8.5: Understanding Percent
Introduction
The Cereal Reorder
Kevin loves his new job at the supermarket. Most of the time he works at the cash register bagging groceries. On Thursdays, Kevin gets to help Ms. Thompson with the food order. Each week, Ms. Thompson has to inventory all of the food that has been sold and fill out a reorder form. Then she sends the form in to the main office so they know how many cases of food to reorder.
Last week Kevin worked with Ms. Thompson on the fruit order. This week, they are going to work on the cereal.
Ms. Thompson tells Kevin that the following amounts of cereal have been sold and will need to be reordered.
\begin{align*}\frac{3}{4}\end{align*}
\begin{align*}\frac{1}{2}\end{align*}
\begin{align*}\frac{1}{4}\end{align*}
After they have completed all of the order forms, Kyle has the task of filling in the sales report. The sales report asks for the amount of cereal boxes sold. It asks for the information in percents.
Kevin knows that he needs to convert each of the fractions to percents, only he can’t remember how to do it.
This is where you come in. Pay attention in this lesson and you will know how to help Kevin convert each fraction to a percent.
What You Will Learn
By the end of this lesson you will learn the following skills:
- Identify equivalent ratios as fractions, decimals and percents.
- Write percents as decimals.
- Write percents as fractions.
- Read and interpret circle graphs of real-world data.
Teaching Time
This lesson focuses on the concept of percents. You have probably heard the word percent before. Percents are used to represent many things or quantities that we see in everyday life. If the teacher says that only 15% of the students brought in their homework, that means something specific.
What is a percent?
A percent is a part of a whole.
Fractions are parts of a whole. Decimals are also parts of a whole. Fractions, decimals and percentages are all related because they are all parts of a whole.
A percent means “out of 100” so when we talk about a percent, we are talking about a part that is out of 100.
Just as we could write ratios in fraction form and ratios in decimal form, we can also write percents in ratio form. Because a percent is comparing a part to the whole of 100, a percent is also a ratio.
What does a percent look like?
A percent uses the sign %. When we see that sign it is the same as saying “out of 100.” If we should see 56%, that is the same as saying “56 out of 100”.
Practice writing percents. Write a percent for each of the following ratios.
- 67 out of 100
- 23 out of 100
- 10 out of 100
Take a minute to check your work with a neighbor.
Because they are all related, we can write equivalent fractions, decimals and percents using the same information.
Let’s look at an example.
Example
Write 14 out of 100 as a fraction, a decimal, and a percent.
First, let’s think about this as a fraction. Fourteen out of 100 means that we have a numerator of 14 and a denominator of 100.
\begin{align*}\frac{14}{100}\end{align*}
This is our fraction.
Next, we can write the decimal. Out of 100 refers to the decimal place “hundredths.” We learned when working with decimals that the hundredths place is two decimal places.
.14
This is our decimal.
Finally, we can write the percent. 14 out of 100 is equal to 14%.
14%
This is our percent.
We can write all three of these as equivalent ratios.
\begin{align*}\frac{14}{100}=.14=14\%\end{align*}
Complete this chart of equivalent ratios.
Check your work with a friend.
II. Write Percents as Decimals
Now that you understand how fractions, decimals and percents are related, we can look at the relationship between them in more detail. Let’s look at the relationship between decimals and percents first.
How are decimals and percents related?
Just as percents are out of 100, decimals can also be written out of 100. When we have a decimal with two decimal places, it is also representing a quantity out of 100.
.34 = 34%
These two quantities are equivalent. The decimal .34 means 34 hundredths or 34 out of 100. 34% means 34 out of 100.
Because decimals and percents are both parts of a whole, we can write percents as decimals.
How do we write percents as decimals?
We write a percent as a decimal by thinking “out of 100 means two decimal places.” You can drop the percent sign and move the decimal point two places to the left. Then the percent will be written as a decimal.
Let’s look at an example.
Example
45%
The % sign is just like two decimal places since both mean out of one hundred or hundredths. We drop the % sign and insert the decimal two decimal places to the left.
45% = .45
Our answer is .45.
Example
Write 15% as a decimal.
First, we drop the % sign and move the decimal point in two places to the left, to represent the hundredths place in the number.
15% becomes .15
Our answer is .15.
Example
Write 5% as a decimal
First, we drop the % sign and move the decimal point in two places. OOPS! This one doesn’t have two places. That’s okay, we can add a zero in for the missing place.
5% becomes .05
Our answer is .05.
Practice a few of these on your own. Write each percent as a decimal.
- 17%
- 25%
- 75%
Check your answers with a friend. Did you put the decimal point in the correct spot?
