Different arithmetic based on the presentation of an equation

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chromechris

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I have an expression in which I am not sure which way to translate it, in order to solve it, it is the following:
[MATH] \frac{-5}{-5+25} [/MATH]
[MATH] \frac{-5}{20} [/MATH]
[MATH] -\frac{1}{4} [/MATH]The arithmetic above gave me a correct answer in my question, however I looked at the expression again and wondered if there was other ways of interpreting and solving it. I tried solving it a different way, see below:
[MATH] \frac{-5}{-5+25} [/MATH]
[MATH] -5/(-5+25) [/MATH]
[MATH] 1-5 [/MATH]
[MATH] -4 [/MATH]Another way I thought of doing it:
[MATH] -5/-5+25 [/MATH]
[MATH] 1+25 [/MATH]
[MATH] 26 [/MATH]
Why can I not solve this problem correctly using the arithmetic from the 2 last ways I tried? What makes the first way the right way to solve the equation. Where are my mistakes, and why are they incorrect? Thank you!
 
chromechris said:
I have an expression in which I am not sure which way to translate it, in order to solve it, it is the following:
[MATH] \frac{-5}{-5+25} [/MATH]
[MATH] \frac{-5}{20} [/MATH]
[MATH] -\frac{1}{4} [/MATH]The arithmetic above gave me a correct answer in my question, however I looked at the expression again and wondered if there was other ways of interpreting and solving it. I tried solving it a different way, see below:
[MATH] \frac{-5}{-5+25} [/MATH]
[MATH] -5/(-5+25) [/MATH]
[MATH] 1-5 [/MATH]
[MATH] -4 [/MATH]Another way I thought of doing it:
[MATH] -5/-5+25 [/MATH]
[MATH] 1+25 [/MATH]
[MATH] 26 [/MATH]
Why can I not solve this problem correctly using the arithmetic from the 2 last ways I tried? What makes the first way the right way to solve the equation. Where are my mistakes, and why are they incorrect? Thank you!
Click to expand...
Are you a TROLL? If not this why did you post the joke that is the above?
Anyone with a modicum of mathematical knowledge (say second grade+) knows:
\(25/5\) means twenty-five divided by five.
\(-5+25=20\)
\(1-5=-4\)
So are you a joke? Please tell us if toy have less that a third grade education.
 
At best [math]\dfrac{-5}{-5+25} = \dfrac{-5}{-5} + \dfrac{-5}{25} = 1 - \dfrac{1}{5}[/math] And this is WRONG! You need to divide by (-5+25) Not divide by -5 and divide by 25.

You really should know that 5/25 is NOT 5 after all 5/1 is 5!!!!
 
chromechris said:
Why can I not solve this problem correctly using the arithmetic from the 2 last ways I tried? What makes the first way the right way to solve the equation. Where are my mistakes, and why are they incorrect? Thank you!
Click to expand...
A better question is, why do you think the alternative ways could be correct? If you have no answer, then you can expect them to be wrong.

In math, you should only make changes that you have a reason for. Otherwise, in evaluating, you should do exactly what it says, and nothing else. That's what you did the first time: It says to add the terms in the denominator, then divide the numerator by that.

Your second way is similar to distributing, and in fact it would have been correct to say 1/(-1 + 5), because the addition is in the denominator, not the numerator. But there is no rule that says a/(b+c) = a/b + a/c. There is a rule that says (a+b)/c = a/c + b/c.

Your third attempt dropped the parentheses. There is no rule that a/(b+c) = a/b + c.

So you just can't do those things.
 
pka said:
Are you a TROLL? If not this why did you post the joke that is the above?
Anyone with a modicum of mathematical knowledge (say second grade+) knows:
\(25/5\) means twenty-five divided by five.
\(-5+25=20\)
\(1-5=-4\)
So are you a joke? Please tell us if toy have less that a third grade education.
Click to expand...
My education does include 3rd grade and the previous grades. Sorry for the extra information, I'm just used to always showing work.
 
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