Hi! Welcome to Math Antics.
In this video, we’re gonna learn how to do another common type of problem involving percents.
We’re gonna learn how to figure out, “What percent is it?”
In our last video, we learned how to do a really common percent problem which was finding a percent of a number.
For example, we learned how you could solve a problem like, “What is 20% of 50?” And the answer to that problem is 10.
So we could say that, “10 is 20% of 50”
Let’s look closely at that statement for a minute.
Notice that there’s three different numbers in it: 10, 20 and 50.
That’s because a percentage is really a relationship between 3 numbers.
Well, actually it’s a relationship between 4 numbers, but the forth number is always 100, so you always know it.
To see what I mean, think back to our video about percents and equivalent fractions.
In that video, we learned that a percent is really an equivalent fraction that has 100 as the bottom number.
So we could rewrite our statement like this: 10 over 50 equals 20 over 100.
This is exactly the same as saying that 10 is 20 PER-CENT of 50.
So these are the four components of a percent problem.
But since we know that 100 is always gonna be the bottom number of this equivalent fraction (the percent)
we can just rewrite it using the percent symbol.
That way we can focus on the other three numbers that can change.
And we’re gonna give each one of these three numbers a name so that we don’t get confused.
We’re gonna call the top number of the fraction, “the part we have’” or just the “part” for short.
And we’re gonna call the bottom number the “total”,
and we’re gonna call the number in front of the percent sign the “percent’” (or percentage).
And since there’s three different numbers that can change in a percentage problem,
that means there’s three different questions that you can ask.
To see these three questions let’s rewrite our original statement (10 is 20% of 50) three different times.
But in the first statement, we replace the ‘10’ with ‘what’ and it becomes, “what is 20% of 50”
In the second statement, we replace the ’20’ with ‘what’ and it becomes, “10 is what % of 50”.
And in the third statement, we replace the ’50’ with ‘what’ and it becomes, “10 is 20% of what?”
Doing this is helpful because, whenever you're given a problem involving percents,
the first thing you need to figure out is WHAT the problem is asking you to find.
...ya know… which number is missing?
In the first statement, the ‘part we have’ is missing.
In the second statement, the ‘percent’ is missing.
And in the third statement, the ‘total’ is missing.
And these three statements represent the three most common types of percentage problems.
The first type is what we learned in the last video, “Finding a Percent of a Number”.
In this type of problem, we know the percent and we know the total, but we don’t know what part of that total we have.
The second type of problem is what we’re gonna learn in this video.
In this type of problem, we know both the total, and we know what part of that total we have.
But we need to figure out what percentage of the total that part is.
We need to find, “What percent is it?”
And the third type of problem is what we’ll learn in the next video.
For that type of problem, we know what part we have and we know what percent of the total it is.
We just don’t know the total itself.
Have I lost you yet?
Don’t worry - it’ll make a lot more sense after we look at a few examples.
So, let’s look at an example of a “type 2” problem,
where we know the part we have and we know the total, but we don’t know what the percent is.
This example is a word problem and it says:
Your uncle, who really likes to travel, has visited 35 of the 50 U.S. states.
What percent of the states has he visited?
The key words in this problem are, “what percent” because they let us know that it’s the percent that’s missing.
So the two numbers that it gives us must be the ‘total’, and the ‘part we have’.
Well… in this case, it’s not really the part we have… it’s the part that our uncle has visited, but you get the idea.
And sometimes it can be hard to tell which number the total is.
Often it’s the bigger number, but not always.
And that’s where the word ‘“of” can help us out.
The word “of” usually goes in front of the number that’s the total.
So when you see “…OF the 50 US states”, it’s a clue that 50 is the total.
Alright then, so we put 50 on the bottom of the fraction and 35 on top.
Now we’re ready to figure out the part we don’t know; the percent.
To find the percent, all we need to do is convert the fraction into its percent form.
That means we need to convert it into an equivalent fraction that has 100 as the bottom number.
Well, one way we could do that would be to look for a number that we could
multiply both the top and bottom numbers by that would change the bottom number into 100.
Well the number 2 looks like it would work.
If we multiply the bottom by 2 (2 × 50 gives us 100) and then we also need to multiply the top by 2 (and 2 × 35 = 70).
So now we can see that 70 over 100 is equivalent to 35 over 50, and since 70 over 100 is just 70%
it means our uncle has visited 70% of the states.
And all I got was this lousy tee-shirt.
Alright, that way of finding a percent seems pretty easy.
You just write the numbers that you know as a fraction,
and then convert that fraction into an equivalent fraction with 100 as the bottom number.
And that tells you what percent it is.
The trouble is, that way is only easy if it’s easy to change the bottom number into 100.
For example, what if instead of 50, you had 80 as the bottom number?
What could you multiply 80 by to get 100? Well, that’s not as easy to figure out.
So, even though finding an equivalent fraction is sometimes a good way to convert a fraction into a percent form,
I’m gonna show you another way that I think is even better.
This second way is based on the fact that a fraction is just a division problem
where the top number is divided by the bottom number.
If you do the division, you’ll end up with the decimal value of the fraction.
And as we saw in our first video about percents, it’s easy to convert from a decimal value into a percent.
You just move the decimal point two places to the right, which is the same as multiplying by 100.
The only drawback to finding the percent this way is that it involves division,
and division can sometimes be tricky if you don’t have a calculator.
But if you do have a calculator, or if you’re really good at long division, then this way works best.
To see this way in action, let’s try this word problem:
Your Aunt has baked 80 cookies, and (because she’s a very nice Aunt) she gave you 28 to take home with you.
What percent of the cookies did she give you?
Okay, so we know that the total is 80, and that the part we got was 28.
That means that our fraction will be 28 over 80.
Using our calculator, we enter 28 divided by 80 and we get 0.35 That’s the decimal form of the fraction.
And now, to go from the decimal form to a percent, we just move the decimal two places to the right. That gives us 35.
So, when our Aunt gave us 28 out of the 80 cookies, she gave us 35% of the cookies that she baked.
Mmmm… mmm….. Oh!
Alright, so… That’s how you find out “What percent is it?”
You make a fraction from the part you have and from the total, and then you convert that fraction into its percent form,
either by figuring out what the equivalent fraction would be
or by just dividing to get the decimal value and turning that into a percent.
Now, this was kind of a complicated lesson, so don’t worry if you're still a little confused.
There’s two things that you can do that will help make it clearer.
First, you can re-watch the video to catch anything you might have missed the first time through.
And second, you can practice using the procedures on your own, which will really help you understand them better.
Good luck, and as always, thanks for watching Math Antics and I’ll see ya next time!
Learn more at www.mathantics.com