Easy Ways To Calculate Percentages

How much is 15%of 210? How about 75% of 440 or 350% of 20? The standard way of calculating percentages can make these problems difficult to do without a calculator. Luckily, there are several tips and tricks you can use to solve percentage problems without a calculator. Once you understand these simple methods, these questions become easy to solve.

It is valuable to know the origin of the term ​percent​ if you want to truly understand how to calculate a percentage. The word ​percent​ comes from the phrase per cent. ​Cent​ is a root that means one hundred, so per cent literally means per one hundred. For example, if you know that 30 percent of the students in a school are boys, that means that there are 30 boys per one hundred students. Another way to say this is that 30 out of 100 students are boys.

Generally, the way to figure out any percentage is to multiply the number of items in question, or ​X​, by the ​decimal​ form of the percent. To figure out the decimal form of a percent, simply move the decimal two places to the left. For example, the decimal form of 10 percent is 0.1. Then, to calculate what 10 percent of is, say, 250 students, simply multiply the number of students by 0.1.

(10 text{ percent of } 250 text{ students } = 0.1 × 250 text{ students} = 25 text{ students})

If you can commit the percentage list below to memory, you will be able to calculate a wide variety of percentages without a calculator.

​50% means ​half​. To calculate 50% of a number, simply divide it by 2. For example, 50% of 26 is 26 divided by 2, or 13.

​25% means ​one fourth​. To calculate 25% of a number, simply divide it by 4. For example, 25% of 12 is 12 divided by 4, or 3.

​10%​ means ​one tenth​. To calculate 10% of a number, simply divide it by 10 or move the decimal point one place to the left. For example, 10% of 230 is 230 divided by 10, or 23.

​5% is ​one half of 10%​. To calculate 5%of a number, simply divide 10% of the number by 2. For example, 5% of 230 is 23 divided by 2, or 11.5.

So how much is 15% of 210? You can use the four key percentages you memorized to figure this out. Consider that 15% is 5%added to 10%. Since 10% of 210 is 21, and 5% is half that, or 10.5, then 15% is 21 added to 10.5, or 31.5.

How about 75% of 440? Here you can figure that 75% is 50% added to 25%. Since 50% of 440 is half that, or 220, and 25% of 440 is one fourth, or 110, then 75% is 220 added to 110, or 330.

In this way you can combine 5%, 10%, 25%, and 50% to calculate a wide variety of percentages in your head. If you need to calculate a percentage that is not a multiple of 5, you can use this technique to estimate the answer very closely.

To calculate a percentage greater than 100%, simply move the decimal of the percent ​two spaces​ to the left and use the answer to multiply the number in question. You can do this to figure out what is 350%of 20. Moving the decimal of the percent two spaces to the left gives you 3.5. Multiplying 20 by 3.5 then gives you the answer, which is 70.