Illustrative Mathematics Unit 6.3, Lesson 16: Finding the Percentage

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Illustrative Math
Grade 6

Lesson 16: Finding the Percentage

Let’s find percentages in general.

Illustrative Math Unit 6.3, Lesson 16 (printable worksheets)

Lesson 16 Summary

The following diagram shows how to find the percent of a number.

Lesson 16.1 True or False: Percentages

Is each statement true or false? Be prepared to explain your reasoning.

1. 25% of 512 is equal to &frac14 · 512.
   
2. 90% of 133 is equal to (0.9) · 133.
   
3. 30% of 44 is equal to 3% of 440.
   
4. The percentage 21 is of 28 is equal to the percentage 30 is of 40.
   

• See Video for Whole Lesson

Scroll down the page for the answer to the “Are you ready for more?” section.

Lesson 16.2 Jumping Rope

A school held a jump-roping contest. Diego jumped rope for 20 minutes.

1. Jada jumped rope for 15 minutes. What percentage of Diego’s time is that?
2. Lin jumped rope for 24 minutes. What percentage of Diego’s time is that?
3. Noah jumped rope for 9 minutes. What percentage of Diego’s time is that?
4. Record your answers in this table. Write the quotients in the last column as decimals.
   

	time (minutes)	percentage	time ÷ 20
Diego	20	100	20/20 = 1
Jada	15		15/20 =
Lin	24		24/20 =
Noah	9		9/20 =

5. What do you notice about the numbers in the last two columns of the table?

Lesson 16.3 - Restaurant Capacity

A restaurant has a sign by the front door that says, “Maximum occupancy: 75 people.” Answer each question and explain or show your reasoning.

1. What percentage of its capacity is 9 people?
2. What percentage of its capacity is 51 people?
3. What percentage of its capacity is 84 people?

Are you ready for more?

Water makes up about 71% of the Earth’s surface, while the other 29% consists of continents and islands. 96% of all the Earth’s water is contained within the oceans as salt water, while the remaining 4% is fresh water located in lakes, rivers, glaciers, and the polar ice caps.
If the total volume of water on Earth is 1,386 million cubic kilometers, what is the volume of salt water? What is the volume of fresh water?

• Show Answer

  Volume of salt water is 0.96 · 1,386 = 1330.56 million cubic kilometers.
  Volume of fresh water is 1,386 - 1330.56 = 55.44 million cubic kilometers.

Lesson 16 Practice Problems

1. A sign in front of a roller coaster says “You must be 40 inches tall to ride.” What percentage of this height is:
   a. 34 inches?
   b. 54 inches?
   
2. At a hardware store, a tool set normally costs $80. During a sale this week, the tool set costs $12 less than usual. What percentage of the usual price is the savings? Explain or show your reasoning.
   
3. A bathtub can hold 80 gallons of water. The faucet flows at a rate of 4 gallons per minute. What percentage of the tub will be filled after 6 minutes?
   
4. The sale price of every item in a store is 85% of its usual price.
   a. The usual price of a backpack is $30, what is its sale price?
   b. The usual price of a sweatshirt is $18, what is its sale price?
   c. The usual price of a soccer ball is $24.80, what is its sale price?
   
5. A shopper needs 48 hot dogs. The store sells identical hot dogs in 2 differently sized packages. They sell a six-pack of hot dogs for $2.10, and an eight-pack of hot dogs for $3.12. Should the shopper buy 8 six-packs, or 6 eight-packs? Explain your reasoning.
   
6. Elena is 56 inches tall.
   a. What is her height in centimeters? (Note: 100 inches = 254 centimeters)
   b. What is her height in meters?
   

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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