYING SAME NUMBERS  ONE (1) 

  1 X 1 = 1 

  1X 2= 1 + 1 = 2

       1 X 3 = 1 + 1 + 1 = 3

     1X 4 = 1 + 1 + 1 + 1 = 4

 1 X 5= 1 + 1 + 1 + 1 + 1 = 5 

1 X 6 = 1 + 1 + 1+ 1 + 1 + 1 = 6    

1 X 7 = 1 + 1 + 1+ 1 + 1 + 1 + 1 = 7

1 X 8 = 1 + 1 + 1+ 1 + 1 + 1 +1 + 1 = 8
1 X 9 = 1 + 1 + 1+ 1 + 1 + 1 +1 + 1 + 1  = 9
1 X 10= 1 + 1 + 1+ 1 + 1 + 1 +1 + 1 + 1 +1 = 10

 ...

By multiplication of ONE  to any numbers, results are always the same number so ONE ( 1 )  Iis known as multiplicative identity.

• BY MULTIPLYING  DIFFERENT NUMBERS 

                                            7  X  3 = 7 + 7 + 7  = 21   (" SEVEN multiplied by THREE equals  TWENTY ONE")   

THIS CAN BE ALSO WRITTEN AS

                                                      7                                                                                             X  3                                                                                             ___
                                   21__

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