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## #1 2005-08-26 09:43:27

mikau
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### factor theoroms

I made a small oberservation which is really obvious but I never quite realized before and it has helped me to simplify quicker once I've solved for the values of some variables.

if xy = 1, then x and y are reciprocals of eachother, so if you know x = 2 you know y = 1/2. Of course solving for x or y does the same thing but its slightly faster to just take the reciprocal.

Likewise, if xy = 5, then x = 5 times the reciprocal of y and y = 5 times the reciprocal of x.  Of course you can just solve for x or y but I find it faster to simply take the reciprocal and multiply times 5.

So obviousy if xy= n then x = n/y and y = n/x      but if I think of it as x = 1/y * n, or y = 1/x*n its slighty faster to do in my head, for me at least.

Likewise, if xyz = 1, then the product of 2 of the variavles equals the reciprocal of the other, and I think if xyz = n, then the product of 2 of the variables will equal n times the reciprocal of the other.

I find its just good to be aware of this, it tends to speed things up.

A logarithm is just a misspelled algorithm.

## #2 2005-08-26 10:45:31

kylekatarn
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### Re: factor theoroms

that's a pretty obvious, but interesting observation

## #3 2005-08-27 02:08:20

mikau
Super Member

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### Re: factor theoroms

Precisly. But the obvious observations are the ones that are most often overlooked. For me at least. lol.

A logarithm is just a misspelled algorithm.

## #4 2005-08-27 08:15:25

MathsIsFun

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### Re: factor theoroms

Inverses in Mathematics: