puzzling parentheses

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plugginaway

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Nov 28, 2008
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Ok folks, I cannot tell you how happy I am to have found this site. I hope that I will be able to pick the brains of those much wiser than I. I have read some of your responses and I think it is most kind of all of you to take the time and help others. I am an English teacher by profession but would very much like to go back and relearn or should I say truly learn all the math I once studied. Ok here are my problems:
Puzzling parentheses:
What's the difference between (5(3-7) + 4^3)/(-2-3)^2 and
5(3-7) + 4^3/(-2-3)^2
Are they the same? Or with the second one, is the division done with just 4^3/(-2-3)^2 and then added to -20?
The text I am using says that the top one equals
5(3-7) + 4^3 over(horizontal fraction line)(-2-3)^2 whereas the bottom one equals
5(3-7) + 4^3 divided by(using the superscript dot, line, subscript dot division symbol) (-2-3)^2

I think one of my difficulties is understanding how a vertical fraction line differs from a horizontal one as well how they both differ from the typical division symbol with dots
i.e. 16/2x ,and 16 over 2x, and 16 superscript dot -line -subscript dot 2x
Any help or links would be appreciated - until then I'll just keep...
plugginaway
 
Hi Denis.
Thank you for your prompt reply. I had felt fairly comfortable using PEMDAS until I ran into this problem. With both equations my numerator is, I believe
-20 +48 over 36 or... the second one has a numerator of -20 + (48over 36). Am I close?
And then I do not understand why the equivalent equation makes a distinction between the types of fraction symbols that are used. I thought they were all pretty interchangeable. Sorry if my response really shows my stupidity. If the answer to my questions still lies in the link you gave me, please feel free to point me there again and I will give it another look. By the way, does Free Math Help have a math font box as they do with smilies?
plugginaway
 
plugginaway said:
i.e. 16/2x ,and 16 over 2x, and 16 superscript dot -line -subscript dot 2x
Click to expand...
"superscript dot -line -subscript dot" is the "old" division sign; / is now used instead; means same thing

16
==
2x
That means 16 is divided by the product of 2 times x

To show properly, brackets required: 16/(2x)
16/2x means 16 divided by 2, multiply result by x: quite a difference; example:
if x=4, 16/2x = 16/2 = 8 * 4 = 32, while 16/(2x) = 16 / 8 = 2
 
Thanks once again Denis for the explanation regarding the three different division symbols.
Based on the above responses would the answers be:
(5(3-7) + 4^3)/(-2-3)^2 =
-20 + 64 / 36
44/ 36
11/9
1 and 2/9

and

5(3-7) + 4^3/(-2-3)^2
5 (-4) + 64/36
-20 + 16/9
-20 + 1 and 7/9
-18 and 2/9
 
plugginaway said:
(5(3-7) + 4^3)/(-2-3)^2 =
-20 + 64 / 36
44/ 36
11/9
1 and 2/9
Click to expand...
Close but no ceegar!
To start, your "-20 + 64 / 36" needs brackets: (-20 + 64) / 36
Then your "36" is wrong: -2-3 = -5 ; (-5)^2 = 25
So answer is 44/25 ; OK?
5(3-7) + 4^3/(-2-3)^2
5 (-4) + 64/36
-20 + 16/9
-20 + 1 and 7/9
-18 and 2/9
Click to expand...
Since (-2-3)^2 = 25:
-20 + 64/25
= (-500 + 64) / 25
= -436 / 25 ; OK?
 
Thanks again. It was really foolish of me to multiply -2 and -3. So...I understand the first one you corrected, but the second one..where did the 500 come from?
Denis wrote:
Since (-2-3)^2 = 25:
-20 + 64/25
= (-500 + 64) / 25
= -436 / 25 ; OK?

why isn't it?:

5(3-7) + 4^3/(-2-3)^2
5 (-4) + 64/25
-20 + (64/25)
-20 + 2 and 14/25
-18 and 14/25
Sorry for my blockheadedness
 
plugginaway said:
Thanks again. It was really foolish of me to multiply -2 and -3. So...I understand the first one you corrected, but the second one..where did the 500 come from?
Denis wrote:
Since (-2-3)^2 = 25:
-20 + 64/25
= (-500 + 64) / 25
= -436 / 25 ; OK?

why isn't it?:

5(3-7) + 4^3/(-2-3)^2
5 (-4) + 64/25
-20 + (64/25)
-20 + 2 and 14/25
-18 and 14/25 <<< Mathematically you need to write it as -18 + 14/25

If you want to write as one fraction then

\(\displaystyle - \, 18 \, + \, \frac{14}{25}\)

\(\displaystyle = - \, \frac{18\cdot 25}{25} \, + \, \frac{14}{25} \,\)

\(\displaystyle = \, - \, \frac{450}{25} \, + \, \frac{14}{25} \,\) ..edited typo pointed out below

\(\displaystyle = - \, \frac{436}{25} \,\)

\(\displaystyle = - \, 17\frac {11}{25}\)

Sorry for my blockheadedness
Click to expand...
 
Subhotosh
Thank you for putting in every step but it is -436/25 right?
I think there was a small typo in your steps when you put in 18/25 instead of 14/25--( I say that with much caution considering your math ability so please forgive me if I am wrong)

so it would be -436/25 and then -17 11/25-yes?

Both you and Denis have been very helpful.Thanks again.
 
plugginaway said:
Subhotosh
Thank you for putting in every step but it is -436/25 right?
I think there was a small typo in your steps when you put in 18/25 instead of 14/25--( I say that with much caution considering your math ability so please forgive me if I am wrong)

so it would be -436/25 and then -17 11/25-yes?

Both you and Denis have been very helpful.Thanks again.
Click to expand...

You are correct
 
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