Unit conversions are easy. Suppose some wiseguy said he was travelling at the speed of 161280 furlongs per fortnight. That sounds pretty impressive, but let's see what it is in miles per hour.
The "per" implies division, so the above can be expressed:
161280 furlongs/fortnight.
We know that we can multiply anything by "one" and it doesn't change its value. And, we know that anything divided by itself is equal to "one." So, we can multiply the above by "one" in the form of a ratio of equal quantities. We know that there are 8 furlongs in a mile, for instance, so such a ratio would be (one mile)/(8 furlongs). Note that the "furlongs" is below the (/). If we multiply the original by this ratio, we have:
161280 furlongs(one mile)/(fortnight(8 furlongs)).
With "furlongs" appearing both above and below the "/," we can consider that part of the ratio to be equal to "one." Or, as it is commonly expressed, the "furlongs" cancel. The result is:
161280 miles/(fortnight(8)) = 20160 miles/fortnight.
I've separated out this part of the total calculation to illustrate the principal involved, but, in fact, the calculation should be carried out in one step:
161280furlongs(mile)(fortnight)(day)/(fortnight(8furlongs)(14days)(24hours))
(It's difficult to show this with a keyboard, but, with pencil and paper, I usually draw a horizontal line across the paper in place of the keyboard's "/.")
Then, when you're certain that the proper units have been cancelled and you have what you want remaining, grab your calculator and tackle the numbers.
Oh, almost forgot: That turns out to be 60 mph.
