20.1: What Are Percentages?
Lesson
Let's learn about percentages.
Exercise \(\PageIndex{1}\): 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?
Exercise \(\PageIndex{2}\): Coins
- 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.
-
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?
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.
Exercise \(\PageIndex{3}\): Coins on a Number Line
A $1 coin is worth 100% of the value of a dollar. Here is a double number line that shows this.
- 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:
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
Definition: 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.
Definition: 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%.
Practice
Exercise \(\PageIndex{4}\)
What percentage of a dollar is the value of each coin combination?
- \(4\) dimes
- \(1\) nickel and \(3\) pennies
- \(5\) quarters and \(1\) dime
Exercise \(\PageIndex{5}\)
- List three different combinations of coins, each with a value of 30% of a dollar.
- List two different combinations of coins, each with a value of 140% of a dollar.
Exercise \(\PageIndex{6}\)
The United States government used to make coins of many different values. For each coin, state its worth as a percentage of $1.
\(\frac{1}{2}\text{ cent }\qquad 3\text{ cents }\qquad 20\text{ cents }\qquad $2\frac{1}{2}\qquad $5\)
Exercise \(\PageIndex{7}\)
Complete the double number to line show percentages of $50.
Exercise \(\PageIndex{8}\)
Elena bought 8 tokens for $4.40. At this rate:
- How many tokens could she buy with $6.05?
- How much do 19 tokens cost?
(From Unit 3.3.5)
Exercise \(\PageIndex{9}\)
A snail travels 10 cm in 4 minutes. At this rate:
- How long will it take the snail to travel 24 cm?
- How far does the snail travel in 6 minutes?
(From Unit 3.3.4)
Exercise \(\PageIndex{10}\)
-
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 \(3\) \(18\) \(4\) \(5\) \(6\) Table \(\PageIndex{2}\) - If you buy \(t\) tacos for \(c\) dollars, what is the unit rate?
(From Unit 3.3.3)