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Proportion

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'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. Time is inversely ... – PowerPoint PPT presentation

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Title: Proportion


1
Proportion
  • OCR Module 9

2
MAIN MENU
Direct Proportion
Direct Proportion involving Squares, Cubes Roots
Inverse Proportion
Inverse Proportion involving Squares, Cubes
Roots
3
Direct Proportion
4
Direct Proportion
  • There is Direct Proportion between two variables
    if one is a simple multiple of the other
  • E.g.Jims wages are directly proportional to
    the hours he works
  • The more hours he works, the more money he earns

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
Reverse Calculation
  • If James earned 84, for how many hours did he
    work?

8
Try these - y ? x
  • 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

Main Menu
9
Direct Proportion
  • Involving squares, cubes and square roots

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

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

12
Try these y ? x²
  • F is directly proportional to M? If F 40 when
    M 2
  • Find F when M 5
  • Find M when F 250
  • P is directly proportional to Q? If P 100 when
    Q 5
  • Find P when Q 4
  • Find Q when P 400
  • R is directly proportional to T? If R 96 when
    T 4
  • Find R when T 5
  • Find T when R 24

Main Menu
13
Try these y ? x3
  • P is directly proportional to Q? If P 400 when
    Q 10
  • Find P when Q 4
  • Find Q when P 50
  • T is directly proportional to S? If T 40 when
    S 2
  • Find T when S 6
  • Find S when T 48

Main Menu
14
Try these y ? vx
  • Y is directly proportional to vX If Y 36 when
    X 144
  • Find Y when X 81
  • Find X when Y 147
  • T is directly proportional to vS If T 4 when S
    64
  • Find T when S 144
  • Find S when T 7

Main Menu
15
Inverse Proportion
16
Inverse Proportion
  • 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

17
Time is inversely Proportional to Men
18
If we have 20 men, m 20
2 days
19
Try these y ? 1/x
  • 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

Main Menu
20
Inverse Proportion
  • Involving squares, cubes and square roots

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

22
Try these y ? 1/xn
  • F is inversely proportional to M? If F 20 when
    M 3
  • Find F when M 5
  • Find M when F 720
  • P is inversely proportional to vQ If P 20 when
    Q 16
  • Find P when Q 1.25
  • Find Q when P 40

Main Menu
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