Concept 3 of 7
Pie Charts: Slices of the Whole
Today's big idea
Pie chart: the whole circle is 360°, and each slice is that fraction of the total.
Angle is never the count; divide by 360, then multiply by the total.
How it works
👀 What's going on?
One pizza, three hungry friends, and nobody wants to be short-changed. A pie chart works the same way, only the pizza is your data. The bigger the slice, the bigger the share.
💡 Here's the trick
Look at the chart above. The whole circle is the total, which is 360° or 100% or all 60 students. Football's slice is a third of the circle, so its angle is a third of 360°.
🪄 How to do it
- 1.Read one slice off the chart above as a fraction or an angle.
- 2.Turn an angle into a fraction by dividing it by 360.
- 3.Multiply that fraction by the total to get a real count.
✍️ Try it
A pie chart of 900 votes gives Green a 40° slice. How many votes is that? Then: what angle would a quarter of the votes need?
40° out of 360° is one ninth, and one ninth of 900 is 100 votes. A quarter of a full circle is 360° ÷ 4 = 90°.
⚠️ Watch out
You might be thinking a 90° slice always means 90 people. The angle is not the count. Ninety degrees is a quarter of the circle, so it means a quarter of whatever the total is.
🌟 Why this matters
A pie chart shows your family where the month's money goes, and shows a school what its pupils eat. It answers what share in one look, without any counting.
Exam tip: Check that all the given angles add to 360° before you trust the leftover slice.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A pie of 84 pens shows 1/3 red. How many pens are RED?”
- 1
Identify the red slice
1/3 of the pie → 1/3 of total. 🥧
- 2
Multiply by total
1/3 × 84
- 3
Compute
84 ÷ 3 = 28.
- 4
Answer ✓
28 pens are red.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
A pie chart shows slices of one whole. The full pie = 360° = the total.
Favourite Sport · 120 students
STEP 1 OF 3
Tap the BIGGEST slice of the pie.
Quick check
✅ VERIFICATION
A pie chart of 72 pens shows the red slice as 100°. How many pens are red?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Frequency & Class-Interval Tables
Frequency = how often. Sum all = total items.