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Proportional Reasoning-1

When two amounts grow together

Rice costs ₹40 a kilogram. A taxi charges ₹50 to start and then ₹12 a kilometre.

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Rice, row by row: the bar climbs.
Step 1 of 3
  1. Rice, row by row: the bar climbs.
  2. Bill ÷ kg = 40, every row — direct proportion.
  3. Taxi: 62, 37, 28.7, 24.5 — the line bends.

The rule

Put each pair of amounts in a row. Divide one amount by the other, row by row. If the answer never changes, the amounts are in direct proportion.

  • Rice costs ₹40, ₹80 and ₹120 for 1, 2 and 3 kg. Dividing by the kg gives 40, 40 and 40.
  • Taxi: 50 + 12 = ₹62 for 1 km. And 50 + 24 = ₹74 for 2 km. Then 62 ÷ 1 is 62 and 74 ÷ 2 is 37. Not the same.

Watch out!

Both amounts rising is not enough. The taxi bill and the distance both rise, but bill ÷ km changes.

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This track

  1. 0 Start here
  2. 1 How much more, and how many times
  3. 2 What 3 : 2 says, and what it does not
  4. 3 The same comparison in bigger numbers
  5. 4 Match the units, then cut it down
  6. 5 Sharing an amount in a ratio
  7. 6 Checkpoint: comparing, writing and sharing
  8. 7 Two ratios that are equal
  9. 8 Find the value of one
  10. 9 When two amounts grow together
  11. 10 A rate is a ratio with units on it
  12. 11 A scale is a ratio you can walk
  13. 12 Checkpoint: proportion, rates and scales
  14. 13 The big picture
  15. 14 Track quiz

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