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Illustrative Math
Grade 6
Lesson 15: Finding This Percent of That
Let’s solve percentage problems like a pro.
Illustrative Math Unit 6.3, Lesson 15 (printable worksheets)
Lesson 15 Summary
The following diagram shows how to find the percent of a number.
Lesson 15.1 Number Talk: Decimals
Find the value of each expression mentally.
(0.23) · 100
50 ÷ 100
145 · 1/100
7 ÷ 100
Scroll down the page for the answer to the “Are you ready for more?” section.
Lesson 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.
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?

Show Answer
From lesson 5.2, we know that 350 people attended the drama play.
50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.
From lesson 5.2, we know that 250 people attended the music concert.
The percentage of the people who attended the music concert also attended the drama play would be 175 ÷ 250 · 100% = 70%
Lesson 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      
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 the expressions that could be used to find 80% of x. Be prepared to explain your reasoning.
Lesson 15 Practice Problems
 a. To find 40% of 75, Priya calculates ⅖ · 75. Does her calculation give the correct value for 40% of 75? Explain or show how you know.
b. If x represents a number, does ⅖ · 75 always represent 40% of that number? Explain your reasoning.
 Han spent 75 minutes practicing the piano over the weekend. For each question, explain or show your reasoning.
a. Priya practiced the violin for 152% as much time as Han practiced the piano. How long did she practice?
b. Tyler practiced the clarinet for 64% as much time as Han practiced the piano. How long did he practice?
 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.
 Order from greatest to least:
 55% of 180
 300% of 26
 12% of 700
 Complete each statement.
a. 20% of 60 is ________
b. 25% of ________ is 6
c. ________% of 100 is 14
d. 50% of 90 is ________
e. 10% of ________ is 7
f. 30% of 70 is ________
 A shopper needs 24 sandwich rolls. The store sells identical rolls in 2 differently sized packages. They sell a sixpack for $5.28 and a fourpack for $3.40. Should the shopper buy 4 sixpacks or 6 fourpacks? Explain your reasoning.
 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.
a. How many chaperones are there?
b. How many children are there?
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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