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I'm a very simple person with basic math knowledge. Recently I run into huge problems when calculating how much I spent.

Sometimes to calculate how much I spent I do a calculation $final sum - start sum$. However at other times I do $start sum - final sum$.

When I take the absolute values, are these two values guaranteed to be equal? I've noticed sometimes when I do it one way, or the other way, I get different numbers. Is it because I made a mistake entering the numbers or it's not guaranteed that absolute values are equal?

Somehow I can't reproduce this error today but I just ran into it yesterday. When I did $start sum - final sum$ I got value $y$, but when I did $final sum - start sum$ I got value $z$. I forgot to write down the numbers.

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  • $\begingroup$ |x|=|-x|. so you must hv done some mistake $\endgroup$ – voldemort Jan 22 '15 at 18:37
  • $\begingroup$ Thanks @voldemort. I've been actually running into this issue for the last few years. I'll try to write numbers down. Somehow when doing money calculations I think there is value $x$ for which this isn't true (because of cents I think). I'll try to get exact dollar and cent values next time. $\endgroup$ – bodacydo Jan 22 '15 at 18:39
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The best way to answer this might be to pick two arbitrary values for your starting sum and your final sum.

So, let $X=startsum$ and $Y=finalsum$

Now, let $x$=100 and $y$=175

$$x-y=-75$$ $$y-x=75$$ $$|-75|=75$$

So you see, any discrepancy between the absolute values of x-y and y-x must be some input error on your part.

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  • $\begingroup$ Thanks. Does this work also if there are cents in the values? $\endgroup$ – bodacydo Jan 23 '15 at 7:35
  • $\begingroup$ I don't think it works if there are cents. $\endgroup$ – bodacydo Mar 7 '15 at 13:10

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