Percentages are found in many contexts beyond practice problems in math textbooks. One of the best examples is sale prices, which are often advertised as a particular percent off of a price. Tips on a restaurant bill are also thought of as percentages of a number. It is important to be able to both calculate the exact percent of a number for some problems and to estimate in your head the percent of a number in other contexts.

## Calculator Method

### Step 1

Convert the percent to a decimal. This can be done very easily by moving the decimal point two spaces to the right. For example, 72 percent is converted to 0.72, 300 percent is converted to 3 and 4 percent is converted to 0.04.

### Step 2

Multiply the number by the decimal. If you are told that 72 percent of all students have cell phones and there are 30 students in the class, you can figure out how many students will have cell phones by multiplying 0.72 times 30 to get 21.6.

### Step 3

Round the answer if needed. Some problems require that the answer be rounded. If you are calculating the percent of a group of people, as in the problem in Step 2, you need to round to the nearest whole number, 22, because there cannot be 21.6 people. Another example is that when calculating sales tax, the answer needs to be rounded to the nearest penny.

## Mental Math Method

### Step 1

Convert the percent into a fraction or a sum of fractions. Percents can be thought of as the number out of 100, so when writing 20 percent as a fraction, it is 20/100.

### Step 2

Reduce the fraction by dividing both the top and bottom by the greatest common factor. In the above example, divide the top and bottom of 20/100 by 20 to get 1/5.

### Step 3

Divide the number you are finding the percent of by the denominator of the fraction. If you were trying to find the discount on an item that was $45 but is now 20 percent off, you would divide $45 by 5 to find that it is $9 off.

### Step 4

Multiply the answer by the numerator of the fraction. Oftentimes the numerator is 1 so this step can be skipped, but if you are calculating 40 percent, or 2/5, of $45 then you will need to multiply $9 by 2 to get $18.

### Step 5

Repeat with multiple calculations for problems that have percents that are not simple fractions. For example, when calculating the tip on a bill at a restaurant, you may be trying to find 15 percent of $27. Rather than converting 15 percent to 15/100 or 3/20, you can think of it as 1/10 plus half of 1/10 because it is much easier to find 1/10 than 3/20. Then you add up 1/10 of $27, which is $2.70, plus half of that, or $1.35, to get a tip of $3.05.

#### Things You Will Need

- Calculator

#### References

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