In July 1861, $366$ inches of rain fell in Cherrapunji, India.  What was the [average](https://artofproblemsolving.com/wiki/index.php/Average) rainfall in inches per hour during that month?
$\text{(A)}\ \frac{366}{31\times 24}$
$\text{(B)}\ \frac{366\times 31}{24}$
$\text{(C)}\ \frac{366\times 24}{31}$
$\text{(D)}\ \frac{31\times 24}{366}$
$\text{(E)}\  366\times 31\times 24$
We can express the number of inches of rain in a [ratio](https://artofproblemsolving.com/wiki/index.php/Ratio), $\frac{366 \text{ inches}}{1\text{  month}}$. We need to find to find the number of hours, but first we need to find the number of days. We know there are 31 days in July, so we get \[\frac{366 \text{ inches}}{1 \text{ month}} \times \frac{1 \text{ month}}{31 \text{ days}}\]
We know there are 24 hours in a day, so we get \[\frac{366 \text{ inches}}{1 \text{ month}} \times \frac{1 \text{ month}}{31 \text{ days}} \times \frac{1 \text{ day}}{24 \text{ hours}}\]
And simplifying gets us $\dfrac{366 \text{ inches}}{31 \times 24 \text{ hours}}$, which is $\boxed{\text{A}}$.
Note that in the simplifying step, we noted that the month and day units cancel, leaving us with only inches per hour.