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Old 10-03-2012, 03:07 PM   #11
cj wisty
Non Ignorant Math Team
 
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i already knew this but when i saw the OP i wondered why that was and its actually pretty obvious and can b proven simply.

if u write all ur numbers in base x (OP says x=10 which is ofc the most commonly used base) and then use timetables of x-1 (OP says x-1=9) and then write out all the timetables u get

1(x-1)=(x-1) obviously cuz x is the base the digit on the left will b 0 and the digit on the right will b (x-1)

2(x-1)=(2x-2) obviously cuz x is the base the digit on the left will b 1 and the digit on the right will b (x-2)

3(x-1)=(3x-3) obviously cuz x is the base the digit on the left will b 2 and the digit on the right will b (x-3)

4(x-1)=(4x-4) obviously cuz x is the base the digit on the left will b 3 and the digit on the right will b (x-4)

and this can b repeated for all two digit numbers when multiplying a number which is 1 under the base.

so eg if we skip to 7 times 9. so here were saying x=10 and (x-1)=9

and so 7 times 9=7(x-1)=7x-7 which means the left hand digit is 6 and the right hand digit is x-7

so we know the left hand digit is 6 and we now need to find out the right hand digit. right hand digit is (x-7) and substituting (x=10) gives us (10-7) which is 3. so the right hand digit is 3. putting these 2 facts together gives us the number 63.

therefore 7 times 9=63
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