Lesson 15

Finding This Percent of That

Let’s solve percentage problems like a pro.

15.1: Number Talk: Decimals

Find the value of each expression mentally.

$$(0.23) \boldcdot 100$$

$$50 \div 100$$

$$145 \boldcdot \frac{1}{100}$$

$$7 \div 100$$

15.2: Audience Size

A school held several evening activities last month—a music concert, a basketball game, a drama play, and literacy night. The music concert was attended by 250 people. How many people came to each of the other activities?

1. Attendance at a basketball game was 30% of attendance at the concert.
2. Attendance at the drama play was 140% of attendance at the concert.
3. Attendance at literacy night was 44% of attendance at the concert.

50% of the people who attended the drama play also attended the music concert. What percentage of the people who attended the music concert also attended the drama play?

15.3: Everything is On Sale

During a sale, every item in a store is 80% of its regular price.

1. If the regular price of a T-shirt is $10, what is its sale price? 2. The regular prices of five items are shown here. Find the sale price of each item. item 1 item 2 item 3 item 4 item 5 regular price$1 $4$10 $55$120
sale price
3. You found 80% of many values. Was there a process you repeated over and over to find the sale prices? If so, describe it.

4. Select all of the expressions that could be used to find 80% of $$x$$. Be prepared to explain your reasoning.

$$\frac{8}{100} \boldcdot x$$

$$\frac{80}{100} \boldcdot x$$

$$\frac{8}{10} \boldcdot x$$

$$\frac{4}{10} \boldcdot x$$

$$\frac85 \boldcdot x$$

$$\frac45 \boldcdot x$$

$$80 \boldcdot x$$

$$8 \boldcdot x$$

$$(0.8) \boldcdot x$$

$$(0.08) \boldcdot x$$

Summary

To find 49% of a number, we can multiply the number by $$\frac{49}{100}$$ or 0.49.

To find 135% of a number, we can multiply the number by $$\frac{135}{100}$$ or 1.35.

To find 6% of a number, we can multiply the number by $$\frac{6}{100}$$ or 0.06.

In general, to find $$P\%$$ of $$x$$, we can multiply: $$\displaystyle \frac{P}{100} \boldcdot x$$

Glossary Entries

• percent

The word percent means “for each 100.” The symbol for percent is %.

For example, a quarter is worth 25 cents, and a dollar is worth 100 cents. We can say that a quarter is worth 25% of a dollar.

• percentage

A percentage is a rate per 100.

For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.