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Conversion of Decimals, Fractions, and Percent

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Have you ever had a job that you loved? Take a look at this dilemma.

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.

\frac{3}{4} of the corn flakes

\frac{1}{2} of the granola

\frac{1}{4} of the rice cereal

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 a percent, only he can’t remember how to do it.

This is where you come in. Pay attention in this Concept and you will know how to help Kevin convert each fraction to a percent.

Guidance

This Concept focuses on 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”.

Because they are all related, we can write equivalent fractions, decimals and percents using the same information.

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.

\frac{14}{100}

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.

\frac{14}{100}=.14=14\%

Complete this chart of equivalent ratios.

Practice writing percents. Write a percent for each of the following ratios.

Example A

67 out of 100

Solution: 67\%

Example B

23 out of 100

Solution: 23\%

Example C

10 out of 100

Solution: 10\%

Now it’s time to help Kevin convert those fractions to percents. Here is the original problem once again.

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.

\frac{3}{4} of the corn flakes

\frac{1}{2} of the granola

\frac{1}{4} of the rice cereal

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: \frac{3}{4} , \frac{1}{2} , \frac{1}{4}

Let’s start with three-fourths. We can create three-fourths as an equal fraction out of 100.

\frac{3}{4}=\frac{x}{100}

\frac{3}{4}=\frac{75}{100}

Next we change the fraction to 75%.

Next we have one-half. We can do the same thing.

\frac{1}{2}=\frac{50}{100}

Next we change the fraction to 50%.

We can do the same work with one-fourth.

\frac{1}{4}=\frac{25}{100}

Our final percent is 25%.

With this help, Kevin can easily complete the sales report.

Vocabulary

Here are the vocabulary words in this Concept.

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.

Guided Practice

Here is one for you to try on your own.

Write the following as a fraction, decimal and percent.

18 out of 100

Answer

 \frac{18}{100}

.18

18\%

Video Review

Here are videos for review.

Khan Academy, Percent and Decimals

James Sousa, Introduction to Percent

Explore More

Directions: Complete the chart of equivalent fractions, decimals and percents.

14. Write .12 as a percent.

15. Write 15 out of 100 as a percent.

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