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Write percents as ratios and ratios as percents

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Recognize and Write Percents

Have you ever tried to figure out scores for a football team? Take a look at this dilemma.

Carla knows that the Springstead Raiders, the high school football team won 80% of their games this year. She is wondering how to understand that percent.

What is a percent? Do you know?

This Concept will help you to understand percents so that you will be able to help Carla by the end of the Concept.


We see percents all around us every day. If you walk into a store of any kind, you will often see a percent sign. Whether it is a sale sign for 10% off or a sign on a bank for a new mortgage rate, by looking all around you, you will see percents.

What is a percent?

Simply, a percent is a part of a whole.

It is a part of a whole that is being compared to 100. In this way, we can also think of a percent as a ratio. Remember that a ratio is a comparison between two quantities.

Fractions and decimals are also parts of a whole.

We can say that fractions, decimals and percents are all related.

Let’s think about percents in a little more detail.

Look at the word “percent.” Its root “cent” means one hundred and “per” implies division or means “for each.” If you have three candies per person, it means three candies for each person. So “percent” means one for every one hundred.

If 25% of the people want chocolate cake, then 25 out of every 100 want chocolate cake. For this reason, percent can be written as a fraction with the denominator being 100.

\begin{align*}25\% = \frac{25}{100}\end{align*}

Now think about this again. Anytime you see a percent, you know that the amount is being compared to 100, or is “out of” 100.

18% means 18 out of 100

We are comparing the quantity of 18 to the whole of 100.

125% means 125 out of 100

Here we have a percent that is greater than 100. This means that we have greater than the total whole included in our percent.

That’s a great question. It is possible because we are thinking about what’s possible not the actual number. It is possible to have 100 percent on a test. However, if there are bonus questions, then you could also have greater than 100 percent. Sales is like this too. If a car salesman needs to sell 5 cars in a week that is 100 percent for him. However, if he sells 8 cars, then he sold greater than 100%.

Remember that a percent is a ratio compared to 100! Write this down in your notebook.

Write each example as a percent.

Example A

23 out of 100

Solution: 23%

Example B

18.5 out of 100

Solution: 18.5%

Example C

97 out of 100

Solution: 97%

Now let's go back to the dilemma from the beginning of the Concept.

If the team won 80% of their games, then Carla can think of this as out of 100. It means that the team won 80 out of 100 games. If the team did not play 100 games, then you can get an idea of how they did by simplifying the ratio.

Take a look at the ratio now.

\begin{align*}80\% = \frac{80}{100} = \frac{8}{10}\end{align*}

This means that the team won 8 out of 10 games. A pretty great season!

Guided Practice

Here is one for you to try on your own.

Write this as a percent.

Carmen saw 100 movies in one year. She chose 60 of the movies as her favorites. The other 40 movies were not her favorites. Write her favorites as a percent and the other movies as a percent too.


To start, let's write the favorites as a percent.

Carmen chose 60 out of 100 as favorites.


Carmen did not choose 40 movies as favorites.


This is our answer.

Video Review

An Introduction to Percents

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Directions: Write the following percents as a ratio with a denominator of 100.

  1. 64%
  2. 3%
  3. 119%
  4. 4.7%
  5. 88%
  6. 99.5%
  7. 12%
  8. 14%

Directions: Write the following as percents.

  1. 12 out of 100
  2. 13.5 out of 100
  3. 87 out of 100
  4. 99 out of 100
  5. 5 out of 100
  6. 3.5 out of 100
  7. 130 out of 100
  8. 175 out of 100

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Decimal In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
fraction A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.
Percent Percent means out of 100. It is a quantity written with a % sign.

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