18 : deviation from base = 8
13 : deviation from base = 3
Now, we cross-add one of the deviations to the number, for instance, 18 + 3. Either way we get 21. That will be our left most number. Now we multiply the deviations, 8 X 3, to get 24. Now since we are using base 10, we leave 4 (from the 24) as the right most number and carry the 2 to the left most number, which is 21. So we get [21 + 2].[4] = 234!
This is explained quite thoroughly in other websites and posts, especially here.
But if that intrigued your interest, how about if we try something else? Lets say we have two numbers, both end with the same number, lets say 23 and 13.
If we want to quickly (and mentally) multiply the numbers, just do this 3 step process:
1. Square the ending number to get the the right-most number of the answer: in this case its 9
2. Add the two first numbers together, (2 + 1) and multiply it with the ending number (3): in this case its 3 X 3. This gives us the middle number, which is 9.
3. To get the left-most number, just multiply the first numbers together, in this case (2 X 1), to get 2.
So, the answer is 299.
Lets try that with a bigger number, lets say (212 X 312). In this case the common ending number is not 2 but 12! So to get the right-most number, we just square the ending number, which is 12 to get 144. But since the ending number is based on ten, we leave 44 as the right-most number of the answer and carry the 1 to add to the middle.
The middle number is simply (2+3) X 12, which is 60. Add the 1 from the carry we just did, and you get 61, which is the middle number.
The left most number is simply (2X3) = 6.
So the answer is: 66144.
Since the idea is to keep the multiplication as simple as possible, this technique can cut your calculation time considerably and even save on paper! I can do this similar calculations in less than 10 seconds, and I would think younger students can do it in less.
What do you think? Email me.
