Calculate Percentages: A Step-by-Step Guide for Students

How to Calculate Percentages

A percentage is another way to write a fraction out of 100. For example, if 70 out of the 100 students at your school have brown hair, you could write this as 70/100, or 70%. If your chances of winning your school's raffle are one out of 100, you could write this as 1/100, or 1%.

Using Equivalent Fractions

Most of the time, calculating percentages is more complex than the examples above because most fractions aren't out of 100. For instance, if you have eaten 3/5 of a pizza, how do you write that as a percentage? Follow the steps below when the denominator of your fraction is a factor of 100:

1. Figure out the numerator and denominator of your fraction. The denominator is the total amount, and the numerator is the amount that you're calculating the percentage for. For the pizza example, we already know that the fraction is 3/5.
2. Determine whether or not your denominator is a factor of 100. If it is, you can use this method. If not, you'll have to use the method explained in the next section. Five is a factor of 100, because 5 x 20 = 100.
3. Find an equivalent fraction with 100 as the denominator. Since 5 x 20 = 100, we also have to multiply 3 x 20 to get 60. The fraction 60/100 = 3/5.
4. Write this fraction as a percentage. In this case, 60/100 = 60%.
5. State your answer relative to the problem. For this problem, we can say that you ate 60% of the pizza.

Using Division

If you get stuck at step two above because the denominator of your fraction is not a factor of 100, you can use the method described in this section. As an example, we'll imagine that Samantha has finished 30 out of the 40 homework problems her teacher assigned, and she wants to figure out what percentage of the problems she has finished. To solve this type of problem, follow these steps:

1. Write your fraction with the total as the denominator and the amount you're calculating the percentage for as the numerator. For this problem, the fraction is 30/40.
2. Divide the numerator by the denominator. If you divide 30/40, you get 0.75 (30 ÷ 40 = 0.75).
3. Multiply the answer to your division problem by 100 to find the percent. Samantha would multiply 0.75 x 100 to get 75 (0.75 x 100 = 75).
4. Put your answer in the context of the question. For instance, Samantha has completed 75% of her homework problems.

Tip: If you move the decimal point in a number to the right two places, you'll get the same result as if you had multiplied the number by 100. For example, 0.23 x 100 = 23, 9.00 x 100 = 900 and 0.05 x 100 = 5.

Repeating Decimals

Sometimes, when you use the method described in the last section, you'll wind up with a repeating decimal in step two. For instance, if you wanted to know what percentage one out of three apples is, you would write the fraction 1/3, and then divide one by three to get a repeating decimal, like this: 1 ÷ 3 = 0.333… Other times, you'll get a decimal that is very long, like 0.809523… In either case, it's fine to round your answer to the nearest tenth or hundredth, and then multiply it by 100 to get your percentage, depending on your teacher's instructions.

Practice Problems

1. Andrew got 18/20 problems on his science quiz correct. What percentage of the problems did he get right?

2. Sonja exercised for 15 minutes. She did jumping jacks for six minutes and jumped rope for nine minutes. For what percentage of the time did she do jumping jacks?

3. Elijah paid $100 for three pairs of jeans. The sales tax on his total purchase was six dollars. At what percentage was his total purchase taxed?

Solutions

1. The fraction is 18/20, and 20 is a factor of 100, so you can write 18/20 as the equivalent fraction 90/100 (20 x 5 = 100 and 18 x 5 = 90). This means that Andrew got 90% of the questions on his test correct.

2. Sonja did jumping jacks for six out of 15 minutes, so the fraction is 6/15. The number 15 isn't a factor of 100, so we have to divide six by 15. Since 6 ÷ 15 = 0.4, and 0.4 x 100 = 40, Sonja spent 40% of her workout doing jumping jacks.

3. Since the tax is six dollars out of $100, it's represented by the fraction 6/100. This means that the purchase was taxed at 6%.