Elementary Math: Understanding Percentages

Getting Ready for Percentages

To understand percentages when they're introduced later in middle school, you'll need to be able to write fractions and convert them to decimals. You'll also need to know how to multiply decimals by whole numbers and other decimals.

Writing Fractions

Before learning about percentages should have a firm grasp of fractions. Fractions represent parts of a whole, and they're written with the total amount on the bottom (in the denominator) and the part of whole on the top (in the numerator).

Often, percentages represent fractions that are out of 100, so we'll use fractions with this denominator in examples. For instance, if there are 100 fifth grade students at your school, and 57 of them are girls, you could say that 57/100 of your classmates are girls. The remaining 43 students must be boys, so you could also say that 43/100 of your classmates are boys.

Converting Fractions to Decimals

Another helpful concept to understand when you're working with percentages is that every fraction has an equivalent decimal. For percentages, you'll generally be converting fractions with base-ten denominators, like 1/100, to decimal form.

To do this, begin by identifying the appropriate place value for the decimal. If the fraction is out of ten (1/10), then you'll need to use the tenths place, which is the first one to the right of the decimal point. If the fraction is out of 100 (1/100), you'll be using the hundredths place, which is to the right of the tenths place.

Once you've identified the correct place value, just write the numerator so that its last digit (the ones digit) is in that place. For instance, 5/100 = 0.05, since the numerator (five) goes in the hundredths place of the decimal. Here are a few more examples:

7/10 = 0.7

7/100 = 0.07

12/100 = 0.12

Multiplying by Decimals

To multiply a whole number by a decimal, use the same process you use to multiply two whole numbers. When you're finished with the multiplication, count the number of digits in the problem that are to the right of the decimal point. For example, if you're multiplying 15 x 2.5, there would be one digit to the right of the decimal point. That number tells you how many decimal places to add to your answer, as you can see in this example:

100 x 3.6 = 360.0

In this case, we added one decimal place to the original answer because there was one decimal place in the problem (3.6). To multiply two decimals together, follow the same process. Here's an example:

10.5 x 3.5 = 36.75

For this problem, the original answer was 3,675, but we moved the decimal point two places to the left to account for the two decimal places in the problem (10.5 and 3.5).