An Easy, Yet Impressive Mental Math Trick You Don’t Know Yet (vol.1)
What if I asked you to multiply 43 by 11? How long would it take you? Give me a few minutes of your time and I’ll show you have to do it in a few seconds.
As it turns out, multiplying a two, even three, digit number by 11 is much more simple than you think. Let’s take the 43 x 11 example from earlier. The answer is, of course, 473. What about 52*11? 572. See the pattern here? These are simple examples, but the principle can be applied in much more complicated scenarios.
In case you missed it, this is the trick: When multiplying a number by 11, say AB x 11, the resulting number has the following format: A [A+B] B. That is, the first digit of the product is the first digit of the non-11 number. The middle digit is the sum of the two digits in the non-11 number, and the last digit is the last digit of the non-11 number. Another example: 35 x 11 = 385.
You may have noticed I’ve only a specific case up until this point: the case in which the sum of A + B is a 1 digit number. So what happens when the sum is a 2 digit number?
Say the sum of A+B is a two digit number, the result will follow this pattern:
AB x 11 = [A +1][Last digit of A+B][B]
Example: 78 X 11 = [7+1] = 858.
7+8 =15, so I keep the 5 for the middle digit, and carry the 1 to the first digit, adding it to 7. Lets look at that again:
84 x 11 = [8 +1] = 924.
Okay, so now you know the trick, but can you apply it to an even larger number? You may need a few minutes to wrap your head around this one:
12345 x 11 = [1+2][2+3][3+4][4+5] = 135795.
Now what about a larger number where the sum of the digits are greater than ten? You have the tools to figure this out on your own now, try 11 x 45678.