##### Basic Math & Pre-Algebra Whether you're leaving a tip at a restaurant or figuring out just how much those stylish shoes are on sale, you can't get away from percentages. While there are numerous percentage calculators online, it's helpful to know how to calculate the percentage of a number by doing some quick math in your head, without any digital assistance.

## What is percentage?

Before learning how to figure out percentages, it's helpful to know that the word percentage comes from the word percent. If you split the word percent into its root words, you see “per” and “cent.” Cent is an old European word with French, Latin, and Italian origins meaning “hundred."

So, percent is translated directly to “per hundred.” If you have 87 percent, you literally have 87 per 100. If it snowed 13 times in the last 100 days, it snowed 13 percent of the time. Of course, if you have 100 percent of anything, you have all of it.

Saying that 50 percent of the students are girls is the same as saying that 1/2 of them are girls. Or if you prefer decimals, it’s the same thing as saying that 0.5 of all the students are girls. This example shows you that percents, like fractions and decimals, are just another way of talking about parts of the whole. In this case, the whole is the total number of children in the school.

You don’t literally have to have 100 of something to use a percent or figure percentage. You probably won’t ever really cut a cake into 100 pieces, but that doesn’t matter. The values are the same. Whether you’re talking about cake, a dollar, or a group of children, 50 percent is still half, 25 percent is still one-quarter, 75 percent is still three-quarters, and so on.

Any percentage smaller than 100 percent means less than the whole — the smaller the percentage, the less you have. You probably know this fact well from the school grading system. If you get 100 percent, you get a perfect score. And 90 percent is usually A work, 80 percent is a B, 70 percent is a C, and, well, you know the rest.

Of course, 0 percent means “0 out of 100” — any way you slice it, you have nothing.

## The percentage formula

You can use this simple percentage formula to find the share of a whole in terms of 100:

Percentage = (Value/Total Value) x 100

As an example, suppose that in a group of 40 cats and dogs, 10 of the animals are dogs. What percentage is that?

Solution: The number of dogs = 10

The total number of animals = 40

Using the percentage formula:

Percentage of dogs = 10/40 x 100 = 25%

## How to calculate percent from decimals and fractions

The number that you convert to find percentage can be given to you in two different formats: decimal and fraction. Decimal format is easier when you're learning how to calculate a percentage. Converting a decimal to a percentage is as simple as multiplying it by 100. To convert .87 to a percent, simply multiply .87 by 100.

.87 × 100=87, which gives us 87 percent.

Percent is often abbreviated with the % symbol. You can present your answer as 87% or 87 percent — either way is acceptable.

If you are given a fraction, convert it to a percentage by dividing the top number by the bottom number. If you are given 13/100, you would divide 13 by 100.

13 ÷ 100 = .13

Then, follow the steps above for converting a decimal to a percent.

.13 × 100 = 13, thus giving you 13%.

The more difficult task comes when you need to know a percentage when you are given numbers that don’t fit so neatly into 100.

Most of the time, you will be given a percentage of a specific number. For example, you may know that 40 percent of your paycheck will go to taxes and you want to find out how much money that is.

## How to calculate percentage of a specific number

To get a percentage of a number, the process is the reverse of what you did earlier. First convert the percentage number to a decimal. Then, you divide your percentage by 100. So, 40 percent would be 40 divided by 100.

40 ÷ 100 = .40

Next, once you have the decimal version of your percentage, simply multiply it by the given number (in this case, the amount of your paycheck). If your paycheck is \$750, you would multiply 750 by .40.

750 × .40 = 300

Let’s try another example. You need to save 25 percent of your paycheck for the next 6 months to pay for an upcoming vacation. If your paycheck is \$1,500, how much should you save?

Start by converting 25 percent to a decimal.

25 ÷ 100 = .25

Now, multiply the decimal by the amount of your paycheck, or 1500.

1500 × .25 = 375

This means you need to save \$375 from each paycheck.

