Math Tip
Is – Of – Percent
Richard C. McNamara
Ph. D. Applied Mathematics
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All rights reserved
1
What is 15 percent of 20?
18 is what percent of 75?
588 is 84 percent of what?
This simple expression can be used to solve all three!
=
%
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2
When working with problems such as the following,
the first step is to recognize which number or word
is associated with the word “is”, which is associated
with the word “of”, and which is associated with
the word “percent”
What is 15 percent of 20?
18 is what percent of 75?
588 is 84 percent of what?
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All rights reserved
3
Next, set up an expression of the form
=
%
Place the appropriate number or word
associated with “is”, “of”, and “percent” into
the corresponding places in that expression
Two of the three will be numbers, and the other
will be the word “what”
Our goal is to determine the value that should
replace the word “what” in the equation
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4
What is 15 percent of 20?
18 is what percent of 75?
588 is 84 percent of what?
Copyright © 2015, Mathlingual, LLC
All rights reserved
=
=
=
5
To determine the missing value, cross-multiply
and divide
What is 15 percent of 20?
Cross-multiply:
=
=
The result of cross-multiplication:
×
=
×
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6
Divide both sides of the equation by whatever
number is being multiplied by the word “what”
In this example, we divide by
×
=
:
×
Result:
×
=
=
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×
=
7
Example 1:
What is 15 percent of 20?
=
%
=
Therefore:
is 15 percent of 20
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8
Example 2:
18 is what percent of 75?
=
%
=
=
Therefore:
×
=
is 24 percent of 75
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9
Example 3:
588 is 84 percent of what?
=
%
=
=
Therefore:
×
=
is 84 percent of 700
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All rights reserved
10