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Hi and welcome to Math Antics.

In today’s video, we’re gonna learn how to do one of the most common calculations with percentages.

We’re gonna learn how to find a percent of a number.

But what does that even mean?

Do numbers have percents that they hide somewhere and then we have to go looking for them like a game of hide and seek?

Gottch ya!

Umm - not exactly.

Finding a percent of a number makes more sense if you remember that a number just represents an amount and that a percent is really just a fraction.

So finding a percent of a number really means finding a fraction of an amount.

Think about it this way…

Let’s say the number 20 represents an amount, like the amount of lady bugs that you found at the park one day.

And let’s also imagine that you agreed to give 25% of all the lady bugs you found to your little sister.

Okay then, so how many is that?

If you have 20 lady bugs, how many is 25% of that amount?

That’s what it means to find a percent of a number.

You’re finding out how much that percent (or fraction) of the total is.

In this case, since our total is 20, we need to know what 25% of 20 is.

So how do we figure that out?

Well, it’s really easy if you remember back to one of our fractions videos; the one about multiplying fractions.

In that video, we learned that when dealing with fractions,

sometimes the word “of” is used instead of the multiplication symbol.

When they say find 1/2 of 16, they really mean find 1/2 times 16.

Well guess what…

Since a percent is just a special fraction… “of” means the exact same thing with percents that it did with fractions.

When we have 25% of 20, that means the same as 25% times 20.

Great! So all we have to do to find a percent of a number is to multiply.

But how do we multiply a percent and a number together?

Do we just forget about the percent sign and multiply the numbers together?

No! If we did it that way, our answer would be WAY too big.

25% should be a smaller part (or fraction) of 20 lady bugs.

But if we did 25 times 20, we’d get 500 lady bugs!! Clearly that’s not the right answer!

Here’s what we have to do instead...

Remember that when you see a percent written like this with the percent sign, it’s an abbreviation for a fraction; in this case, 25 over 100.

So we need to use that fraction form when we multiply since we’re really multiplying by a fraction.

Now some of you may also remember that percents have a decimal form. We’ll get to that in just a minute.

Okay then, if we use the fraction form of our percent, then our problem becomes: 25/100 times 20.

Now that’s a problem we know how to do.

To multiply fractions, we just multiply the top numbers, and then we multiply the bottom numbers to get the answer.

And we can just write 20 as a fraction by putting a 1 as the bottom number, because 20 over 1 is the exact same value as 20.

So, let’s go ahead and multiply.

On the top, we have 25 × 20 which gives us 500.

And on the bottom, we have 100 × 1 which is just 100.

So our answer is 500 over 100.

Now 500 over 100 might seem like a strange answer, but that’s just because we still need to simplify it.

500 over 100 simplifies to 5 over 1, and 5 over 1 is just 5.

That’s much better. So, 25% of 20 is 5.

Alright, so to find a percent of a number, we just need to multiply the fraction form of the percent by the number and we have our answer.

But, there’s another slightly different method that you can use that works especially well if you’re allowed to use a calculator.

In our first percentages video, we learned that percents have both a fraction form and a decimal form.

We’ve already seen how we can use the fraction form to find a percent of a number, but we can also use the decimal form if we want to instead.

The procedure starts the same. If you need to find 25% of 20, you first replace the word “of” with the multiplication symbol.

Next, we’ll replace the percent, but with its decimal form this time. 25% is the same as the decimal 0.25

Then, all we have to do is multiply.

And although I could easily do the decimal multiplication by hand, I happen to have a calculator, so I’m gonna use it.

I just enter 0.25 × 20, hit equals, and I get 5.

Yep - That’s the same answer we got when we used the fraction form of 25%. Oh Yeah!

So that’s how you find a percent of a number. You just multiply the number by either the fraction form OR the decimal form of the percent.

Either way will give you the right answer, so you can choose whichever will be easier for you to do.

Let’s see a couple more examples before you practice on your own.

This next one involves money.

Pretend that your best friend has a job walking dogs and offers to give you 35% of whatever he earns if you help walk some of the dogs.

If your friend earns $80 that week, how much of the money will you get?

In other words, you need to figure out what 35% of 80 is.

Okay then, let’s start by replacing the “of” with the times symbol.

And next we have to decide if we want to replace the percent with its fraction form or its decimal form.

I think I’ll use the decimal form for this one which means I'll replace the 35% with 0.35

Now, all we have to do is multiply 0.35 times 80, and that’s 28.

That means you’ll get 28 dollars if you help your friend walk those dog.

Cha-ching!

Okay then… In the last two problems, we found a percent of a number,

which, like we learned at the beginning of the video, just means finding a fraction of an amount.

And like you’d expect when finding a fraction of something, the answer was smaller than the amount we started with.

But remember, fractions can be ‘improper’ too which means that their value is greater than 1.

And in the same way, percents can be greater than 100%. So you might come across situations like this…

Suppose that last year, your school had 400 students, but this year it has 120% of that amount.

Well, 100% would mean the exact same number of students as last year,

so 120% must mean that there’s more students now, but how many students?

To find out, we need to calculate what 120% of 400 is.

Great, we know just how to do that.

We just multiply 400 by the fraction form OR the decimal form of 120%.

Let’s use the decimal form again.

To get the decimal form of 120%, we move the decimal point over 2 places to the left, and we get 1.20

So we multiply 1.20 times 400 which gives us 480.

So this year there’s 480 students at school.

Alright then, that’s how you find the percent of a number.

And it’s a really useful math skill that has a LOT of real-life applications so it’s important to learn how to do it right.

As always, the best way to learn math is to practice on your own.

Thanks for watching Math Antics, and I’ll see ya next time.

Learn more at www.mathantics.com