When you calculate a percent you are showing what part of something is in a decimal. Like a fraction, it divides up a whole into parts. Percent means “out of 100” so we divide the whole we are looking at into 100 parts.
A tiny percentage, such as 2%, means that a small part (only 2 parts out of all 100 parts) of that whole is there. The larger the percent, the closer toward that whole you are moving, so 78% is almost the entire thing. If you have 100%, you have the entire piece of whatever you are counting.
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Let’s start by taking a look at a very common percentage that gets used all the time. When dining out, it’s courtesy to add a tip to your bill. That is often 15% of the total on your check. So how to figure what that 15% of the bill is?
One Way: Decimal
Percentages are written with that funky little % at the back. Another way to write that same number without any special notation is as a decimal.
15% = 0.15
If you take that decimal and multiply it with your original total price of dinner, the product will be 15% of that.
So let’s say the total bill for dinner was $43.
43 * 0.15 = 6.45
So 15% of $43 is $6.45. Your total bill will be $49.45.
This method works for figuring any percentage, if you know what percent you are looking for. Just convert the percent to a fraction, multiply and there’s your answer.
Say there’s a sale that’s taking 20% off. You had your eye on a new TV that’s going for $550. 20% off seems like a great deal but you want to make sure you have the budget, because you don’t want to spend more than $500.
20% is 0.20 as a decimal. Multiply that with 550. This will give you the percentage off that the store is offering.
550 * 0.20 = 110
20% of $550 is $110. They are taking 20% off, so subtract that $110 and the end price will be $440. That falls under your budget!
Another Way: Fractions
Fractions are another way to show parts of a whole. ½ means there is 1 part of 2, one half. ⅝ means that there are 5 parts of 8. These fractions can also be represented as percents. 20% is the same as 20/100 or ⅕ if you reduce. 88% is the same as 88/100 or, again, reduced to 22/25.
What’s a bit more tricky about this is that percents represent parts of 100 and fractions can have as little or as many parts as we like, even over 100 parts.
How do we figure out what percent a fraction represents?
Using the example of tipping from before, we know that 15% means 15 of 100 parts or 15/100. That can be reduced to 3/20, if you want to make things a little easier. Let’s say dinner cost $71 this time. A way to figure out the number for the tip is to set it up to look like this.
x/71 = 3/20
What that means is that when we figure out what x is, the resulting fraction x/71 will match 3/20.
We need to cross multiply so we end up with this:
71 * 3 = 20 * x
213 = 20x
When we solve for x we’ll have the magic number we need, the 15% of $71.
213/20 = x
10.65 = x
So your tip for the meal would be $10.65.
We can double check that by using the original decimal of 0.15 and multiplying it out.
71 * 0.15 = 10.65
It matches, showing that the long way around with fractions works as well.
For a great refresher, Fun Simple Useful Math for Kids (don’t let the name fool you!) has a lot of good content dealing with percentage calculations as well as fractions and decimals.
Sometimes, you will need to calculate what percentage a fraction is representing. For example, what is 13/28 as a percent? We know that 14/28 is the same as ½ when it’s reduced and that’s 50%, but 13 is just shy of that.
Using the method we used when we figured out what 20% of the price of the TV was, we need to calculate what the percent is. That means we don’t know how much out of 100 that 13/28 equals. Let x stand in for that number out of 100 and our equation looks like this:
28 * x = 13 * 100
28x = 1300
Solve for x.
x = 1300/28
x = 46.285…
That means the fraction 13/28 is about the same as 46.285% or just over 46%.
Another, even faster way of coming to that same answer is to simply divide the numerator (the top number) by the denominator (the number on the bottom). This will give you a decimal.
13/28 = 0.46285…
Since we know percents are a kind of decimal, 13 parts out of 28 makes that 46%, the same answer from the other, longer method using cross multiplying.
Even though this is the simplest way because it has the fewest parts involved, it can be daunting to figure out how to divide numbers that are very different from each other. This class, The Secrets of Mental Math, will help you learn how to multiply and divide these kinds of numbers, and even much bigger numbers, with ease, all in your head.
When calculating percentages, it’s important to know what the end number is you are looking for. Is is a percentage of a certain number? Is it simply out of 100? Are you attempting to translate a fraction into a decimal, so it’s obvious what the percentage is and not just how many parts it is?
If you’d like to also improve your math for business and making sure you shine in interviews, FastMath Case Interview Preparation covers all manner of percents associated, from those percentage calculations to compounded interest.
Whatever the result you are attempting to find, knowing which number you’re trying to get to, whether it’s parts of 100 or what a fraction translates to as a decimal, that will help you determine the best way to figure out the percentage calculation and the best way to go about it.