Finding the whole from a percentage

40 percent of the pupils in a school walk to school. That's two hundred and forty pupils. How many pupils are in the school? Let's draw it. This blue bar is the whole school. Every pupil in it. That's one hundred percent. The whole school is what we're looking for, so we mark it with a question mark. Now for the 40 percent. The whole bar is the whole school, and that's one hundred percent. 40 percent is this much of it, here at the front. The two hundred and forty pupils who walk fill just that part. They're a part of the school, not the whole school. Now we can work it out. 40 percent is two hundred and forty. To get 1 percent, we divide by 40. Two hundred and forty divided by 40 is 6. The whole school is one hundred percent, so that's one hundred times 6, which is six hundred. There are six hundred pupils in the school.

Your turn. This pie chart shows the drinks sold at a school stall. The part for milk is a right angle. One hundred and twenty-five cartons of milk were sold. How many drinks were sold in all? Pause and work it out. Try it first. Pause if you like. Let's finish it. A right angle is 90 degrees, and a full turn is three hundred and sixty degrees. So the milk part of the chart is 90 out of three hundred and sixty. Write the part over the whole, and simplify it first. 90 over three hundred and sixty is one quarter. Then one quarter times one hundred percent is 25 percent. So 25 percent is one hundred and twenty-five cartons. To get 1 percent, we divide by 25. One hundred and twenty-five divided by 25 is 5. And one hundred percent is one hundred times 5, which is five hundred drinks. So, here's the rule. One hundred and twenty-five came with a percentage, so one hundred and twenty-five is a part. Five hundred is the whole, and it is bigger. The percentage is the part over the whole, times one hundred percent. Then down to 1 percent, And up to one hundred percent.