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, for example:
If two pencils cost $1.50, how many pencils can you buy with
The number of pencils is directly proportional to the cost.
This video shows how to solve direct proportion questions
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 when
x increases y
will decrease, and vice versa, by an amount such that xy
Knowing that the product does not change also allows you to form an equation
to find the value of an unknown variable for 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?
The number of men is inversely proportional to the time taken to do the job.
Usually, you will be able to decide from the question whether the values are
directly proportional or inversely proportional.
How to solve inverse proportion questions.
How to use indirect proportion to work out problems
How to use a more advanced form of indirect proportion where the use of square numbers is involved.
The following video gives more examples of direct proportions / variations and indirect proportions / variations.
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