what is direct proportion and indirect proportion
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Inversely Proportional:::::::
Inversely Proportional: when one value decreases at the same rate that the other increases.
Example: speed and travel time
Speed and travel time are Inversely Proportionalbecause the faster we go the shorter the time.
As speed goes up, travel time goes downAnd as speed goes down, travel time goes up
This:y is inversely proportional to x
Is the same thing as:y is directly proportional to 1/x
Which can be written:
y = kx
Example: 4 people can paint a fence in 3 hours.
How long will it take 6 people to paint it?
(Assume everyone works at the same rate)
It is an Inverse Proportion:
As the number of people goes up, the painting time goes down.As the number of people goes down, the painting time goes up.
We can use:
t = k/n
Where:
t = number of hoursk = constant of proportionalityn = number of people
"4 people can paint a fence in 3 hours" means that t = 3 when n = 4
3 = k/4
3 × 4 = k × 4 / 4
12 = k
k = 12
So now we know:
t = 12/n
And when n = 6:
t = 12/6 = 2 hours
So 6 people will take 2 hours to paint the fence.
How many people are needed to complete the job in half an hour?
½ = 12/n
n = 12 / ½ = 24
So it needs 24 people to complete the job in half an hour.
(Assuming they don't all get in each other's way!).
Directly proportional::::::::
as one amount increases,
another amount increases at the same rate.
∝ The symbol for "directly proportional" is ∝
(Don't confuse it with the symbol for infinity∞)
Example: you are paid $20 an hour
How much you earn is directly proportional to how many hours you work
Work more hours, get more pay; in direct proportion.
This could be written:
Earnings ∝ Hours worked
If you work 2 hours you get paid $40If you work 3 hours you get paid $60etc ...
Inversely Proportional: when one value decreases at the same rate that the other increases.
Example: speed and travel time
Speed and travel time are Inversely Proportionalbecause the faster we go the shorter the time.
As speed goes up, travel time goes downAnd as speed goes down, travel time goes up
This:y is inversely proportional to x
Is the same thing as:y is directly proportional to 1/x
Which can be written:
y = kx
Example: 4 people can paint a fence in 3 hours.
How long will it take 6 people to paint it?
(Assume everyone works at the same rate)
It is an Inverse Proportion:
As the number of people goes up, the painting time goes down.As the number of people goes down, the painting time goes up.
We can use:
t = k/n
Where:
t = number of hoursk = constant of proportionalityn = number of people
"4 people can paint a fence in 3 hours" means that t = 3 when n = 4
3 = k/4
3 × 4 = k × 4 / 4
12 = k
k = 12
So now we know:
t = 12/n
And when n = 6:
t = 12/6 = 2 hours
So 6 people will take 2 hours to paint the fence.
How many people are needed to complete the job in half an hour?
½ = 12/n
n = 12 / ½ = 24
So it needs 24 people to complete the job in half an hour.
(Assuming they don't all get in each other's way!).
Directly proportional::::::::
as one amount increases,
another amount increases at the same rate.
∝ The symbol for "directly proportional" is ∝
(Don't confuse it with the symbol for infinity∞)
Example: you are paid $20 an hour
How much you earn is directly proportional to how many hours you work
Work more hours, get more pay; in direct proportion.
This could be written:
Earnings ∝ Hours worked
If you work 2 hours you get paid $40If you work 3 hours you get paid $60etc ...
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Answer:
Like Direct and Indirect(Inverse) Unitary Methord, Direct and Indirect(Inverse) Proportion stands for same. Direct Proportion means when both mean and extreme increases or decreases at the same time. In Indirect(Inverse) Proportion, when mean or extreme increases or decreases the other becomes opposite(if mean or extreme increases other decreases or if mean or extreme decreases the other increases).
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