The data in the figure below represents
the number of stars
earned by 140 performers
in a talent competition.
So, notice along the horizontal axis,
we have the number of stars earned
and notice the vertical axis
is not the number of performers.
It's the percent of performers earning
a particular number of stars.
Our question is
how many performers
earned exactly four stars?
We'll notice here's four
on the horizontal axis,
which represents the number of stars.
And, based upon the height
of this bar, we can determine
that 5% of the performers
earned four stars.
So, to answer the question,
we want to determine what is
5% of 140?
There are several ways
to answer this question.
Whenever determining the
percent of a number, though,
we can convert the percent
to a decimal and multiply.
So, to convert 5% to a decimal,
we drop the percent sign
and move the decimal point
to the left, two places.
Or, if we want, we can
drop the percent sign
and divide by 100.
Notice, five divided by 100
does give us .05 or 0.05.
So, we'd have 0.05
and then, times 140, of
means multiplication,
this product will give us 5% of 140.
So, .05 times 140
is equal to seven,
which means seven performers
earned four stars.
Let's also answer this
question more formally
using a percent equation as
well as a percent proportion.
So, using a percent equation,
we use these key words
to set up our equation,
where is means equals,
of means multiplication
and what, what number and what percent
represents the unknown, so
we write down a variable.
So, looking at our question, here,
the first word is what,
so we write down a variable, let's use x.
Is means equals.
We know 5% as a decimal is 0.05,
of means multiplication
and then, we have 140
and notice how this product
is the same product we have here
and therefore we know x equals seven,
giving us the same result.
And now, using the percent proportion,
we can use key words is
over of equals p over 100,
but this is really setting up two ratios
where we compare the part to the whole
and the percent to 100.
So, because we're looking
for the part of 140
that earned four stars,
our first ratio would
be the unknown x to 140
must be equal to the
percent compared to 100
and since we have 5% it
would be five to 100.
Now, we cross-multiply and solve for x.
So, x times 100 must equal 140 times five,
X times 100 is 100x.
140 times 5 is equal to 700.
Dividing both sides by 100,
we get the same result: x equals 7.
So, here are three ways
we can determine the percent of a number.
I hope you found this helpful.
