ratio and proportion direct, indirect partitive.ppt

ratio and proportion

1. ProportionProportion
OCR Module 9

2. Direct Proportion
involving Squares,
Cubes & Roots
Direct Proportion
Inverse Proportion
Inverse Proportion
involving Squares,
Cubes & Roots
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3. Direct Proportion

4. Direct ProportionDirect Proportion
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

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

6. If he works for 12 hours, he earns Php 72.
What will he earn if he works 32 hours?
HW
kHW
1272 k
1272k
6k
HW 6
326W
192Php

7. Reverse CalculationReverse Calculation
If James earned Php 84, for how many
hours did he work?
HW 6
H684
684H
hours14

8. Try these - y Try these - y ∝∝ x x
1.If F = 20 when M = 5
a.Find F when M =3
b.Find M when F = 28
2.If P = 150 when Q = 2
a)Find P when Q = 6
b)Find Q when P = 750
3.If R = 17.5 when T = 7
a)Find R when T = 9
b)Find T when R = 50
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9. Direct Proportion
Involving squares, cubes and square roots

10. Directly proportional to the square Directly proportional to the square
of .......of .......
The cost of a square table
is directly proportional to
the square of its width.
The cost of table 10cm
wide is Php 200
2
WC
2
kWC
2
10200 k
k100200
2k
2
2WC

11. Find
a)the cost of a table 18cm wide
b)The width of a table costing Php 882
2
2WC
2
182C
648PhpC
2
2882 W
2882
2
W
441
2
W
441W
cmW 21

12. Try these – y Try these – y ∝∝ x x²²
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1.F is directly proportional to M²
If F = 40 when M = 2
a.Find F when M =5
b.Find M when F = 250
2.P is directly proportional to Q²
If P = 100 when Q = 5
a)Find P when Q = 4
b)Find Q when P = 400
3.R is directly proportional to T²
If R = 96 when T = 4
a)Find R when T = 5
b)Find T when R = 24

13. Try these – y Try these – y ∝∝ x x
33
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1.P is directly proportional to Q³
If P = 400 when Q = 10
a.Find P when Q =4
b.Find Q when P = 50
2.T is directly proportional to S³
If T = 40 when S = 2
a)Find T when S = 6
b)Find S when T = 48

14. Try these – y Try these – y ∝∝ √x √x
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1.Y is directly proportional to √X
If Y = 36 when X = 144
a.Find Y when X =81
b.Find X when Y =147
2.T is directly proportional to √S
If T = 4 when S = 64
a)Find T when S = 144
b)Find S when T = 7

15. Inverse Proportion

16. Inverse ProportionInverse 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. 1.It takes 4 men 10 days to build a
brick wall. How many days will it take
20 men?
2.If Jim works for 12 hours, he earns
Php 720. What will he earn if he
works 32 hours?

18. Time is inversely
Proportional to Men
t ∝
m
1

19. t =
m
k
4
10
k

40104k
t =
m
40
If we have 20 men, m = 20
t =
20
40
= 2 days

20. Try these – y Try these – y ∝∝ 1/x 1/x
1.M is inversely proportional to R
If M = 9 when R = 4
a.Find M when R =2
b.Find R when M = 3
2.T is inversely proportional to m
If T = 7 when m = 4
a)Find T when m = 5
b)Find m when T = 56
3.W is inversely proportional to x.
If W = 6 when x = 15
a)Find W when x = 3
b)Find x when W = 10
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21. Inverse Proportion
Involving squares, cubes and square roots

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

23. Try these – y Try these – y ∝∝ 1/x 1/x
nn
1.F is inversely proportional to M²
If F = 20 when M = 3
a.Find F when M =5
b.Find M when F = 720
2.P is inversely proportional to √Q
If P = 20 when Q = 16
a)Find P when Q = 0.64
b)Find Q when P = 40
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