Updated December 20, 2020
By Timothy Banas
How much is 15 percent of 210? How about 75 percent of 440 or 350 percent 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.
What Does 'Percent' Mean?
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}
Some Easy Percentages to Remember
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 percent means half. To calculate 50 percent of a number, simply divide it by 2. For example, 50 percent of 26 is 26 divided by 2, or 13.
25 percent means one fourth. To calculate 25 percent of a number, simply divide it by 4. For example, 25 percent of 12 is 12 divided by 4, or 3.
10 percent means one tenth. To calculate 10 percent of a number, simply divide it by 10 or move the decimal point one place to the left. For example, 10 percent of 230 is 230 divided by 10, or 23.
5 percent is one half of 10 percent. To calculate 5 percent of a number, simply divide 10 percent of the number by 2. For example, 5 percent of 230 is 23 divided by 2, or 11.5.
How to Do Percentages In Your Head
So how much is 15 percent of 210? You can use the four key percentages you memorized to figure this out. Consider that 15 percent is 5 percent added to 10 percent. Since 10 percent of 210 is 21, and 5 percent is half that, or 10.5, then 15 percent is 21 added to 10.5, or 31.5.
How about 75 percent of 440? Here you can figure that 75 percent is 50 percent added to 25 percent. Since 50 percent of 440 is half that, or 220, and 25 percent of 440 is one fourth, or 110, then 75 percent is 220 added to 110, or 330.
In this way you can combine 5 percent, 10 percent, 25 percent, and 50 percent 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.
How to Compute Percentage Greater Than 100 Percent
To calculate a percentage greater than 100 percent, 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 percent 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.
