Calculate Basic Percentages: Help Using Percentages in Math

When you're solving real-world problems involving taxes, discounts and tips, it's important to know how to calculate basic percentages. Keep reading to learn how.

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.

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