Illustrative Mathematics Unit 6.4, Lesson 9: How Much in Each Group? (Part 2)

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Illustrative Math
Grade 6

Lesson 9: How Much in Each Group? (Part 2)

Let’s practice dividing fractions in different situations.

Illustrative Math Unit 6.4, Lesson 9 (printable worksheets)

Lesson 9 Summary

The following example shows how to use diagrams and multiplication and division equations to find the amount in one group.

Lesson 9.1 Number Talk: Greater Than 1 or Less Than 1?

Decide whether each of the following is greater than 1 or less than 1.

1. ½ ÷ ¼
   
2. 1 ÷ ¾
   
3. ⅔ ÷ ⅞
   
4. 2⅞ ÷ 2⅗
   

• See Video for Whole Lesson

Lesson 9.2 Two Water Containers

• Show Water Containers

  

1. After looking at these pictures, Lin says, “I see the fraction ⅖.” Jada says, “I see the fraction ¾.” What quantities are Lin and Jada referring to?
2. How many liters of water fit in the water dispenser?
   Write a multiplication equation and a division equation for the question, then find the answer. Draw a diagram, if needed. Check your answer using the multiplication equation.

Lesson 9.3 Amount in One Group

Write a multiplication equation and a division equation and draw a diagram to represent each situation and question. Then find the answer. Explain your reasoning.

1. Jada bought 3½ yards of fabric for $21. How much did each yard cost?
2. 4/9 kilogram of baking soda costs $2. How much does 1 kilogram of baking soda cost?
3. Diego can fill 1⅕ bottles with 3 liters of water. How many liters of water fill 1 bottle?
4. 5/4 gallons of water fill 5/6 of a bucket. How many gallons of water fill the entire bucket?
   

Are you ready for more?

The largest sandwich ever made weighed 5,440 pounds. If everyone on Earth shares the sandwich equally, how much would you get? What fraction of a regular sandwich does this represent?

Lesson 9 Practice Problems

1. A group of friends is sharing 3½ pounds of berries.
   a. If each friend received 5/4 of a pound of berries, how many friends are sharing the berries?
   b. If 5 friends are sharing the berries, how many pounds of berries does each friend receive?
   b. Priya has picked 1½ cups of raspberries, which is enough for ¾ of a cake. How many cups does she need for the whole cake?
   
2. ⅔ kilogram of soil fills ⅓ of a container. Can 1 kilogram of soil fit in the container? Explain or show your reasoning.
   
3. After raining for ¾ of an hour, a rain gauge is ⅖ filled. If it continues to rain at that rate for 15 more minutes, what fraction of the rain gauge will be filled?
   a. To help answer this question, Diego wrote the division equation ¾ ÷ ⅕. Explain why this equation does not represent the situation.
   b. Write a multiplication equation and a division equation that does represent the situation.
   
4. 3 tickets to the museum cost $12.75. At this rate, what is the cost of:
   a. 1 ticket?
   b. 5 tickets?
   
5. Elena went 60 meters in 15 seconds. Noah went 50 meters in 10 seconds. Elena and Noah both moved at a constant speed.
   a. How far did Elena go in 1 second?
   b. How far did Noah go in 1 second?
   c. Who went faster? Explain or show your reasoning.
   
6. The first row in the table shows a recipe for 1 batch of trail mix. Complete the remaining rows with recipes for 2, 3, and 4 batches of the same type of trail mix.
   

number of batches	cups of cereal	cups of almonds	cups of raisins
1
2
3
4

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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