How does one calculate proportions? Eww! Hi, I'm Jimmy Chang, I've been teaching college math for almost a decade and we're here to calculate and define proportions. Now proportions, they are associated with that one thing that we generally don't like to work with besides work problems and that is fractions. But unfortunately, you know fractions and proportions are part of life and the good news though is there are ways that you can figure out how you would put the numbers in that fraction form. Now the key though is to look for those words so you know what numbers need to be on top and what numbers need to be on the bottom. Now here's a couple of words that pop up a lot in proportions. The first word is per and the second word is to. Here's an example of each. Take for example the phrase thirty miles per gallon. Now the emphasis here, the focus here is on the word per because the word or numbers that are right after the word per is going to give you an indicator as to what goes on the bottom. Now, per gallon the implication here is per one gallon. Sometimes the one is not written, but what that tells you though is because the word gallon is right after the per, that tells you right away that the word gallon is going to go in the denominator. That will always be the case. Where does that put the thirty miles? That tells you instantly that thirty miles is in the numerator on top. So to indicate this as a proportion, thirty miles per gallon is going to be thirty miles on top, one gallon at the bottom. Now, the other example is the word to. To has the same function as the word per. The to tells you what number goes on top, what numbers go on the bottom. One practical use of it is calculating odds. When you see the phrase for example the odds are sixteen to three, again, the number or words after the word to tells you immediately what goes in the denominator, because the number three is after the word to, that tells you the three belongs at the bottom. That makes the sixteen go on top. So the words per and to give you great indicators as to what numbers you are dividing by. And my name is Jimmy Chang and that is exactly how you define proportions.