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How would you simplify something like: $(1184 / 60) / 60$ How do you figure out what to divide the number by just once to come out the same as when you divide it twice?

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$(a/b)/c=a/(bc)$.${}{}{}{}{}{}$

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    @Marshall: You could call it "multiplying numerator and denominator by $b$" as in $\frac{\frac{a}{b}}{c}=\frac{b\times\frac{a}{b}}{b\times c} =\frac{a}{b c}$2012-05-29
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$\rm Hint\!:\ (A/B)/C\ = X$

$\rm\ \ \iff\ A/B\ =\ C\ X$

$\rm\ \ \iff\ \ \ \: A\, =\, BC\ X$

$\rm\ \ \iff\ A/(BC) = X$

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Sandwich: The bread goes on top, the ham and cheese in the bottom: $\frac{\quad\frac{a}{b}\quad{\leftarrow\text{bread}\atop \leftarrow\text{cheese}}\quad}{\quad\frac{c}{d}\quad{\leftarrow\text{ham}\atop\leftarrow\text{bread}}\quad} = \frac{ad}{bc}\quad{\leftarrow\text{bread}\atop\leftarrow\text{ham and cheese}} $

You have $a=1186$, $b=60$, $c=60$, and $d=1$: $\frac{\quad\frac{1186}{60}\quad}{60} = \frac{\quad\frac{1186}{60}\quad}{\frac{60}{1}} = \frac{(1186)(1)}{(60)(60)}.$

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    Now you $m$ade me hungry.2012-05-29