## Complex fraction simplification

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
chillywings
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Joined: Thu Mar 06, 2014 6:43 pm
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### Complex fraction simplification

Hi, so I'm working through some problems and see two apparently contradicting rules for simplifying a 'fraction over a fraction'. Sorry I cannot figure out how to write proper expressions here... I'm just going to type them out as best as I can.

First, there's x/5 over 2. My solution was to move the 2 up to the top and get 2x/5. Book says no, answer is x/10. Apparently, instead of multiplying by 2/2, I must multiply by 1/2. Ok, this makes sense if you plug in x=1, then .2/2 is .1, not .4. And dividing a number by 5 then also by 2 would be the same as dividing by 10. Damn, don't know where I got that idea from.

Along comes another problem, where we have 1/(x+1)/x. Solution? x/(x+1). Wtf? Thought I couldn't do that? But this makes sense by multiplying by x/x. Now, in the first problem, the 'small fraction' is in the top portion of the 'big fraction'. In the this one, it's in the bottom portion. But last I checked PEMDAS, this shouldn't make a freaking difference

Could someone explain the difference here? I'm clearly missing something...

Thank you

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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### Re: Complex fraction simplification

First, there's x/5 over 2.
Which of the following do you mean?

. . . . .$\mbox{a. }\, \frac{x}{\left(\frac{5}{2}\right)}$
. . . . .$\mbox{b. }\, \frac{\left(\frac{x}{5}\right)}{2}$
we have 1/(x+1)/x.
Which of the following do you mean?

. . . . .$\mbox{c. }\, \frac{1}{\left(\frac{x\, +\, 1}{x}\right)}$
. . . . .$\mbox{d. }\, \frac{\left(\frac{1}{x\, +\, 1}\right)}{x}$

chillywings
Posts: 2
Joined: Thu Mar 06, 2014 6:43 pm
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### Re: Complex fraction simplification

b and c. Thanks for the conversion. Do I merely have to operate as though those parenthesis are there all the time?

. . . . .$\mbox{b. }\, \frac{\left(\frac{x}{5}\right)}{2}$
. . . . .$\mbox{c. }\, \frac{1}{\left(\frac{x\, +\, 1}{x}\right)}$