Question

25. Tiffany deposited two checks into her account this month. One check was for $70 and the second was for $25. Her balance at the end of the month was $204 and she made no withdrawals. Write and evaluate an expression that shows Tiffany's balance at the beginning of the month.
[] 204 + 70 + 25; $299
[] 204 - 70 + 25; $159
[] 204 + 70 - 25; $249
[] 204 - 70 - 25; $109

Answer 1

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