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.

    Two equivalent tape diagrams, each partitioned the same.  The top diagram is labeled 100%, partition labeled 80%.  The bottom diagram is labeled x, partition labeled with a question mark.

  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.

Two tape diagrams, each partitioned once in the same place. Top diagram labeled 100% with the partition labeled 49%. Bottom diagram labeled x with the partition labeled point 49 x.

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.

A triple number line.

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.

    A quarter (coin)
    A diagram of two bars with different lengths.
  • 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%.

    a double number line