Lesson 10: What Are Percentages?

Let’s learn about percentages.

10.1: Dollars and Cents

Find each answer mentally.

  1. A sticker costs 25 cents. How many dollars is that?
  2. A pen costs 1.50 dollars. How many cents is that?
  3. How many cents are in one dollar?
  4. How many dollars are in one cent?

10.2: Coins

  1. Complete the table to show the values of these U.S. coins.

    An image of 6 U.S. coins. A penny, nickel, dime, quarter, half dollar, and dollar coin are presented.​ Coins Copyright Owner: United States Mint License: Public Domain Via: United States Mint
      coin penny nickel dime quarter half dollar dollar
    row 1 value (cents)            

    The value of a quarter is 25% of the value of a dollar because there are 25 cents for every 100 cents.

    A diagram of two bars with different lengths. The top bar is labeled 1 Quarter and 25 cents is labeled inside the bar. The bottom bar is labeled 1 Dollar. It is 4 times longer than the top bar and 100 cents is labeled inside the bar.

  2. Write the name of the coin that matches each expression.

    1. 25% of a dollar
    2. 5% of a dollar
    1. 1% of a dollar
    2. 100% of a dollar
    1. 10% of a dollar
    2. 50% of a dollar
  1. The value of 6 dimes is what percent of the value of a dollar?
  1. The value of 6 quarters is what percent of the value of a dollar?

10.3: Coins on a Number Line

An image of a 1 dollar coin.

A \$1 coin is worth 100% of the value of a dollar. Here is a double number line that shows this.

A double number line for “value of coins in dollars” with 7 evenly spaced tick marks. The top number line has the number 0 is on the first tick mark and 1 on the fifth. The remaining tick marks are blank. The bottom number starting with the first tick mark 0 percent, 25 percent, 50 percent, 75 percent, 100 percent, 125 percent and 150 percent are labeled.
  1. The coins in Jada’s pocket are worth 75% of a dollar. How much are they worth (in dollars)?
  2. The coins in Diego’s pocket are worth 150% of a dollar. How much are they worth (in dollars)?
  1. Elena has 3 quarters and 5 dimes. What percentage of a dollar does she have?
 

Summary

A percentage is a rate per 100.

We can find percentages of \$10 using a double number line where 10 and 100% are aligned, as shown here:

 
A double number line for the dollar value of money: 0, 2.50,5.00, 7.50, 10.00, 12.50, 15.00 and percentages: 0, 25, 50, 75, 100, 125, 150.
 

Looking at the double number line, we can see that \$5.00 is 50% of \$10.00 and that \$12.50 is 125% of \$10.00.

Practice Problems ▶

Glossary

percent

percent

The word percent means “per 100” or “for each 100” and is usually written symbolically like this: %.

percentage

percentage

A percentage is a quantity described by a rate per 100.