The Mathematic Discovery

This is just a quick post that documents another method for checking your multiplication. I learned this from my dad, and he learned from an old fashioned Asian teacher back in Vietnam. Anyway, I thought it was really useful and helpful, a much easier and "simpler" method than using division to check your work (or a calculator, like in today's world).

Ok, so I don't know if this method is an official one or that it has a name, but I call it the X method. And it works for me.

Sample
Problem   1 Both Single Digits
        9  
     x 3 
      27
So make an X, notice how the X has 4 spaces? (I can't draw or at least I don't know how to with this blog so I need to describe it). Well, we will write a number in each space, and I will show you how. So in the Top Space, we will call it Space A (the V part of the X), Space B is the bottom space, Space C is the right space, and space D will be the left space.

1. Take the factor, in this case 9 and write it in Space A and take the 2nd (which is 3) and write it at the bottom.
2. Now take top value (which is 9) and the bottom value which is 3 and multiple them together which would give you 27. (yes, I know at this point you are probably thinking that is stupid...that's not a "method" to checking your multiplication, but I assure you I am starting with a simple example, I will provide other more complex problems).

3. 27 is the numbers 2 and 7 right? so take the SUM of 2 and 7 = 9.....--> 27 ==> 2+7 = 9 and write that number in the right space of the X

4.Now take the product of the original problem which is 27, which is the number 2 and 7. Take the sum of 2+7 = 9.

5. You should now see that the right space(C) and the left space(D) are the same number. And having that they are the same number, it means you did your multiplication correctly.

Problem 2- 1 single digit, 1 double digit
      23
   x   3
      69

1. Take the first factor, in this case 23 and take the sum of its digits which is 2+3 = 5 and write it in Space A and take the 2nd factor, which is 3 and write it at the bottom Space B.
2. Now take top value (which is 5) and the bottom value which is 3 and multiple them together which would give you 15. (yeah, notice that it is different than the previous problem?).

3. 15 is the numbers 1 and 5 right? so take the SUM of 1 and 5 = 6.....--> 27 ==> 1+5 = 6 and write that number in the right space of the X

4.Now take the product of the original problem which is 69, which are the numbers 6 and 9. Take the sum of the two numbers....6+9 = 15. Since it is 15, you must first do a 1+5 =6 ..now write 6 in Space D (left space).

5. You should now see that the right space(C) 6 and the left space(D) 6 are the same number. And having that they are the same number, it means you did your multiplication correctly.

NOTE*- Notice that when I had a number greater than 9, I do the SUM of the two digits (e.g 15 --> 1+5 =6 instead of 15)? The reason is to keep the checking process simple and to prevent miscalculation with numbers. Of course you can keep the 2 digit number, but then you must do it for both calculations in space C and D. Keeping it 1 digit is easier.
Now let's do a bigger number and check for its correction

Problem 3 - 2 double digits           
            25
       x   17
          425


1. Take the first factor, in this case 25 and take the sum of its digits which is 2+5 = 7 and write 7 in Space A and take the 2nd factor, which is 17 so you take 1+7 = 8 and write 8 at the bottom Space B.

2. Now take top value (which you wrote down from the prev step 7) and the bottom value which is 8 and multiple them together which would give you 56.

3. 56 is the numbers 5 and 6 right? so take the SUM of 5 and 6 = 11, 11 is still >9 so you need to take the sum of 11 so....1+1 = 2 and write that number in the right space of the X

4.Now take the product of the original problem which is 425, which are the numbers 4,2,5. Take the sum of the three numbers....4+2+5 =11. Since it is 11 (which is greater than 9) you must take the sum of the two digits 1+1=2 ..now write 2 in Space D (left space).

5. You should now see that the right space(C) 2 and the left space(D) 2 are the same number. And having that they are the same number, it means you did your multiplication correctly.

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This method should work for natural numbers, I don't know if they work any other realm of numbers e.g. integers, decimals etc. The method should also work for numbers in the hundreds, and thousandths place.

I know this seems to take a lot longer to do, however, the checking is much simpler, by keeping the numbers allowed when added to be no greater than 9, and thus easier to check compared to long division to check your math, but that's just me.

-The Social Nerd