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Proportional Reasoning-2

Workers and days, speed and time

6 people paint a hall in 12 days. How long do 9 people take?

6 × 12 = 72.
Step 1 of 3
  1. 6 × 12 = 72.
  2. 72 ÷ 9 = 8 days.
  3. Check: 9 × 8 = 72.

If everyone works at the same speed, 9 people take 8 days.

Rule: Multiply the pair you were given. Divide by the new amount. Multiply back — it must give the same number.

The given pair is 6 people and 12 days. Their product is 72. The new amount is 9 people. The product stays 72. So 9 people take 72 ÷ 9 = 8 days.

A road is 180 km long. A speed of 60 km/h means 60 km in each hour. At 60 km/h the trip takes 3 hours, because 60 × 3 = 180. The road stays 180 km. So at 40 km/h it takes 180 ÷ 40 = 4.5 hours. Check: 40 × 4.5 = 180.

Drag the new crew. Read the three steps.

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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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