Beginner confused by minus sign preceding parentheses

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 $$8+9$$?

• Indeed, this is referred to the second parenthesis: $-(-a-b)=+(a+b)$. – Crostul Nov 15 '16 at 13:40

Note that $$-8-9=-(8+9)=-17.$$
• 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!! – Steven Thate Nov 15 '16 at 16:05
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.