Question 750312
If I tripled one quarter of a fraction and multiplied it by that fraction, i would get one twelfth.
<pre>
Replace the words "a fraction" and "that fraction" with F
</pre>
  If I tripled one quarter of F and multiplied it by F, i would get one twelfth.
<pre>
Replace the words "one quarter of F" with {{{1/4}}}F
</pre>
  If I tripled {{{1/4}}}F and multiplied it by F, i would get one twelfth.
<pre>
Replace the words "If I tripled" with "3×"
</pre>
  3×{{{1/4}}}F and multiplied it by F, i would get one twelfth.
<pre>
Replace the words "and multiplied it by" by "×"
</pre>
 3×{{{1/4}}}F×F, i would get one twelfth.
<pre>
Replace the words ", i would get" with an equal sign "=":
</pre>
 3×{{{1/4}}}F×F = one twelfth.
<pre>
Replace the words "one twelfth" with {{{1/12}}}
</pre>
 3×{{{1/4}}}F×F = {{{1/12}}}
<pre>
We simplify that by changing 3×{{{1/4}}} to  {{{3/4}}}
and F×F to F²

 {{{3/4}}}F² = {{{1/12}}}

We clear the fractions by multiplying both sides by 12.

 9F² = 1

We divide both sides by 9

  F² = {{{1/9}}}
   F = {{{""+- 1/3}}}
</pre>
What is the original fraction.
<pre>
Either {{{1/3}}} or {{{-1/3}}}

Edwin</pre>