Calculate Basic Percentages: Help Using Percentages in Math

How to Calculate Percentages

Percentages are commonly used to indicate that a product is discounted. They are also used as the basis for calculating sales taxes, tips and grades. A percentage represents a fraction of 100, and it is indicated using the '%' sign. For instance, the fraction 5/100 = 5% and 90/100 = 90%.

Set Up a Proportion

It's fairly straightforward to calculate a 15% tip for your $100 dinner (15% of $100 equals $15), but when you want to calculate a percentage in real life, it's usually not out of 100. How do you calculate a 15% tip if your dinner costs $72.13?

One way is to set up a proportion, which tells you that two pairs of numbers have the same relationship to one another. To calculate a 15% tip for your $72.13 meal, you could set up and solve this proportion:

15/100 = x/72.13

By solving this proportion for x, you can figure out what number has the same relationship to 72.13 that 15 has to 100. In other words, the value of x will be 15% of 72.13, just like 15 is 15% of 100. Here's how you solve the proportion:

1. Cross-multiply and place the results on opposite sides of the equals sign, like this: 100x = 15(72.13).
2. Simplify as needed. This equation can be simplified to 100x = 1,081.95.
3. Isolate the variable. In this example, divide both sides of the equation by 100 to get this result: x = 10.8195.
4. Round out your answer as necessary, and state it in the correct unit of measure. Since x = $10.8195, it would be reasonable to round this up to $10.82.

Multiply by a Decimal

Another way to calculate a percentage of a number is to multiply it by a decimal equal to that percentage. This method works because every percentage represents a fraction, and every fraction can be converted into a decimal. For instance, 70% = 70/100, and 70/100 = 0.70. Likewise, 3% = 3/100, which equals 0.03.

To demonstrate this, you can solve the same problem from the previous section, which was to calculate a 15% tip for a meal that cost $72.13. First, convert 15% to a decimal: 15% = 15/100 = 0.15. Next, multiply $72.13 by 0.15 to get $10.8195 (72.13 x 0.15 = 10.8195). Note that this is the same answer you got earlier by solving the proportion for x.