III. Write Percents as Fractions
A percent is also related to a fraction because they are both parts of a whole. Just like we could write percents as decimals, we can also write percents as fractions.
How do we write a percent as a fraction?
To write a percent as a fraction, we have to think of it as “out of 100” once again.
A fraction is a ratio comparing certain quantities. Six out of 10 would be written as six-tenths. The ten becomes our denominator.
We can use this information to write a percent as a fraction.
Let’s look at an example.
Example
Write 44% as a fraction.
44 % means 44 out of 100. 44 becomes the numerator and 100 becomes the denominator.
\begin{align*}44\%= \frac{44}{100}\end{align*}
Our answer is \begin{align*}\frac{44}{100}\end{align*}
What about when we have a percent that doesn’t have two places, like 7%?
To convert 7% to a fraction, you simply write it over 100. Because 7 percent means 7 out of 100.
Practice writing percents as fractions.
- 68%
- 13%
- 21%
Take a few minutes to check your work with a neighbor.
IV. Read and Interpret Circle Graphs of Real-World Data
A circle graph is a visual way of displaying data that is written in percents. The circle of a circle graph represents 100%. The parts of the whole that the items being graphed represent are shown in pie shaped wedges. Each wedge shows what part of 100 that item represents.
This is a graph of data about a student’s spending habits. You may remember seeing this circle graph in an earlier lesson. Here is the data on the graph.
Savings = 50%
Baseball Cards = 10%
Food = 40%
By looking at the circle graph, we can see that out of 100 % of his money, this student saves half (or 50%). He spends a small fraction on baseball cards and the rest is spent on food.
Notice that all three percents add up to 100%.
A circle graph shows information out of 100.
Real Life Example Completed
The Cereal Reorder
Now it’s time to help Kevin convert those fractions to percents. Here is the original problem once again. Reread the problem and underline all of the important information.
Kevin loves his new job at the supermarket. Most of the time he works at the cash register bagging groceries. On Thursdays, Kevin gets to help Ms. Thompson with the food order. Each week, Ms. Thompson has to inventory all of the food that has been sold and fill out a reorder form. Then she sends the form in to the main office so they know how many cases of food to reorder. Last week Kevin worked with Ms. Thompson on the fruit order. This week, they are going to work on the cereal. Ms. Thompson tells Kevin that the following amounts of cereal have been sold and will need to be reordered.
\begin{align*}\frac{3}{4}\end{align*}
\begin{align*}\frac{1}{2}\end{align*}
\begin{align*}\frac{1}{4}\end{align*}
After they have completed all of the order forms, Kyle has the task of filling in the sales report. The sales report asks for the amount of cereal boxes sold. It asks for the information in percents.
Kevin knows that he needs to convert each of the fractions to percents, only he can’t remember how to do it.
We can start to solve this problem by helping Kevin convert each of the fractions to a percent. We can do this by forming equal fractions to start.
We have three fractions to work with: \begin{align*}\frac{3}{4}\end{align*}
Let’s start with three-fourths. We can create three-fourths as an equal fraction out of 100.
\begin{align*}\frac{3}{4}=\frac{x}{100}\end{align*}
\begin{align*}\frac{3}{4}=\frac{75}{100}\end{align*}
Next we change the fraction to 75%.
Next we have one-half. We can do the same thing.
\begin{align*}\frac{1}{2}=\frac{50}{100}\end{align*}
Next we change the fraction to 50%.
We can do the same work with one-fourth.
\begin{align*}\frac{1}{4}=\frac{25}{100}\end{align*}
Our final percent is 25%.
With this help, Kevin can easily complete the sales report.
Vocabulary
Here are the vocabulary words that are found in this lesson.
- Percent
- means out of 100, it is a quantity written with a % sign, and is a part of a whole (100)
- Fraction
- a part of a whole, related to decimals and percents.
- Decimal
- a part of a whole shown by a decimal point, hundredths means two decimal places.
- Circle Graph
- a visual way of showing percents, a circle graph means 100. The entire circle represents 100 and each percent represents a quantity out of 100.
Technology Integration
Khan Academy, Percent and Decimals
James Sousa, Introduction to Percent
Other Videos:
http://www.mathplayground.com/howto_perfracdec.html – Converting fractions and decimals to percents
http://www.teachertube.com/members/viewVideo.php?video_id=141903 – This video compares fractions, decimals, and percents. You'll need to register at the site to view this video.
Time to Practice
Directions: Complete the chart of equivalent fractions, decimals and percents.
Directions: Write each percent as a decimal.
14. 54%
15. 11%
16. 6%
17. 12%
18. 89%
19. 83%
20. 19%
21. 4%
22. 9% Directions: For questions 23 - 31, take the percents in numbers 14 – 22 and write them as fractions.
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