Per (or per-1) for dummies

If you're an expert quantifier, you'll lose nothing by moseying along.

Fuller title: Equivalence of two quantities, such as x A’s are equivalent to y M’s, where x is a specific quantity of A’s and y is a specific quantity of M’s

Suppose 200 A’s (A is an object of some kind, an apple, for example) is “equivalent” to 50 M’s (M is an object of some kind that isn’t A, a melon, for example).

Question 1. How many A’s are equivalent to 1 M?

To answer that, divide the count of A’s by the count of M’s. In the example here, that is 200/50 = 4. That is, 4 A’s are equivalent to 1 M.

Question 2. How many M’s are equivalent to 1 A?

To answer that, divide the count of M’s by the count of A’s. In the example here, that is 50/200 = 0.25. That is, 0.25 M’s are equivalent to 1 A. To say that in different words, we can say that 25 M’s are equivalent to 100 A’s, or that one can trade 25% of a certain amount of M’s for the amount of M’s in A’s; we can also say that one-quarter M is equivalent to 1 A.

Point to remember: whatever object count we set to 1 (count of M, 50, in our example) goes to the denominator.

In general, this concept of “equivalence” carries to any construct that includes “per” when it means “per 1”. For example, if you travel 500 miles in 10 hours, then how many miles have you traveled per hour? The “1” goes with the hours, so the answer would be “you have traveled 500/10 miles per hour,” or “you have traveled 50 miles per hour.” We know that as the average traveling speed.