Give your friend another blank piece of paper and tell her/him to write a three digit number, all different digits and no zeros. Let's suppose 371 was chosen.
Then ask her/him to reverse the numbers and subtract the smaller from the larger: 371-173=198
Once that is done tell your friend to reverse the difference and add it to the original difference: 198 + 891=1089
Sometimes the difference is 99 but tell your friend if the difference is a two digit number to add a zero at the end and treat the zero as a regular number:
990 +099=1089
Now that all the adding is done tell your friend to look at the piece of paper you gave her/him before. The secret of course no matter what three digit number your friend had chosen the answer will always be 1089.
If you do not tell your friend the secret she/he will be wondering how you got that number on that piece of paper.
So what is going on here? Well, if you take numbers (2 digits or more) and reverse it and subtract the smaller from the larger you will always have a number that can be divided evenly by 9.
In case of three digit numbers (all different digits) the number 9 will always be in the middle, not only that but the first and last digits will always add up to 9. Example: 198
This time let's say your friend chose the number 276:
672 - 276=396 396 + 693=1089 Here will go again
the same answer: 1089
Since the first and last digits add up to the sum of the middle digit it means that the difference can also be divided evenly by 11. :)
If you want to multiply 23 by 11 all one has to do is add the 2 and the 3 and put it in the middle 253. Put the calculator down you can do this one and similar ones in your head.
Here is another example: 11 x 71 =781 notice again the first and last total equals the sum of the middle digit.
However multiplying by 11 to a number you have to carry takes a little work but it can be done in your head:
19 x 11=209
Watch the 1089 video below:
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