Very simple fraction

Nov 2009
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Can \(\displaystyle \frac{3+x}{3}\) be simplified to \(\displaystyle \frac{x}{3}\)
 
Feb 2010
191
80
Can \(\displaystyle \frac{3+x}{3}\) be simplified to \(\displaystyle \frac{x}{3}\)
No, because \(\displaystyle \frac{3+x}{3} = \frac{3}{3}+\frac{x}{3} = 1 + \frac{x}{3}\).

You can't just get rid of the 3 in the numerator.

Hope that helps :)

Mathemagister
 
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Dec 2007
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Ottawa, Canada
Can \(\displaystyle \frac{3+x}{3}\) be simplified to \(\displaystyle \frac{x}{3}\)
Sure...but your final solution will be incorrect (Giggle)
 
Dec 2009
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Can \(\displaystyle \frac{3+x}{3}\) be simplified to \(\displaystyle \frac{x}{3}\)
If x approaches infinity,

then \(\displaystyle \frac{x+3}{3}\) will be indistinguishable from \(\displaystyle \frac{x}{3}\)

in other words x has to be so large that x is "no different" from x+3
 

undefined

MHF Hall of Honor
Mar 2010
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Chicago
If x approaches infinity,

then \(\displaystyle \frac{x+3}{3}\) will be indistinguishable from \(\displaystyle \frac{x}{3}\)

in other words x has to be so large that x is "no different" from x+3
Along these lines we would write that, for "large" x (in fact, for x with "large" absolute value),

\(\displaystyle \frac{x+3}{3} \approx \frac{x}{3}\)

If this is part of some larger, more complicated equation, it may be useful to replace the original expression with an approximation. This practice is often done when modeling actual data in the sciences.
 
Feb 2010
191
80
Along these lines we would write that, for "large" x (in fact, for x with "large" absolute value),

\(\displaystyle \frac{x+3}{3} \approx \frac{x}{3}\)

If this is part of some larger, more complicated equation, it may be useful to replace the original expression with an approximation. This practice is often done when modeling actual data in the sciences.
A more mathematically tight way of writing that would be

\(\displaystyle \lim_{x\rightarrow \pm \infty} \frac{3+x}{3} = \lim_{x\rightarrow \pm \infty} \frac{x}{3}\)
 

mr fantastic

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Dec 2007
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Can \(\displaystyle \frac{3+x}{3}\) be simplified to \(\displaystyle \frac{x}{3}\)
Let x = 1 in your proposed simplification. Does 4/3 = 1/3?
 
Dec 2007
3,184
558
Ottawa, Canada
Thanks Mr F.
WHY spend time (even 1 second) in trying to somehow reason out
that (a + b) / b = a / b ....
 

undefined

MHF Hall of Honor
Mar 2010
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Thanks Mr F.
WHY spend time (even 1 second) in trying to somehow reason out
that (a + b) / b = a / b ....
Haha, I thought the amount of discussion generated by the original post was pretty silly too, but Archie Meade's post seemed like an interesting spin to me (like in those lateral thinking problems that I also often find silly, but can have interesting solutions), which I thought was worth a little extra commentary, and apparently mathemagister felt a little more extra commentary was appropriate in response to my post, which contributed to this thread being ridiculously long. Next we'll be discussing how the proposed simplification relates to the Riemann hypothesis and P vs NP. (Rofl)
 
Jul 2009
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Melbourne
You can only cancel fractions when 2 numbers/pronumerals are multiplied. You can't do it when their added or subtracted