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WHY DO WE MULTIPLY FROM RIGHT?

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Why do we multiply from right to left?

Multiplication is one of the arithmetic operations that we all use to study in our early classes. It makes our calculations easy and fast and helps us in finding patterns hidden in the number system. With the help of multiplication, we are able to perform our daily calculations very conveniently.

Going into the method of multiplication and as the title of says: -“Why do we multiply from right to left”? Is this the only way of doing multiplication? Is it predefined in the rulebooks of mathematics? Ahh! a lot of confusions.

Let us first try to figure out the meaning of multiplication. Multiplication as we know it, is repeated addition of the same number into one another. In order to get rid of adding, again and again, the same number or to make the calculations easy, we devised one more arithmetic operation known as multiplication. Through this operation, we can find the sum when a number is added to itself tens of thousands or even millions of times, in a very small unit of time and doing very fewer calculations. (Again the mathematics is fulfilling its need of making calculations easy. Here mathematics is making mathematics easy).

The approach that we follow to carry out multiplication of numbers, is what we have learned from our childhood. Let us understand by an example:

Say we want to multiply the number 32 by 4 :
We first use to write this down in the form like:
Then first multiply 4 by 2  to get 8 and then multiply 4 by 30 to get 120 . And write the answer as .

Now in doing this calculation, what we are performing is multiplying the unit numbers first and then the tens number and then add them together.

On the hidden part, we are using the distributive law.
i.e.,

4×(2+30)=4(2) + 4(30) .

\ \ \ \ \ \ \ \ \ \ =8+120 .

\ \ \ \ \ \ \ \ =128 .

This method now seems natural to us, as it’s been inculcated into deep our minds and understanding.

But we never argued, why do we always use this method of multiplication? Is there any other method also by which we can multiply any two numbers?

Let’s now take the title of the article seriously and raise the question “Why do we multiply from right? Why not from left? Why not from the middle or why not from anywhere?

When we multiply from right we used to decompose the multiplier into units, tens, hundreds, thousands and so on and so forth in increasing order, and then use to the multiply the multiplicand by all of the decomposed numbers and add the results to get the final result.

Multiplication from the left would be the same as multiplication from right, just the difference will be in the order of multiplication from the decomposed numbers and the addition.

For example, for the same question done above, the multiplication from the left would be like this:
Say we want to multiply the number 32 by 4:

In this we first multiply 4 by 30 to get 120 and then multiply 4 by 2 to get 8. And write the answer after addition them together as: 128. .

Now in doing this calculation, what we are performing is multiplying the tens number first and then the unit number and then add them together.

On the hidden part, we are using the distributive law. .

i.e.,

4×(30+2)=4(30)+4(2) .

\ \ \ \ \ \ \ \ \ \ =120+8 .

\ \ \ \ \ \ \ \ =128 .

The approach would be the same, just the order has been changed in this approach. We are using here a property that addition holds, which is a commutative property of addition.

According to this property the order doesn’t matter for doing addition:

i.e., for any given numbers a or b: .

a+b=b+a .

For example: .

2+30=30+2 .

32=32 .

So, there is no difference in performing the multiplication from the left or from the right.

Same kind of approach would be followed in performing multiplication from anywhere in between in the number, and there will be no difference in the solution.

Let’s understand by an example:

Say we want to multiply the number 425 by 3:

In order to perform multiplication from anywhere, we first decompose the number 425 into its units, tens, and hundreds:

i.e.,

425=400+20+5 .

First we can multiply the number 20 by 3 to get: 60 .

Then multiply the number 400 by 3 to get: 1200 .

Then multiply the number 5 by 3 to get: 15 .

Now, adding the results of all we get: .

425 \times 3 =1200+60+15 .

425 \times 3=1275 .

And, in this way, we can perform the multiplication from anywhere in the number.

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