The first thing to do is to start with something not quite so
complicated, so you can get used to the ideas first. But let's go
ahead with this one, to check your work.
Here's one way I write these to demonstrate how to think it through:
(18/2){[(9 x 9 - 1)/ 2]-[5 x 20 - (7 x 9 - 2)]}
\____/ \_________/ \_________/
9 {[ 80 / 2]-[5 x 20 - 61 ]}
\______________/ \____________________/
9 { 40 - 39 }
\_______________________________________/
9 * 1
\____________________/
9
So you're correct, and your work was fine. The only thing I did
differently was to evaluate 18/2 earlier, because nothing stood in its
way; I could have waited as you did.
What parentheses do is to contain a subexpression that has to be fully
evaluated before it can be used in any containing expression. That's
why you work from the inside out: you can't use what's inside until
you evaluate it all, so you might as well start there. But if you
forgot to, you'd still have a reminder. Here's an example:
2[(3 + 7)(3 - 2) - 3(2 + 2)]
If I didn't bother with the inside-out "rule", I might just start
trying to evaluate at the left (paying attention to the order of
operations, of course): 2 times ... what? Well, the second number in
that multiplication is the whole thing inside [...], so I have to put
it on hold until I do that. So I focus on
(3 + 7)(3 - 2) - 3(2 + 2)
Now I start that. The first piece is (3 + 7), so I evaluate that
whole thing and get 10. Now I have to multiply it by (3 - 2), so I
stop and evaluate that, which gives 1. Now I can multiply 10 by 1 and
get 10. So I keep going; I have to subtract something from that, but
since the next bit is a product, I have to do that first. I'll have 3
times the next parenthesis; that's 3 times 4, so I have 12. The
subtraction I put off is 10 - 12 = -2.
Now, this is what the whole [...] is, so I go back and do that last
multiplication:
2*(-2) = -4
shows the reflection about y-axis i.e, (x,y)→(-x,y).