Name the whole first

There are 75 books on a shelf. 15 of them are comic books. Express the number of comic books as a percentage of the number of books on the shelf. Start with the whole. Here's one bar for all 75 books on the shelf. The question asks for a percentage of the number of books on the shelf, so the shelf is the whole, and the whole is all 75 books. The whole is always one hundred percent, so 75 books is one hundred percent. Now the part. 15 of those 75 books are comic books, and those 15 are inside the same shelf, not beside it. The blue piece is the 15 comic books, and the rest of the bar is the books that are not comics. A part turns into a percentage in two steps, and the first one is a fraction. The part is the 15 comic books. The whole is the 75 books on the shelf. So the part goes over the whole: 15 over 75. 15 and 75 both divide by 15. That leaves 1 over 5, so the comic books are one fifth of the shelf. One fifth is a fraction. It is not a percentage yet. Percent means out of one hundred, so here's the very same bar with a second reading under it: nothing at this end, one hundred percent at the far end. The blue stops here, and that is the mark the comic books reach on the hundred. The second step asks for that same fraction with one hundred as the whole. One hundred percent is 1 whole, so multiplying by it leaves the amount alone and changes only the way it is written. One fifth, times one hundred percent. One fifth of one hundred is 20, so one fifth is 20 percent. So the comic books are 20 percent of the shelf. A part turns into a percentage as the part over the whole, times one hundred percent.

Your turn. Here's a new question, and a new whole. A lesson lasted 45 minutes. 18 minutes of the lesson were spent on practice. Express the time spent on practice as a percentage of the length of the whole lesson. Try it first. Pause if you like. Let's finish it together. The question asks for a percentage of the whole lesson, so the whole is all 45 minutes of it, and not the part that is left over. 45 minutes is one hundred percent. Same rule as before. The part over the whole, times one hundred percent. The part is the 18 minutes spent on practice. So the part goes over the whole: 18 over 45. 18 and 45 both divide by 9. That leaves 2 over 5, so practice took two fifths of the lesson. Two fifths, times one hundred percent, is that same two fifths counted out of one hundred. Two fifths of one hundred is 40, so two fifths is 40 percent. 40 percent of the whole lesson was spent on practice. Two questions, two different wholes, one method. A part turns into a percentage as the part over the whole, times one hundred percent. In both, find the whole first. It comes after the words, percentage of.