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When is a fraction simplified?

"A fraction is simplified if the numerator and denominator do not have any common factors other than 1."

This is what I read on this website: http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut3_fractions.htm

I think a fraction is simplified when the numerator or denominator have common factors other than 1. For example: $\frac {14} 6 = \frac73$

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"It 'is' already simplified" and "it 'is' to be simplified". Seems to be your problem. –  Mr.ØØ7 Apr 23 '13 at 9:04
    
@exploringnet can you answer my question? –  Samama Fahim Apr 23 '13 at 9:08
    
I have not fully understood what problem do you have , but think you have been confused by the language. –  Mr.ØØ7 Apr 23 '13 at 9:09
    
7 and 3 have no common factors other than 1. –  Jack M Apr 23 '13 at 9:10
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It happens sometimes when you are too much into the mathematics and ignore the English !! :) –  lsp Apr 23 '13 at 9:20

2 Answers 2

up vote 2 down vote accepted

"A fraction is simplified if the numerator and denominator do not have any common factors other than 1."

The is used here says that it is(currently) simplified, already simplified.

Whereas

"I think a fraction is simplified when the numerator or denominator have common factors other than 1. For example: $14/6=7/3$"

Here is means it is(needs to be) simplified when it is not.

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Most of the time english confuses me too. –  Mr.ØØ7 Apr 23 '13 at 9:18
    
I don't think that your explanation of the second sentence is correct. Can you give other examples of such usage in English to support that meaning? –  Math Gems Apr 23 '13 at 18:49

You are getting confused between "A fraction 'is' simplified" and "A fraction 'can' be simplified".

In the example that you provided:

$\dfrac{7}{3}$ is the 'simplified fraction' and $\dfrac{14}{6}$ is the fraction that is getting simplified to $\dfrac{7}{3}$.

The example is given to make you understand that $\dfrac{14}{6}$ is simplified to $\dfrac{7}{3}$ and it cannot be simplified further making it a 'simplified fraction'

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