## Dealing with percents greater than 100 percent

100 percent means “100 out of 100” — in other words, everything. So when I say I have 100 percent confidence in you, I mean that I have complete confidence in you.

What about percentages more than 100 percent? Well, sometimes percentages like these don’t make sense. For example, you can’t spend more than 100 percent of your time playing basketball, no matter how much you love the sport; 100 percent is all the time you have, and there ain’t no more.

But a lot of times, percentages larger than 100 percent are perfectly reasonable. For example, suppose I own a hot dog wagon and sell the following:

• 10 hot dogs in the morning
• 30 hot dogs in the afternoon
The number of hot dogs I sell in the afternoon is 300% of the number I sold in the morning. It’s three times as many.

Here’s another way of looking at this: I sell 20 more hot dogs in the afternoon than in the morning, so this is a 200% increase in the afternoon — 20 is twice as many as 10.

## Solving percent problems

When you know the connection between percents and fractions, you can solve a lot of percent problems with a few simple tricks. Other problems, however, require a bit more work. In this section, I show you how to tell an easy percent problem from a tough one, and I give you the tools to solve all of them.

A lot of percent problems turn out to be easy when you give them a little thought. In many cases, just remember the connection between percents and fractions, and you’re halfway home:

• Finding 100% of a number: Remember that 100% means the whole thing, so 100% of any number is simply the number itself:
• 100% of 5 is 5
• 100% of 91 is 91
• 100% of 732 is 732
• Finding 50% of a number: Remember that 50% means half, so to find 50% of a number, just divide it by 2:
• 50% of 20 is 10
• 50% of 88 is 44
• 50% of 7 is (or or 3.5)
• Finding 25% of a number: Remember that 25% equals one-quarter, (1/4), so to find 25% of a number, divide it by 4:
• 25% of 40 = 10
• 25% of 88 = 22
• 25% of 15 = 15/4 = 3 3/4 = 3/75
• Finding 20% of a number: Finding 20% of a number is handy if you like the service you’ve received in a restaurant, because a good tip is 20% of the check. Because 20% equals 1/5 , you can find 20% of a number by dividing it by 5. But I can show you an easier way: Remember that 20% is 2 times 10%, so to find 20% of a number, move the decimal point one place to the left and double the result:
• 20% of 80 = 8 x 2 = 16
• 20% of 300 = 30 x 2 = 60
• 20% of 41 = 4.1 x 2 = 8.2
• Finding 10% of a number: Finding 10% of any number is the same as finding of that number. To do this, just move the decimal point one place to the left:
• 10% of 30 = 3
• 10% of 41 = 4.1
• 10% of 7 = 0.7
• Finding 200%, 300%, and so on of a number: Working with percents that are multiples of 100 is easy. Just drop the two 0s and multiply by the number that’s left:
• 200% of 7 = 2 x 7 = 14
• 300% of 10 = 3 x 10 = 30
• 1,000% of 45 = 10 x 45 = 450

## Turning the problem around

Here’s a trick that makes certain tough-looking percent problems so easy that you can do them in your head. Simply move the percent sign from one number to the other and flip the order of the numbers.

Suppose someone wants you to figure out the following:

88% of 50

Finding 88% of anything isn’t an activity anybody looks forward to. But an easy way of solving the problem is to switch it around:

88% of 50 = 50% of 88

This move is perfectly valid, and it makes the problem a lot easier. It works because the word of really means multiplication, and you can multiply either backward or forward and get the same answer. As I discuss in the preceding section, “Figuring out simple percent problems,” 50% of 88 is simply half of 88:

88% of 50 = 50% of 88 = 44

As another example, suppose you want to find

7% of 200

Again, finding 7% is tricky, but finding 200% is simple, so switch the problem around:

7% of 200 = 200% of 7

In the preceding section, I tell you that, to find 200% of any number, you just multiply that number by 2:

7% of 200 = 200% of 7 = 2 x 7 = 14