You have 120 cows and 90% of them are female. How many female cows do you have?

In order to find the answers to questions like the one above, you need to know how to do this kind of calculation:

90% of 120

This page will show you three ways to do this problem. In order to understand what we'll show you, you need to understand what percents mean, and how to convert them to decimals or fractions. You also need to be able to reduce fractions.

You also need to understand that when you find a percent of something, the answer has the same units as the number you are finding the percent of. For example:
50% of 200 carrots is 100 carrots       10% of  $300 is  $30        25% of 80 units is 20 units


Now let's look at the three methods for finding a percent of a number:



Method 1: The Quick and Easy Way:


The easiest way to find a percent of a number is to know the fractional equivalent for some common percents. At the right are some of these often-used percents and the fractional value for each. You'll need to memorize these.

Method 1 involves using the fraction instead of the percent. For example, if you were asked:

"What is 50% of 36?"

you would instead ask yourself:

"What is half of 36?"

This makes it easy to get the answer 18.

The advantage of this method is that it is fast ... faster even than using a calculator. This will be a big advantage in later Math courses where you won't have a lot of extra time to do basic calculations.

Here are some more examples:


Finding one-tenth of a number is always easy, because this is the same as dividing by ten.

You just have to move the decimal point back one place.

There are many numbers you can find a quarter of, without using a calculator.



Knowing that this percent is really one-third will let you find the answer mentally before the person next to you has even turned on their calculator!

Some percents are really easy. One hundred percent is the whole thing.

By the way, notice that 'of' means that you multiply.

One drawback of this quick method is that you will need to memorize some conversions. But your teacher will expect you to know them anyway, so that's nothing to worry about.
The other drawback is that the quick method won't work for percents for which you don't know the fraction, or for which the fraction isn't a simple one. It also won't work if the calculation is too difficult to do in your head.
For example, if you were asked to find 29% of 123.9, the quick method isn't very useful. You're unlikely to be able to do twenty-nine hundredths of 123.9 mentally. For problems like that we need a new method.



Method 2: Using Decimals and a Calculator:

This method requires that you either know the decimal value for the percent, or can find it.

Fortunately it is very easy to change a percent to a decimal. Since a percent is really just a fraction over one hundred, you just need to move the decimal point two places to the left.

In order to do a question like this:

28% of 115

you must convert 28% to 0.28 by moving the decimal back two places.
Then you use a calculator, remembering that  'of'  means that you multiply:
0.28 x 115 = 32.2


Here are some more examples:








This method isn't quite as fast as the previous one. It's big advantage is that is will work for every question you encounter. You just need to be able to convert the percent to a decimal so you can enter it on your calculator.



Method 3: Using Fraction Operations:


This method uses fraction multiplication rules.

First you change the percent to a fraction over 100. You can reduce this fraction if you want to; we didn't.

Then you rewrite the number as a fraction over 1.

Now you have a fraction multiplication question; you multiply the tops and multiply the bottoms.


Finally, you divide your answers to get a decimal. This step will always be easy, because you're always dividing by 100. If you want, you can instead just reduce your answer to a simpler fraction.

This method takes longer, and requires more effort. You may still require a calculator to do the multiplication. However, this is a valuable method to learn, because it is something you will find useful in later High School courses.

Here are a few more examples of Method 3. Follow each step carefully and make sure you understand what we did.




You need to know how to find a percent of a number all three ways. To help you learn the methods, we have some more practice questions for you. They're in the form of a quiz; after you submit your answers, we'll email you back and tell you how you did.

>>> Try the QUIZ <<<


Mr. Willis's Page