Percents and Their Relationships with Fractions and Decimals Study Guide

Updated on Oct 3, 2011

Introduction to Percents and Their Relationships with Fractions and Decimals

We use only 10% of our brains. Imagine how smart we would be if we used the other 60%!

—Ellen Degeneres (1958– )

This lesson will examine the basics of percents and their relationships with fractions and decimals. Learn how to find percent values in equations and word problems.

Most likely, you have encountered the percent (%) symbol sometime during your life—maybe when receiving a test score or even looking through a store's sales flyer. When you see a number followed by the percent symbol, you can think of the percent as a ratio comparing that number to 100.

Percents can be expressed in two different ways:

  1. as a fraction (just put the number over 100):
  2. as a decimal (move the decimal point two places to the left): 5% = 0.05


Get familiar with some common fraction and decimal equivalents to percents.

Percent Fraction Decimal
25% 0.25
50% 0.50
75% 0.75
100% 1

Finding the Percent of a Number

Recall that the word of tells you to multiply. When you take the percent of a number, you should multiply.

Suppose you are purchasing a graphic novel that usually costs $8, but the comic book store is selling it for 25% off. How much do you take off of $8?

Remember that , or , so you are taking off of $8; of $8 translates to × 8, which equals $2 off. So, the graphic novel is yours for the price of $6!

What if you are asked to find the percent of a percent of a number? Don't panic just yet! When you take the percent of a percent, all you need to do is multiply. Let's try one:

      40% of 20% of 600 =
      0.40 of 0.20 of 600 =
      0.40 × 0.20 × 600 = 48
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