Percent means out of a hundred

A hundred square is made up of one hundred small squares of the same size. 37 of the squares are shaded. What percentage of the hundred square is shaded? Percent means out of a hundred, so the first thing worth checking is the whole. Count the rows. There are ten of them, and every row holds 10 small squares. Ten rows with 10 in each, so we multiply 10 by 10: the whole hundred square is one hundred small squares. Now take just one of those small squares. The whole square is one hundred equal parts, and this is 1 of them. So 1 square out of one hundred is 1 hundredth of the whole square. And out of a hundred is exactly what percent means. So 1 hundredth of this square is 1 percent of it. The shaded squares are counted the same way. Three whole rows are shaded, and that's 10, 20, 30. Then 7 more in the next row, and 30 plus 7 is 37. So 37 out of the one hundred small squares are shaded, and the one hundred small squares are the whole square. That count can be written three ways, and every one of them is the same 37 squares. 37 out of one hundred parts is the fraction 37 over one hundred. The first decimal place holds tenths and the first two hold hundredths, so 37 hundredths is zero point three seven. And out of a hundred is what percent means, so 37 out of one hundred is 37 percent. Three spellings, one quantity. Not one square has moved.

Now the same reading, away from the squares. A car park has exactly one hundred parking spaces. 15 of the spaces are occupied. What percentage of the spaces is empty? One hundred spaces, so draw one small square for each space and shade the 15 that are taken. Try it first. Pause if you like. The 15 occupied spaces are the ones the question gives, and it asks about the empty ones. Every space that isn't shaded is empty. The car park holds one hundred spaces and 15 are taken, so one hundred minus 15 leaves 85 empty spaces. Now read those 85 empty spaces against the whole car park. 85 empty out of one hundred spaces is 85 over one hundred. 85 hundredths again, so as a decimal that's zero point eight five. And out of a hundred is what percent means, so 85 out of one hundred is 85 percent of the spaces. Percent means out of a hundred. The whole car park is one hundred spaces, and one hundred out of one hundred is one hundred percent. The 15 spaces occupied by cars are 15 out of one hundred, so they are 15 percent of the car park. The 85 empty spaces are 85 over one hundred, zero point eight five, and 85 percent. Those are three spellings of one quantity, not three answers.