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?
 Attendance at a basketball game was 30% of attendance at the concert.
 Attendance at the drama play was 140% of attendance at the concert.
 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.
 If the regular price of a Tshirt is $10, what is its sale price?
 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 
You found 80% of many values. Was there a process you repeated over and over to find the sale prices? If so, describe it.

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%.