### Unit 6: Percentages

Now that we have studied fractions and decimals, we are ready to explore percents. Percents are just fractions and decimals written in a different way. For example, we can describe one half in many ways: 0.5 as a decimal, 1/2 as a fraction, and 50% as a percent. These all mean the same thing!

We see percents all the time in the real world, especially in sales at stores. For example, a store might advertise that it is selling clothing at 50% off. So, a $10 shirt would be reduced to $5. A week later, the store may post a sign saying that there is an additional 20% off the sale price of the shirts. How do we determine the new discounted price of the shirt?

We will learn how to answer that question in this unit. We will also convert between percents and fractions or decimals, and learn about percentage increases and decreases. We will explore how to calculate percents in scenarios that you will see in the real world, such as calculating tips at a restaurant or sale prices at a store.

**Completing this unit should take you approximately 2 hours.**

Upon successful completion of this unit, you will be able to:

- identify the components of a percent problem;
- convert between percent, decimal, and/or fraction notation;
- use proportional relationships to solve multi-step percent problems; and
- apply percent concepts in practical applications.

### 6.1: Describing the Meaning of Percent

We first need to learn what percents are and how we write them using the % symbol. Percents are essentially a ratio of a number to 100. We can think of percents as fractions with a denominator of 100. For example, we can say that 15/100 is 15%.

Watch these videos to see how percents are related to fractions with a denominator of 100.

### 6.2: Converting Between Decimals, Fractions, and Percents

As we saw in the first section, percents are related to fractions. We know from Unit 4 that fractions can be written as decimals. Therefore, we can write percents as decimals as well.

Watch these two videos for worked examples of how to do conversions with percents.

Read this section and pay attention to the table that shows how to convert percents to fractions and decimals. Also pay close attention to the problems in Sample Set B. Then, try Practice Set B and check your answers.

### 6.3: Determine the Percent Given Two Numbers

Often we need to calculate percents with real numbers.

For example, let's say I have a class of 23 students, and 11 of them got an A on a test. What percent of my class earned an A on that test? We can also determine real numbers from percent information. For example, if a pair of pants costing $32 is on sale for 20% off, how much are the pants with the sale price? We can calculate these types of problems using math techniques we have already learned in this course.

Watch this video for examples of how to determine percents from real numbers. This video also shows examples of determining real numbers from percents.

After you watch the video, do this assignment to practice these types of problems. Check your answers by looking at the solutions at the end of the document.

### 6.4: Percent Increase or Decrease and Other Percent Applications

One important application of percents is calculating percent increases and decreases. This comes up in many applications. One example of a percent decrease is determining sale prices. An example of percent increases is getting a raise on your salary. Other important applications of percents are sales tax and commission. When you buy something in the United States, you often pay a certain percent as sales tax that is not listed on the price of the item. How do you determine the actual price you will pay?

Watch this video to see some examples of real-world applications of percents.

After you watch the video, do this assignment. Check your answers at the end of the document.

Watch this video to see examples of these important applications.

After you watch the video, do this assignment. Check your answers at the end of the document.