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 dramatic 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 dramatic play was 140% of attendance at the concert.
  1. Attendance at literacy night was 44% of attendance at the concert.

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
    row 1 regular price \$1 \$4 \$10 \$55 \$120
    row 2 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. Which of the following expressions 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.

A triple number line with 5 tick marks. For the top number line, starting with the first tick mark, the numbers 0, the fraction 6 over 100, end fraction, times x, the fraction 49 over 100, end fraction, times x, x, and the fraction 135 over 100, end fraction, times x, are labeled. For the middle number line, starting with the first tick mark, the numbers 0, 0 point 0 6, times x, 0 point 4 9, times x, x, and 1 point 3 5, times x are labeled. For the bottom number line, starting with the first tick mark, the numbers 0, 6 percent, 49 percent, 100 percent, and 135 percent are labeled.

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

Practice Problems ▶