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Proportional Reasoning-2

What a chart says, and what it holds back

Someone shows a chart with four slices and no numbers on it. How many picked cricket?

A chart, four slices, no total.
Step 1 of 4
  1. A chart, four slices, no total.
  2. Cricket's slice: 3 of 8.
  3. "How many voters?" — no total.
  4. Total written: 40 voters.

You cannot tell. The chart shows only shares. A share is a group's part, like 3 of 8.

Rule: A chart with no numbers gives shares, not counts. Write the total beside it, and every count comes back.

The shares alone show which slice is bigger. Cricket is 3 of 8, which is under half of the votes. You cannot say how many people that is. You need the total.

One known count and its slice give the total. A 90° slice is a quarter of the circle. That is because 4 × 90° = 360°. Take 18 children in that slice. The whole circle is 4 such slices. So the total is 4 × 18 = 72 children.

Each chart has no total. Find how many people were asked.

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This track

  1. 0 Start here
  2. 1 One circle for the whole set
  3. 2 A slice is a share of the turn
  4. 3 Draw a chart, then check it closes
  5. 4 What a chart says, and what it holds back
  6. 5 Two charts that look the same
  7. 6 When one grows and the other shrinks
  8. 7 Which kind is it, or neither
  9. 8 Workers and days, speed and time
  10. 9 A ratio with three parts
  11. 10 Share a whole in many parts
  12. 11 Checkpoint: ratios with many terms
  13. 12 The big picture
  14. 13 Track quiz

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