>> Hi, this is Julie Harland
and I'm YourMathGal.
Please visit my website
at yourmathgal.com,
where you could search for any
of my videos organized
by topic.
In this video we learned how
to solve percent problems
using proportions,
and we do these two problems
on this video.
Here is a problem,
if 3 out of 20 people are
absent from a class,
what percent
of the class is absent?
So notice,
the number of students absent,
that's 3 and the total number
of students
in the class is 20,
we can write
that as a portion,
the total number
of students absent
over the total number
of students.
So I'm going to write
that as 3 over 20.
Now, remember, if you want
to write that as a percent,
it says if you had a hundred
students, like,
what would the number
of students be absent?
So, the percent over here has
to be something over 100.
This is a ratio we're
looking for.
Now, 'cause we have two
ratios, right,
3 over 20 equals something
over a hundred.
Let's see if we could figure
this out from what we know
about fractions first of all.
Well, if I have a fraction
with 20 in the denominator
and I want it to be 100,
I could just multiply the
denominator by 5
which means I multiply the
numerator by 5.
And notice I would get 15
out 100.
So just sort of thinking
about it this way,
let's say 15 percent
were absent.
Now, it doesn't always work
out quite that easily
but you could do this.
But we can set
up what's called a proportion
to figure out this problem.
So let's see how that works.
So, here is a setup
for solving a problem
using proportions.
We have what's called the
base, that's our original
number or our total.
In our problem that will be
about total number
of students normally
in the class.
And the amount,
in this case we're talking how
many were absent
so it's the other number.
I'm going to put or part.
I'm careful with this
because sometimes the amount
might be bigger
than the original number
so be careful,
it's not always smaller
and there is the percent.
We have to be careful
of is this thing I have here,
this percent is just a number.
If you're going to write it
as a percent you would have
put the percent sign after it.
So what we have is
that if I take the amount
absent over the total number
of students,
it's the same thing
as writing this other number
over a hundred which will end
up being the percent,
my 15 percent.
So here is this problem,
if 3 out of 20 people are
absent from a class,
what percent
of the class is absent?
All right,
so what would the amount be
and what would the base be?
A lot of people have trouble
figuring that out
and I always look
for the word of,
and it's the number
after that.
That will usually always be
the base.
In other words,
the base is the total number
or the normal amount
of students in the class.
So our base here will be 20,
so our amount is the
other number.
So that would be this number
here, will be the amount.
And we're looking
for the percent.
Notice it says what percent,
so we can't put a number
in that so let's use
the variable.
And I'm just going to use P
so you remember
that you were looking
for the percent.
So I'm going
to have this proportion
and this is just always a
hundred right here,
you don't have
to put anything else
and you already know
that number.
This is going
to give us a proportion,
3 over 20,
that's one fraction,
equals P over 100.
So let's write that out,
3 over 20 equal P over 100.
Now, there's different ways
you could figure this out,
what P is equal to.
But when you're done,
remember if somebody asked you
what percent, you're going
to have to remember to write
that number
and then write the percent
sign afterwards.
I don't really
like using proportions 'cause
it confuses people
and they think, well,
I'm going to have
to multiply it by 100 percent.
But it's already built
into this problem
that you have it
over a hundred.
So, how do you solve this?
You could do it
by the way I showed you.
In the example,
we could just say we're going
to multiply top and bottom
by 5 and you could figure
out that P is going to be 15.
But usually it's not easy
to see that,
so we can use
cross multiplication.
Remember what you could do
if you have two fractions
equal to each other,
you could multiply the
numerator and denominator of--
the numerator of one fraction
with the denominator
of the other fraction is the
same thing as the denominator
of one fraction
with the other numerator.
So it doesn't matter
which I put first.
So I'm going to put 20 times P
which is 20 times P equals 3
times 100, 3 times 100, okay?
And then if I want to solve
for P, you could divide both
sides by 20.
Now, you could have put 300
here and then divide it by 20.
I just like to leave things
to cancel at the end.
So let's see,
I could divide numerator
and denominator by 20, right,
100 divided by 20 is going
to be 5 up here.
So notice that I get P is 15.
If you're using a proportion,
remember the percent,
is just-- that's just the
number part of the percent,
so your final answer will be
15 percent.
All right,
so here is the next problem.
What percent of 52 is 39?
Again, we're looking
for the percent.
So remember,
we've got the amount
over the base is going
to be P over 100.
In this case, let's write
down what the amount is
and what the base is.
You know what,
it's always easier
to find the base.
Look for the word of, of 52,
all right.
So the base is 52
so the base is 52
so the other number
in this case,
unless it's a percent, right,
so just the number is
the amount.
It sometimes comes
after the word is
but not always.
All right,
so we've got the amount
over the base.
So you see
where the fraction is going
to be?
It's going to be 39 over 52,
if you always write the amount
first and then the base.
So I'm going to write
that over here, 39 over 52,
is equal to--
now, I'm looking for P, right,
so I'm going
to write P over 100.
And then I'm going
to use my cross multiplication
again, so I'm going
to write it as 52 times P,
all right,
I'm going to multiply those
two together.
52 times P, you don't have
to put a dot there.
You could just write 52 P
equals those two numbers
multiplied together,
39 times 100.
And again, I'm not going
to multiply this
out because I'm always hoping
things are going to cancel.
So let's see,
let's divide both sides by 52.
All right,
now on this side the 52's
cancel so I'm going
to find my P
and if anything cancel
over here, well,
actually 13 goes into both
of these numbers then
if you don't know,
then you can always prime
factor to figure that out.
So, if I divide 39
by 13 I get 3.
And if I divided 52
by 13, I get 4.
Anything else cancel?
Well, I've got 100
over 4 here, right,
so I also could cancel.
Let's do, what color the one
do you have that on,
this color, 1 and 25,
so I get 25 percent.
And listen,
you could do this totally
different, you know,
when you've got 39 times 100
over 52.
Maybe you decide
to divide the numerator
and denominator
by 4 first, right?
So just keep in mind,
there's all sorts
of ways you could cancel this.
So if I divide 4 into both
of these numbers
or let's say only 2,
you need the 2
into both numbers,
you could do that,
divided by 2.
That's 50 divide this by 2,
is 26, then you could do it
again, right?
Divide these two numbers by 2.
So if I divide by 2, again,
that's 25 and divide
that by 2 is 13, all right?
And then hopefully now you
know that 13 goes into 39
so I can cancel again.
Notice you're still going
to get 3 times 25.
So this is just a matter
of dealing with fractions
and of course,
you could also do this
by doing it
in your calculator 'cause it
happens to come out evenly.
You could have 3,900 or 52.
If you put
that in a calculator you're
going to get 75, right?
So don't get confused
because of the reducing here.
Anyway, P was 75,
actually I just want
to write P
with just the number 75,
right, in this problem.
But what I want
to know is what percent,
so then I have to remember
to write the percent.
P in this equation is not--
is just the number that goes
in front of the percent sign,
okay.
So you don't want
to write P equals 75 percent
'cause then you have up here,
75 percent over 100,
with just doesn't make any
sense mathematically.
So we'll do some more problems
on the next video.
We've only done problem,
we're finding the percent
but sometimes you're given the
percent and you'll need
to find the amount
or the base.
[ Pause ]
Please visit my website
at yourmathgal.com,
where you can view all
of my videos
which are organized by topic.