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.

    ​

    coin penny nickel dime quarter half dollar dollar
    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.

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

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


Find two different sets of coins that each make 120% of a dollar, where no type of coin is in both sets.

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.

Double number line, 7 evenly spaced tick marks. Top line, value of coins, dollars. Beginning at first tick mark, labels: 0, blank, blank, blank, 1, blank, blank. Bottom line, percent. Scale 0 to 150, by 25’s.
  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)?
  3. 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.

Glossary Entries

  • percent

    The word percent means “for each 100.” The symbol for percent is %.

    For example, a quarter is worth 25 cents, and a dollar is worth 100 cents. We can say that a quarter is worth 25% of a dollar.

    A quarter (coin)
    A diagram of two bars with different lengths.
  • percentage

    A percentage is a rate per 100.

    For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.

    a double number line