### Unit 7: Percentages

We use percentages every day. For example, how about when your aunt's coffee shop advertised pumpkin spice lattes for 50% off – you and your aunt knew this meant **half off**, and so did the individuals in the ensuing rush of new customers. In this unit, we explore how to compute percentages. What does this mean, and how do we think about percentages more generally?

In this unit, we answer this question and lots of others that involve percentage computations and applications. For example, we will convert between percents and fractions or decimals and learn about percentage increases and decreases. We will also explore how to calculate some real-world uses, such as restaurant tips and sale prices.

**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.

### 7.1: Describing the Meaning of Percent

What is a percentage or a percent? One clue is in the name itself: per-cent. We frequently use the word per to compare or divide quantities, as in rates and ratios, and the leftover word cent means centum or one hundred in Latin. The term percent refers to a quantity expressed as a fraction (per) whose denominator is 100 (cent).

For example, we can write . We pronounce the percentage symbol, %, percent. Isn't it telling that it looks a lot like our division symbol ?

We see percentages all the time in the real world – frequently in sales at stores. During a sale, a store might mark their shirts 50% down so that a $20 shirt now costs $10. A week later, the store may announce customers can take an additional 20% off the sale price. How do you determine the new discounted price of the shirt? (Try it!)

Watch these videos to better understand how percents relate to fractions with a denominator of 100.

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

As we discussed above, a percentage is just a new name for our dear old friend the fraction. Of course, we can also write these friendly rationals in decimal notation. All of this tells us we can convert between all three forms of expression.

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

Read this text. Pay attention to the table on making conversions to a fraction, decimal, and a percent for an overview. Also pay close attention to the worked problems in Sample Set B. Complete the practice problems and check your answers.

### 7.3: Determine the Percent Given Two Numbers

It can be useful to express ratios or fraction information in terms of percentages. For example, let's say I have a class of 23 students, and 11 of them earned an A on a test. What percent of the class earned an A?

It is also useful to know how to reverse this process. When given percentage information, we may want to express it as fraction information. For example, if a pair of pants that normally costs $32 is on sale for 20% off, what is the new, actual price? Can you figure this out?Watch this video to see some worked examples. Many of these problems will show you how to set up and answer questions like the two examples presented above.

Complete this assessment to practice working with percents and check your answers.

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

Watch this video to see worked problems of these real-world applications and how percentages can help us understand the questions and examples mentioned just above.

Complete this assessment to practice calculating percent increases, decreases, and discounts. Be sure to check your answers.

Two more important applications of percents include sales tax and commision. When you purchase an item most states require you to pay a certain percent as sales tax (usually not listed on the item's price tag). How do you determine the real price you need to pay? For example, how much do you need to give the cashier to buy a $20.00 shirt with an 8% sales tax?

We calculate commissions in the same way. How about if you work at the store and your store manager has agreed to give you an 8% commission for your sale?

Watch this video for worked examples of these applications.Complete this assessment to practice calculating sales tax and commissions. Be sure to check your answers.