Areas and Multiplication

Representation of areas was further developed by putting lengths instead of putting balls. So it gave accurate measurements of areas.  

Hence the area of a rectangle is stated as the space covered by l – length up to the perpendicular length b namely breadth.

Since Area of a rectangle is the multiplication of length and breadth it is equivalent to l * b or b * l.

It gave the unit of (metre)^2 for areas because  l, b  both are lengths. Unit of the length is metre. 
Hence the units is metre * metre = metre^2.       

Thus we measured areas using lengths.

Multiplication is the large continuous application of same addition process. It was made only to simplify the addition process. When we are concerned the additions of same amounts many times we tried to calculate it easily by remembering it.

Adding 6 for 5 times

6 + 6 + 6 + 6 + 6

This can be written simply as 5*6 or 5 X 6

And thus multiplication was stated by putting the symbol ‘ X ’  between the two numbers where multiplication has to be done.  The commutative property of multiplication is already explained in the area of a rectangle.

          e.g.         5*6= 5 rows of 6 columns balls = 30 balls

It is also equivalent to the multiplication of 6*5 because 6 rows of 5 columns balls = 30

Thus the area of any rectangle is l*b or b*l.

After mugging up easy multiplications we often used it in large multiplications.

e.g.  5 *36

We can do 36*5 or 5*36.

Being same multiplication also done as same as addition and so in multiplication the calculation starts from 1^st decimal place to the other decimal places.

First multiply the 1^st decimal of two numbers and so 5*6 = 5 times 6 or 6 times 5= we know the mugged up answer is 30. Hence we put 0 in the 1st decimal place of the answer and it left 3 in the 2^nd decimal place. Next the multiplication is done in the 2^nd decimal place. So, multiply 5 with 3 which is the addition of 3 for 5 times or 5 for 3 times gives 5*3=3*5 =15

And already there is number 3 which was left in the 2^nd decimal place by the multiplication of 1^st decimal place. So the total in 2^nd decimal place is 15 + 3 = 18.  

Here 8 will be filled in second decimal place and 1 was left in 3^rd decimal place. Hence there is no number in 3^rd place of the question we will put 1 in the 3^rd decimal. Therefore 5*36 is 180.

Thus we can do multiplication between any two numbers using the same rules mentioned above.

The common form of multiplication is x*y=z

The multiplication was used widely in all areas.

To make more simple, in multiplication we will put bracket signs around the numbers instead of putting multiplication sign. 
It is      (x)(y) = (y)(x) = z   instead of  x*y = y*x = z

Hence it is only the simple addition process and so

x, y, z ϵ N.

Being the same multiplication doesn't have anything extra information from addition.  

All the rules which undergoes for addition will also undergoes for multiplication. 

Some properties are…

Commutative property

                                       x*y = y*x

Associative property

                                           (x*y)*z = x*(y*z)