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5.3: Write Percents as Fractions

Difficulty Level: At Grade Created by: CK-12
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Have you ever known a high school team to make the play-offs? Take a look at this dilemma.

The local high school’s football season has just ended. At lunch, Carla, Mario and Cinda spent some time talking about the season and how the Springstead Raiders had finally made the play-offs.

“I love football season. Those Friday night games are so much fun!” Mario said biting into his sandwich.

“Definitely, and we did so much better this year than last year. This year we won 10 out of 12 games. Last year, we only won eight out of 12 games,” Carla said.

“Yes, so this year the percentage of games that we won definitely increased,” Cinda commented.

“Well that is obvious,” Mario said. “What was last year’s percentage compared to this year’s?”

“To figure that out, we have to change the fraction of games that we won to a percentage and we have to do that with both last year’s statistics and this year’s statistics,” Carla explained.

Carla is on the right track. To understand the percentage of wins, you need to know how to convert fractions to percentages. This Concept is all about fractions, decimals and percentages and how to work with them. You will also see how proportions can be very helpful when doing this work. Pay attention and you will be able to use what you have learned at the end of the Concept.

Guidance

Percents can be written as ratios with a denominator of 100 or they can be written as decimals. Well, if they can be written as a ratio with a denominator of 100, then those ratios can be simplified as we would simplify any fraction. Likewise, any fraction can be written as a percent using reverse operations.

To write a percent as a fraction rewrite it as a fraction with a denominator of 100. Then reduce the fraction to its simplest form.

Write 22% as a fraction.

First, write this as a fraction with a dominator of 100.

\begin{align*}22\% = \frac{22}{100}\end{align*}

Next, simplify the fraction.

\begin{align*}\frac{22}{100} = \frac{11}{50}\end{align*}

How can we convert a fraction to a percent?

To convert a fraction to a percent, we need to be sure that the fraction is being compared to a quantity of 100. Let’s look at one.

\begin{align*}\frac{28}{100}\end{align*}

This means that we have 28 out of 100. This fraction is being compared to 100, so we can simply change it to a percent.

\begin{align*}\frac{28}{100} = 28\%\end{align*}

Here is another one.

\begin{align*}\frac{3}{5}\end{align*}

This fraction is not being compared to 100. It is being compared to 5. We have three out of 5. To convert this fraction to a percent, we need to rewrite it as an equal ratio out of 100. We can use proportions to do this.

First, write this ratio compared to a second ratio out of 100.

\begin{align*}\frac{3}{5} = \frac{\boxed{}}{100}\end{align*}

We don’t know what the part out of 100 is, so we need to solve the proportion. We can use multiplication to create equal ratios or a proportion.

\begin{align*}5 \times 20 &= 100\\ 3 \times 20 &= 60\\ \frac{3}{5} &= \frac{60}{100} = 60 \%\end{align*}

Write each example as a percent.

Example A

\begin{align*}\frac{44}{100}\end{align*}

Solution:  \begin{align*}44\%\end{align*}

Example B

\begin{align*}\frac{1}{2}\end{align*}

Solution:  \begin{align*}50\%\end{align*}

Example C

\begin{align*}\frac{4}{5}\end{align*}

Solution:  \begin{align*}80\%\end{align*}

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

First, let’s write two fractions to represent the given data for games won last year and this year by the football team.

Last year: 8 out of 12 games were won.

\begin{align*}\frac{8}{12}\end{align*}

This year: 10 out of 12 games were won.

\begin{align*}\frac{10}{12}\end{align*}

Now we can take these two fractions and create proportions to determine the correct percent of games won.

\begin{align*}\frac{8}{12} = \frac{x}{100}\end{align*}

Next, we cross multiply and solve for the percent.

\begin{align*}12x = 800\end{align*}

\begin{align*}x = 66.6\%\end{align*} or 67% is last year’s percentage of games won.

Now let’s figure out this year’s scores.

\begin{align*}\frac{10}{12} &= \frac{x}{100}\\ 12x &= 1000\end{align*}

\begin{align*}x = 83.3\%\end{align*} or 83% of this year’s games were won.

Vocabulary

Ratio
a comparison between two quantities.
Percent
a ratio that is being compared to the quantity of 100. Percent means out of 100.
Fraction
a part of a whole written using a numerator and a denominator.
Decimal
a part of a whole written in base ten place value.
Proportion
two equal ratios form a proportion.

Guided Practice

Here is one for you to try on your own.

Kary's baseball team won 9 out of 12 games. What percent of the games played did the team win? What percent did of the games played did the team lose?

Solution

First, write the number of games won as a fraction.

\begin{align*}\frac{9}{12}\end{align*}

Next, write this as a proportion with a denominator of 100.

\begin{align*}\frac{9}{12} = \frac{x}{100}\end{align*}

Now cross-multiply and solve for \begin{align*}x\end{align*}.

\begin{align*}75\%\end{align*}

The team won 75% of their games.

Since we know that a percent is out of 100, we can simply figure out the percent that the team lost by using subtraction.

\begin{align*}100 - 75 = 25\end{align*}

The team lost \begin{align*}25\%\end{align*} of their games.

Practice

Write the following percents as fractions in simplest form.

1. 16%
2. 40%
3. 2%
4. 4%
5. 45%
6. 20%
7. 18%
8. 10%

Write the following fractions as percents. Round when necessary.

1. \begin{align*}\frac{2}{3}\end{align*}
2. \begin{align*}\frac{23}{30}\end{align*}
3. \begin{align*}\frac{4}{75}\end{align*}
4. \begin{align*}\frac{21}{2}\end{align*}
5. \begin{align*}\frac{4}{5}\end{align*}
6. \begin{align*}\frac{6}{10}\end{align*}
7. \begin{align*}\frac{3}{25}\end{align*}

Vocabulary Language: English

Decimal

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

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

Percent means out of 100. It is a quantity written with a % sign.
Proportion

Proportion

A proportion is an equation that shows two equivalent ratios.

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Date Created:
Jan 23, 2013