How is finding a unit rate similar to solving a proportion

A unit rate is a quantity per one unit. For example, miles per hour (mi/h). The "one unit" is 1 hour.
However, 10 miles per 2 hours (10 mi/2h) would not be a unit rate because it is per 2 hours, not 1. The unit rate for 10 mi/2h would be 5 mi/h.

You can find the unit rate by simply dividing the numerator by the denominator. (The fraction bar is a division bar!)
In simplifying 10 mi/2h, I divided the numerator (10mi) by the denominator (2h).
10 divided by 2 is 5, so the unit rate is 5 mi/h.