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Proportionality Explained: Direct and Inverse Relationships

Learn about direct and inverse proportion involving squares, cubes, and roots with practical examples. Understand constant of proportionality and how to calculate wages, costs, and other variables. Practice reverse calculations to master the concept.

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Proportionality Explained: Direct and Inverse Relationships

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  1. Proportion OCR Module 9

  2. Direct Proportion Direct Proportion involving Squares, Cubes & Roots Inverse Proportion Inverse Proportion involving Squares, Cubes & Roots MAIN MENU

  3. Direct Proportion

  4. There is Direct Proportion between two variables if one is a simple multiple of the other • E.g.“Jim’s wages are directly proportional to the hours he works” • The more hours he works, the more money he earns Direct Proportion

  5. Or... Wages = k x Hours k is the “constant of proportionality”

  6. If he works for 12 hours, he earns £72. What will he earn if he works 32 hours?

  7. If James earned £84, for how many hours did he work? Reverse Calculation

  8. If F = 20 when M = 5 • Find F when M =3 • Find M when F = 28 • If P = 150 when Q = 2 • Find P when Q = 6 • Find Q when P = 750 • If R = 17.5 when T = 7 • Find R when T = 9 • Find T when R = 50 Try these - y ∝ x Main Menu

  9. Direct Proportion Involving squares, cubes and square roots

  10. The cost of a square table is directly proportional to the square of its width. • The cost of table 10cm wide is £200 Directly proportional to the square of .......

  11. Find • the cost of a table 18cm wide • The width of a table costing £882

  12. F is directly proportional to M² If F = 40 when M = 2 • Find F when M =5 • Find M when F = 250 • P is directly proportional to Q² If P = 100 when Q = 5 • Find P when Q = 4 • Find Q when P = 400 • R is directly proportional to T² If R = 96 when T = 4 • Find R when T = 5 • Find T when R = 24 Try these – y ∝ x² Main Menu

  13. P is directly proportional to Q³ If P = 400 when Q = 10 • Find P when Q =4 • Find Q when P = 50 • T is directly proportional to S³ If T = 40 when S = 2 • Find T when S = 6 • Find S when T = 48 Try these – y ∝ x3 Main Menu

  14. Y is directly proportional to √X If Y = 36 when X = 144 • Find Y when X =81 • Find X when Y =147 • T is directly proportional to √S If T = 4 when S = 64 • Find T when S = 144 • Find S when T = 7 Try these – y ∝ √x Main Menu

  15. Inverse Proportion

  16. There is Inverse Proportion between two variables if one increases at the rate at which the other decreases • E.g.“It takes 4 men 10 days to build a brick wall. How many days will it take 20 men?” • The more men employed, the less time it takes to build the wall Inverse Proportion

  17. Time is inversely Proportional to Men t∝

  18. t= t= t= If we have 20 men, m = 20 = 2 days

  19. M is inversely proportional to RIf M = 9 when R = 4 • Find M when R =2 • Find R when M = 3 • T is inversely proportional to m If T = 7 when m = 4 • Find T when m = 5 • Find m when T = 56 • W is inversely proportional to x. If W = 6 when x = 15 • Find W when x = 3 • Find x when W = 10 Try these – y ∝ 1/x Main Menu

  20. Inverse Proportion Involving squares, cubes and square roots

  21. Essentially, these are similar to the problems seen in the previous section on Inverse Proportion. • Try the questions overleaf What’s the difference?

  22. F is inversely proportional to M² If F = 20 when M = 3 • Find F when M =5 • Find M when F = 720 • P is inversely proportional to √Q If P = 20 when Q = 16 • Find P when Q = 0.64 • Find Q when P = 40 Try these – y ∝ 1/xn Main Menu

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