Lesson 10
What Are Percentages?
Let’s learn about percentages.
10.1: Dollars and Cents
Find each answer mentally.
- A sticker costs 25 cents. How many dollars is that?
- A pen costs 1.50 dollars. How many cents is that?
- How many cents are in one dollar?
- How many dollars are in one cent?
10.2: Coins
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Complete the table to show the values of these U.S. coins.
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.
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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
- The value of 6 dimes is what percent of the value of a dollar?
- 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.](https://staging-cms-im.s3.amazonaws.com/mM6Ng7dHxbqT7mrySbR4KfeQ?response-content-disposition=inline%3B%20filename%3D%226-6.3.D1_Image_3.2.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.D1_Image_3.2.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T074652Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=08a38ac2cde35d39e1a434746a72cfb7af6c74e45533ff97a22493ba5efe2cda)
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.](https://staging-cms-im.s3.amazonaws.com/1FgEv52oRmRLrQD9UD9pn6vd?response-content-disposition=inline%3B%20filename%3D%226-6.3.D1_Image_12.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.D1_Image_12.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T074652Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3052c5c9c2780793484d38c4c49f7b72ac524c545e4f49f12c04ab19251710e3)
- The coins in Jada’s pocket are worth 75% of a dollar. How much are they worth (in dollars)?
- The coins in Diego’s pocket are worth 150% of a dollar. How much are they worth (in dollars)?
- 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.](https://staging-cms-im.s3.amazonaws.com/6AukNWRRRXqjd8nmMyBA3EH7?response-content-disposition=inline%3B%20filename%3D%226-6.3.D1_Image_15.png%22%3B%20filename%2A%3DUTF-8%27%276-6.3.D1_Image_15.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T074652Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7e01705b3c96b3081a1602f5241824e39935b011906e84574369a2b21a96c9bb)
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.
- 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%.