Introduction to Percentages
> ... Math > Division and Percentages > Introduction to Percentages


In this lesson, you will learn about percentages and how they work. A percentage (%) tells you what part of a whole something is. Percent is a word that literally has two parts to it. Per means “out of” and cents means “one hundred.” So percent means out of one hundred.

This video illustrates the lesson material below. Watching the video is optional.

Out of One Hundred

Example 1
This box has been divided into one hundred parts.

The image shows a box that is divided into a hundred parts.

Figure 1

Ten out of one hundred parts are colored in. This represents 10 out of one hundred parts and is written as 10%.

This image shows that ten out of one hundred parts are colored in.

Figure 2

Example 2
Fifty out of one hundred parts are colored in. This represents 50 out of one hundred, or 50%.

Fifty out of one hundred parts are colored in.

Figure 3

Example 3
Consider this another way. Look at this whole block. This represents one whole, or one whole unit, or one. It’s represented in place value as 1 or 1.0. One in the one’s place.

The image shows a whole block.

Figure 4

This can be divided into other smaller sections. For example, it’s now divided into one hundred parts.

One whole block is divided into one hundred smaller sections.

Figure 5

Each one of these parts represents one one-hundredth. Just one of these little squares equals 0.01, or one out of one hundred, because you have one in the hundredths place value. Percent, meaning per one hundred or out of one hundred, uses this same concept. As a percentage, one of these little squares is 1%, or one out of one hundred.

Where Do We Use Percentages?

There are lots of examples in the natural world where percentages are used. Here are some examples:

  • Taxes
    • Taxes are often calculated as a percent. Some places have a property tax on any property that you own and that tax is assessed as percent of the value of the property. Some places have a sales tax. Every time you buy something, you pay taxes on that item based on how much the item costs.
    • For example, suppose you buy something that costs a dollar and there is a 7% tax on the item. The item will actually cost $1.07 because of the extra tax you must pay.
  • Store Discounts
    • Suppose a store is having a 20% off sale, and you buy an item for one dollar. Twenty percent of $1.00 is $0.20 or twenty one-hundredths. If the item originally costs $1.00 and you are getting a sale of 20%, you will only have to pay \(1.00–0.20\), which is $0.80.
  • Sales Commission
    • Some jobs are based on commission, meaning you are paid a percent of how much you sell or how much money you have brought into the company.
    • For example, suppose you earn a 15% sales commission on anything that you sell and you sold $100 worth of products for your company this month, how much money would you earn? If you are making 15% of every $100, that means out of a hundred you get $15.
  • Interest Rates
    • Banks use interest rates to express how much money they charge for loans. Credit card companies use interest rates to indicate how much they charge based on what you owe on the card.
    • For example, a loan interest rate might be 5.25% and a credit card interest rate may be 19.99% or sometimes even higher.
  • Tithing
    • In The Church of Jesus Christ of Latter-day Saints, tithing is 10% of someone’s earnings. For every $1 earned, a person pays $0.10 in tithing.

Things to Remember

  • Percent means out of a hundred. You can calculate the percentage based on how much you are taking out of a hundred.

Practice Problems

  1. What does a percent mean? (
    Out of 100.
  2. If an item purchased at a store costs $1 and has a sales tax rate of 6%, what will be the total amount paid for the item? (
    Video Solution
    | Transcript)
  3. If a tire store is having a sale for 10% off any tire, and you purchase a tire that normally costs $100, what is the sale price of the tire after the 10% is taken off? (
    Solution: $90
    100% represents the original price of the tire.
    This is a picture of a round circle that is all the same color. In the top left corner is says, “One hundred percent original price of the tire.” This means that the original price of the tire is 100%.

    Since the tire is 10% off, you can subtract 10% from 100%. \(100\% − 10\% = 90\%\).
    This is the picture of a round circle like the circle in the previous image except this time there is a pie shaped wedge of the circle colored a different color.  This wedge is not very big compared to the rest of the circle. To the left of this wedge is a line with the words, “Discount 10%.” The rest of the circle also has a line pointing out to the right which says, “Tire 90%.”

    So you will be paying 90% of the original price.
    Since the original price is $100, you can follow the same pattern to get the discounted price: \($100 - $10 = $90\).
  4. If you earn 20% commission for any sale you make, and you sell $100 worth of product, how much will you earn for that sale? (
    Video Solution
    | Transcript)
  5. If you earn $100 and pay tithing at a rate of 10%, how much money will you pay in tithing? (
    Solution: $10
    100% represents your earnings. Tithing is 10% of what you earned. If you earn $100, then you would pay $10. In this situation the \(90\% = $90\) of your earnings and \(10\% = $10\) for tithing.
    This 10 by 10 grid holds 100 squares, the blue 10% represents tithing, and the 90% represents the earning after tithing.
    The image has a grid or large square with 100 small squares inside, 10 squares going down and 10 going across.  A column of 10 squares is shaded in blue on the left side, with the word 10% written above the column.  The rest of the unshaded squares have the word 90% written across the top.

    Need More Help?

    1. Study other Math Lessons in the Resource Center.
    2. Visit the Online Tutoring Resources in the Resource Center.
    3. Contact your Instructor.
    4. If you still need help, Schedule a Tutor.