One Sector, Three Forms

A pie chart can turn one circle into a whole crowd. Pick one coloured sector... and you can uncover its fraction, its percentage, and even its exact count. The trick is knowing what that slice means.

See the complete circle as ONE whole. Every sector is a share of that same whole. Focus on the two straight radii around the named sector, then compare its angle and area with the full turn. If a sector is one of four equal quarters, its fraction is one quarter. A whole is one hundred per cent, so one quarter is twenty-five per cent. For a semicircle, the fraction is one half, and the percentage is fifty per cent. To find a count, the total MUST be given. Multiply the sector's fraction by that total. Do not count sectors as though each sector were one person; their sizes represent shares, not individual votes.

Let's work through an example. A pie chart shows the favourite after-school clubs of two hundred and forty pupils. The coding sector is marked with a right angle at the centre. Express the coding sector as a fraction, a percentage, and a number of pupils. A right angle is one quarter of a full turn. Watch the circle divide into four matching quarters. The coding sector takes exactly one of them, so its fraction is one quarter. Now convert the fraction. One quarter of one hundred per cent is twenty-five per cent. For the count, split two hundred and forty into four equal groups. Two hundred and forty divided by four is sixty. So the coding sector represents sixty pupils.

Remember the route: compare the named sector with the whole, write its fraction, convert that fraction to a percentage, then multiply by the supplied total if a count is asked for. Check that your three answers describe the SAME slice. Fraction, percentage, count... one sector, three forms. You can read the story hidden inside any clear pie chart!