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Apologies for the possibly vague question title. I honestly don't know how to concisely phrase my issue.

I'm going back to school and am doing some self-studying before math placement exams. I was a slacker in high school (live and learn), so while I'm sure this has a really simple explanation to it, I can't get to it on my own.

Here is the simple problem I am trying to solve:

$$ \left( - \frac{2}{9} - \frac{1}{4} \right) - \left[ - \frac{5}{18} - \left( \frac{1}{2} \right) \right] $$

Eventually, supposedly incorrectly, I simplified it to the following:

$$ \left( \frac{-8-9}{36} \right) - \left( \frac{-10+18}{36} \right) \Rightarrow \frac{1}{36} - \frac{8}{36} \Rightarrow - \frac{7}{36} $$

After feeling good about having slogged through that, I used the Photomath app on my phone to capture the problem and check to make sure my solution was correct.

Photomath came up with a different solution: $ - \frac{25}{36} $

Thankfully Photomath has a handy feature that displays the steps it took to simplify the expression. I noticed it treated the first grouping differently than I did, it came up with: $ \left( - \frac{8+9}{36} \right) $.

It included the note: "When there is a '-' sign in front of the parenthesis change the sign of each term in parenthesis."

I'm confused, because in that first group/parenthesis, there is no minus sign in front of it. Why would it then change $-8-9$ to $8+9$?

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  • $\begingroup$ Indeed, this is referred to the second parenthesis: $-(-a-b)=+(a+b)$. $\endgroup$ – Crostul Nov 15 '16 at 13:40
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Note that $$-8-9=-(8+9)=-17.$$

"When there is a '-' sign in front of the parenthesis change the sign of each term in parenthesis" can be written as "When we change the sign of each term we write all of them in a parenthesis with a '-' in front".

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  • $\begingroup$ Thank you. I was treating $-8-9$ as "negative 8 minus negative nine" which when I think about it, doesn't make much sense. Reading it as $(-8)+(-9)$ helped. Thanks!! $\endgroup$ – Steven Thate Nov 15 '16 at 16:05
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You did just right. The problem is in the second set -- within the brackets. The $-(1/2)$ should have become $-9/18$, so that you'd get $\frac{-10-18}{36}$.As @mfl points out, you then have to do the arithmetic correctly on the negative numbers that you get.

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  • $\begingroup$ I wish I could "accept" both answers :) Between the two of them, and a number of cracks and "doh" and "ah-ha" moments, I finally got it. Thanks :) $\endgroup$ – Steven Thate Nov 15 '16 at 16:06
  • $\begingroup$ No prob. I think you accepted the right one. :) $\endgroup$ – John Hughes Nov 16 '16 at 2:13

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