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Lesson 15Finding This Percent of That

Let’s solve percentage problems like a pro.

Learning Targets:

  • I can solve different problems like “What is 40% of 60?” by dividing and multiplying.

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

Are you ready for more?

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.

    An diagram showing how to find 80 percent of a number

  4. Select all 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

Lesson 15 Summary

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

An diagram showing how to find 49 percent of a number

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

Lesson 15 Practice Problems

    1. To find 40% of 75, Priya calculates \frac{2}{5} \boldcdot 75 . Does her calculation give the correct value for 40% of 75? Explain or show how you know.
    2. If x represents a number, does \frac{2}{5} \boldcdot x always represent 40% of that number? Explain your reasoning.

  2. Han spent 75 minutes practicing the piano over the weekend. For each question, explain or show your reasoning.

    1. Priya practiced the violin for 152% as much time as Han practiced the piano. How long did she practice?
    1. Tyler practiced the clarinet for 64% as much time as Han practiced the piano. How long did he practice?
  3. Last Sunday 1,575 people visited the amusement park. 56% of the visitors were adults, 16% were teenagers, and 28% were children ages 12 and under. Find the number of adults, teenagers, and children that visited the park.

  4. Order from greatest to least:

    • 55% of 180
    • 300% of 26
    • 12% of 700

  5. Complete each statement.

    1. 20% of 60 is ________
    2. 25% of ________ is 6
    3. ________% of 100 is 14
    1. 50% of 90 is ________
    2. 10% of ________ is 7
    3. 30% of 70 is ________

  6. A shopper needs 24 sandwich rolls. The store sells identical rolls in 2 differently sized packages. They sell a six-pack for $5.28 and a four-pack for $3.40. Should the shopper buy 4 six-packs or 6 four-packs? Explain your reasoning.

  7. On a field trip, there are 3 chaperones for every 20 students. There are 92 people on the trip. Answer these questions. If you get stuck, consider using a tape diagram.

    1. How many chaperones are there?
    2. How many children are there?