What is a percent?
A percent is a number that expresses a ratio in terms of 100.
Percentages and Ratios (and Fractions too)
Okay. Great. What does THAT mean?
Well, a ratio is a relationship between two numbers. If a math class has 12 boys and 15 girls, we would say the ratio of boys to girls is 12:15. (We could also say the ratio of girls to boys is 15:12.) And just an FYI, we could also write the ratio of boys to girls this way: 12/15.
Wait a minute, that last thing is a fraction!
Yup, the same thing. A ratio is the same thing as a fraction; it's just written out differently.
Alright, that's what a ratio is, but what does "in terms of 100" mean?
That's the really vital part. "In terms of 100" means, if the right-hand side of the expression "12:15" (the "15") were actually "100" what number would we use to replace the "12" so we can still maintain the ratio of 12:15?
The answer is "80". We can say that the ratio 12:15 is the same as 80:100 or 80%. That is, the class has 80% the number of boys has it has girls. Can you figure out which of the below percent calculators I used to come up with this answer? If not, don't worry. Just stay tuned.
One thing first though, notice I DID NOT say the class is 80% boys. That would not be correct at all. More below
If I want to know what percentage of the class is made up of boys, I would still use the same calculator, but the ratio is no longer 12:15, but rather it is 12:27. Why?
Because to know the percentage of boys in the class, we need to write the ratio as the number of boys to the total number of students in the class. So the first ratio (12:15) is the number of boys relative to the number of girls and the second ratio (12:27) is the number of boys relative to the entire class size.
Percentages Are Normalized Ratios
This is all well and good. But why would I want to take a perfectly good ratio of 12:15 or 12:27 and in essence convert the right side to 100?
Glad you asked!
And the answer to your question is why we use percentages.
Percents give us a way to accurately compare two or more relationships incorporating different sizes or amounts.
For example, you just received the results of a math test, and you got 45 right answers out of a total of 52 questions. Your friend gets a back a science test, and she got 39 questions right out of 44. Who did better? Scroll up to percentage calculator 1 to find the answer. And now you know what calculator I used to normalize the above 12:15 ratio to a percent.
Normalize is just a fancy word meaning to make the same. When you convert a ratio to a percent, it can be said that you are normalizing the ratio. And we normalize the ratios to compare results.
Calculator 1 converts any ratio to a percent. That is, it answers the question "what percent is 'X' of 'Y', i.e., 'X:Y' or 'X/Y'"?
To use it, first understand the ratio. For example, if you earn $1,000 a week and you have $183 taken out of your pay, and you want to know what percentage of your pay gets deducted from the total then the ratio you want to convert is 183:1000. Enter 183 as "This number" and the 1,000 as the "is what percent of this number." The result is 18.3%. Or you have 18.3% deducted from your pay.
Calculator 1 can also be used as a fraction to percent calculator. How? If you've been following along, you probably already know. But for those who may have skipped ahead, the answer is simple. Take any fractions, for example, "27/82", and enter the numerator (27) into "This number." Then take the denominator (82) and enter it into "is what percent of this number." The percentage is 32.9268%.
Notice also that percentage calculator 1 works as a percent to decimal calculator as well.
Are you getting the idea?
Do you see the relationship between percents, ratios, and fractions?
If not, this would be a good place to stop and review what I've written so far. The balance of the material builds on what we've learned. Go ahead, and I'll wait.
Other Calculations Involving Percentages
What happens when we know the percent, but we don't know one of the two numbers in the ratio?
- Imagine we want to know "X" is 20% of what number "Y" if "X" equals 2,250. (The ratio looks like this: 2250:Y). You have to pay 20% of an upcoming doctor's bill, and the insurance company will pay the balance. You have $2,250. What is the maximum amount the bill can be so that you'll still have enough to cover your share? Use Percentage Calculator 2
- Or suppose we want to know what number "X" is 90% of "Y" if "Y" is 145? (The ratio looks like this: X:145). An "A" grade is 90% or above. If there are 145 questions on the test, how many do I have to get right to get an "A"? Use Percentage Calculator 3
- Finally, what if you need to know the percentage change (increase or decrease) between amount or size "X" and "Y"? An item you have been thinking of purchasing had cost $249.95 and now costs $199.95. The ratio is 249.95:199.95. What is the percent the price dropped? (We would ask what is the "discount?") We can easily flip the calculation on its head. Suppose the price had been $199.95 and is now $249.95 (199.95:249.95), what is the percent increase? Use Percentage Calculator 4
Why do the above two calculations have different results?
Notice ratios need not have only integer (whole number) parts. Frequently, many people need to do percentage calculations involving money, as we see above.
Want to read more about percentages? Check out this Wikipedia article.