define direct and inverse proportion and give examples.
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DIRECTLY PROPORTIONAL:
Two values x and y are directly proportional to each other when the ratio x : y or is a constant (i.e. always remains the same). This would mean that x and y will either increase together or decrease together by an amount that would not change the ratio.
If two pencils cost $1.50, how many pencils can you buy with $9.00?
Solution:
The number of pencils is directly proportional to the cost.
pencils
INDIRECTLY PROPORTIONAL:
Two values x and y are inversely proportional to each other when their product xy is a constant (always remains the same). This means that whenx increases y will decrease, and vice versa, by an amount such that xyremains the same.
Two values x and y are directly proportional to each other when the ratio x : y or is a constant (i.e. always remains the same). This would mean that x and y will either increase together or decrease together by an amount that would not change the ratio.
Knowing that the ratio does not change allows you to form an equation to find the value of an unknown variable.
Example:If two pencils cost $1.50, how many pencils can you buy with $9.00?
Solution:
The number of pencils is directly proportional to the cost.
pencils
INDIRECTLY PROPORTIONAL:
Two values x and y are inversely proportional to each other when their product xy is a constant (always remains the same). This means that whenx increases y will decrease, and vice versa, by an amount such that xyremains the same.
Knowing that the product does not change also allows you to form an equation to find the value of an unknown variable
Example:
It takes 4 men 6 hours to repair a road. How long will it take 8 men to do the job if they work at the same rate?
Solution:
The number of men is inversely proportional to the time taken to do the job.
Let t be the time taken for the 8 men to finish the job.
4 × 6 = 8 × t
24 = 8t
t = 3 hours
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inverse proportion;
when one value decreases at the same rate that the other increases.Example: speed and travel time
direct proportion;
When one quantity increases constantly or decreases constantly with respect to another quantity then the two quantities are called directly proportional to each other. In the airplane example, we would say that the quantity C is directly proportional to S multiplied by a constant (k). We can write this formula as C = kS.
when one value decreases at the same rate that the other increases.Example: speed and travel time
Speed and travel time are Inversely Proportional because the faster we go the shorter the time.
As speed goes up, travel time goes downAnd as speed goes down, travel time goes updirect proportion;
When one quantity increases constantly or decreases constantly with respect to another quantity then the two quantities are called directly proportional to each other. In the airplane example, we would say that the quantity C is directly proportional to S multiplied by a constant (k). We can write this formula as C = kS.
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