A slice of the pie

A pie chart shows the parts of a whole as slices of a circle. Its strength is speed: you can see at a glance which share is biggest, without reading a single number.

Here's a grade table for 40 students: A 12, B 10, C 8, D 6, E 4. How do we turn it into slices?

Each slice's angle must be proportional to its number of students. And the whole circle is 360°. So the problem is simply: divide 360 in the ratio 12 : 10 : 8 : 6 : 4.

First simplify, as with any ratio. The HCF of those five numbers is 2, so divide through: 6 : 5 : 4 : 3 : 2.

Add the terms: 6 + 5 + 4 + 3 + 2 = 20. Then 360 ÷ 20 = 18° per part.

Always check: 108 + 90 + 72 + 54 + 36 = 360.

Now draw it. Draw a circle with centre A and a radius AB. From AB, measure 108° anticlockwise with a protractor and draw radius AC: that slice is Grade A.

From AC measure 90° and draw AD; from AD measure 72° and draw AE; carry on for the last two. Then colour and label each slice. The last one should close exactly onto AB; if it doesn't, the arithmetic slipped somewhere.