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Amazing 9
Thanks S Froggatt


Every student writes down their telephone number (without area code) or any number of as many digits. 
Now shuffle these digits around to make a smaller number. 
Example :  6358 can be shuffled to make 3865. 
The more digits in their number, the better!

Now subtract the small number from the big number and tell them to keep the answer to themselves. 
Now highlight any digit (not a 0) in their answer.
Add up all the other digits:

3 4 1 6 2 2 9 => 3+1+6+2+2+9 = 23

Now go around the class, asking for the final answers and IMMEDIATELY tell the pupils which number they highlighted :
Answer = “23” 
“You highlighted "4”

One of the most incredible properties of our number system is its power to make tricky calculations very easy. 
Since we write our numbers in base 10, it follows that when we subtract the digits from a number we always end up with a multiple of 9. 
(This is basically saying that 1000 – 1 and 100 – 1 and 10 – 1 are all multiples of 9.)

One of the properties of any multiple of 9 is that its digital root (the sum of its digits, with the addition repeated until a single digit is reached) is also 9.

Putting these two together we can see that the answer to the subtraction is always going to be a multiple of nine. 
All you have to do is answer back with the smallest number that will make their total up to a multiple of 9. 
If it is already a multiple of 9, then they must have crossed out 0 or 9, but zero was forbidden, therefore 9 is the answer.

Decimals to fractions 

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