# How to Work out Percentages

Percentages are a part of math that, once learned, can help with not only math but common cross curricular subjects such as science as well. Percentages can be taught on many different levels as simple as what percent of Jimmy’s soccer ball is white or even how data grows as a percent over time. The problems span all across multiple math classes including geometry and algebra.

To begin, the basic calculation of a percent should be learned. Many teachers initially teach students to set up a problem as a proportion, “is or are”/”of” = percent/100. This requires the student to understand a word problem such as this one: Darla’s class has 18 girls and 12 boys. What percent of the children in Darla’s class are girls? The “is or are” of this problem is the number of girls as stated, “are girls?” The “of” of this problem is the number of total children as stated, “of the children.” The proportion set up would be 18/30 = percent/100. The answer to the problem would be 60% once the proportion is solved.

Some students find the “is or are”/”of” method confusing or unnecessary. Another technique taught is how to convert a decimal to a percent. In the Darla example, you would first make a fraction. This would, once again, be 18/30 (the same as is or are/of). Second, you divide the fraction, and it equals 0.6. Third, you move the decimal place two places to the right, and this is the same as multiplying by 100. You still end up with 60%. Overall, these methods end up with the same result always.

The key to all percent problems is finding out how to set up the fraction. This takes an eye for key vocabulary. The numerator (is or are) of the fraction is the “part,” in the problem, and the denominator (of) is the “whole.” In more advanced problems the formula change/original can be used to calculate change. Here are some ways percentages are often used.

Simple problem 1: Joe loves cola so much that he figured one cola equals 27 gulps. If he takes 4 gulps, what percent of the cola did he drink? The fraction in this situation will be the number of gulps taken / total number of gulps, and this is 4/27. If you divide the fraction, the decimal is 0.1481… If you move the decimal place over two places to the right (which is same as multiplying by 100), you get 14.81% when rounded to the nearest hundredth.

Advanced problem 1: If the cola company increases cola to 32 gulps, what is the percent increase? This is the problem that requires the change/original formula. The fraction would be 32-27/27 which equals 5/27. This fraction as a decimal is 0.185… If you move the decimal place over two places to the right (which is the same as multiplying by 100), you get 18.52% when rounded to the nearest hundredth.

You now have the basics of percentages enough to work backwards. You can never multiply a number by a percent. You must use the decimal form of the percent. To get a percent back into its decimal form, you move the decimal two places to the left (which is the same as dividing by 100). Common problems that require working backwards are tax problems.

For example, Tim bought a teddy bear for his girlfriend for \$25. If the store charges 8.25% tax, what is the total price Tim paid? First, you must understand the answer equals \$25 + the amount paid in tax. To calculate the amount paid in tax, you convert the percent into a decimal, and multiply the decimal by the price. The percent as a decimal equals .0825. This decimal times \$25 equals \$2.0625, which is the amount paid in tax. Overall, Tim will pay \$27.0625 for the teddy bear.

A shortcut for problems such as the one above is stated here. When trying to calculate the total price of something including tax, you can take the percent as a decimal, add 1, and multiply that number by the price. You add one because the price, when multiplied by one, will preserve its original price along with adding the tax. To prove it, 1.0825 times \$25 still equals \$27.0625.

One must remember a percent is a fancy way of saying part to whole or change over original. Percentages are nothing to be intimidated by as they are just another form of numbers. In summation, this article hopefully was 100% satisfactory.