Read it again any time, including while you work through the exercises.
You have probably seen a pie chart before: a disc cut into coloured slices, like a pizza. Each slice stands for a category, and the bigger the slice, the more that category weighs in the total. It is the perfect tool to show how a whole is shared out.
The golden rule: the full disc represents the TOTAL, and a full turn measures 360 degrees. Half of the disc (180 degrees) therefore represents half of the total, a quarter (90 degrees) represents a quarter of the total. The angle of each slice is proportional to its quantity.
To compute the angle of a category, you always follow the same recipe: take the category's share of the total (a fraction), then multiply by 360. For example, if 10 students out of 40 choose tea, the share is 10/40, that is one quarter, and the angle is one quarter of 360, which is 90 degrees.
You can also read the other way: if a slice measures 120 degrees, it represents 120/360 of the total, that is one third. A pie chart is proportionality dressed up as a picture.
One last check, always: the sum of all the angles must be exactly 360 degrees. If you get 350 or 370, there is a mistake somewhere!
20 students vote for their favourite sport: 10 for football, 5 for swimming, 5 for tennis. Compute the angle of each slice of the pie chart.
- 1
foot : 10/20 × 360 = 180
Football is half of the total, so half of the disc: 180 degrees.
- 2
natation : 5/20 × 360 = 90
Swimming is one quarter of the total, so one quarter of 360: 90 degrees.
- 3
tennis : 5/20 × 360 = 90
Same share as swimming, so same angle: 90 degrees.
- 4
180 + 90 + 90 = 360
I check: the angles add up to exactly 360 degrees, the disc is complete.
Result: Football: 180°, swimming: 90°, tennis: 90°.