Lesson 10What Are Percentages?

Let’s learn about percentages.

Learning Targets:

  • I can create a double number line with percentages on one line and dollar amounts on the other line.
  • I can explain the meaning of percentages using dollars and cents as an example.

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 images” via the United States Mint. Public Domain.
    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. 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?

Are you ready for more?

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.
“Coin images” via the United States Mint. Public Domain.

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?

Lesson 10 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 Terms

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.

“Coin images” via the United States Mint. Public Domain.
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.
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 with 5 evenly spaced tick marks. The top number line is labeled “volume, in liters” and starting with the first tick mark, 0, 9, 18, 27, and 36 are labeled. The bottom number line is not labeled and starting with the first tick mark 0, 25 percent, 50 percent, 75 percent, and 100 percent are labeled.

Lesson 10 Practice Problems

  1. What percentage of a dollar is the value of each coin combination?

    1. 4 dimes
    2. 1 nickel and 3 pennies
    3. 5 quarters and 1 dime
    1. List three different combinations of coins, each with a value of 30% of a dollar.

    2. List two different combinations of coins, each with a value of 140% of a dollar.

  2. The United States government used to make coins of many different values. For each coin, state its worth as a percentage of $1.

    “Coin images” via the United States Mint. Public Domain.

     
    1. \frac{1}{2} cent
    2. 3 cents
    1. 20 cents
    2. $2 \frac{1}{2}
    1. $5
  3. Complete the double number to line show percentages of $50.

  4. Elena bought 8 tokens for $4.40. At this rate:

    1. How many tokens could she buy with $6.05?
    2. How much do 19 tokens cost?
  5. A snail travels 10 cm in 4 minutes. At this rate:

    1. How long will it take the snail to travel 24 cm?
    2. How far does the snail travel in 6 minutes?
    1. 3 tacos cost $18. Complete the table to show the cost of 4, 5, and 6 tacos at the same rate.
      number of tacos cost in dollars rate in dollars per taco
      3 18
      4
      5
      6

      b. If you buy t tacos for c dollars, what is the unit rate?