Question 164517
I can only tell you how I do it. I had a very good teacher in 
high school demonstrate it, and it stuck pretty good in
college.
The best way to learn is do do REALLY long coversions.
Convert cm/sec to miles/hr
OK-I've got to get rid of that cm on top
I can do it like this:
(cm)(miles/cm)
Stop and think- Why can I do this? The only way I can do it
and not change what I started out with is if the (cm/mile)=1,
then (cm)x1 = (cm).
So, as long as I have calculated the EXACT number of cm in 1 mile
or the EXACT fraction of a mile in 1 cm, then I am doing (cm)x1 = (cm)
OK
(cm)(miles/cm) = miles because the cm on top cancels with the
one on the bottom.But what if I don't know the conversion (miles/cm)?
Maybe I should try (meters/cm)
(cm)(meters/cm) = meters. But I want miles. I've got more work to do
(cm)(meters/cm)(miles/meter) = miles
Can you see that cm on top and bottom are the same as (cm/cm)
and meters on top and bottom are the same as (meters/meters)?
Again, what if I don't know the conversion (miles/meter)?
What if I only know (feet/meter)? Then I can do:
(cm)(meters/cm)(feet/meter)(miles/feet) = miles
You can look at it like this:
(cm/cm)(meters/meters)(feet/feet)(miles)
I'm left with miles which is what I want, but
it only works if my conversions are EXACTLY correct
How many miles are in 1 foot?
A very small fraction of a mile: {{{1/5280}}}miles to be exact
How many feet are in a meter? Around {{{3}}}, but you can look it up.
If you get the idea of units cancelling on the top
and bottom, you're OK. Keep practicing long conversions to get it 
right. Remember if somewhere you say (11 inches/1 foot), you'll
be wrong even if your units are correct