20.1: What Are Percentages?

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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.

Figure $\PageIndex{1}$: By United States Mint. Public Domain. United States Mint. Source.

Table $\PageIndex{1}$
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.

Figure $\PageIndex{2}$: 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.

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.

Figure $\PageIndex{7}$: 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.

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.

Table $\PageIndex{2}$
number of tacos	cost in dollars	rate in dollars per taco
$3$	$18$
$4$
$5$
$6$

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

(From Unit 3.3.3)

number of tacos	cost in dollars	rate in dollars per taco
\(3\)	\(18\)
\(4\)
\(5\)
\(6\)