Lesson 5
How Many Groups? (Part 2)
Problem 1
Use the tape diagram to find the value of \(\frac12\div\frac13\). Show your reasoning.
![A tape diagram.](https://cms-im.s3.amazonaws.com/7XLbpxP4oNv4Cbsd1CXhBGxM?response-content-disposition=inline%3B%20filename%3D%226-6.4.PP.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%276-6.4.PP.Image.07.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T035645Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=db242e31f72a5b245eebeebd6d1bd5e03ddff3f7160b4f7825d2f4d9d8ed3b92)
Solution
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Problem 2
What is the value of \(\frac12\div\frac13\)? Use pattern blocks to represent and find this value. The yellow hexagon represents 1 whole. Explain or show your reasoning.
![Four pattern blocks: One large yellow hexagon, one blue rhombus, one red trapezoid, and one green triangle.](https://cms-im.s3.amazonaws.com/uFibi3z56gSECu4FGdVdjGoL?response-content-disposition=inline%3B%20filename%3D%226-6.4.B1.Image.03.png%22%3B%20filename%2A%3DUTF-8%27%276-6.4.B1.Image.03.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T035645Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b4ffbf52d77afab50f89a142f43d0a78c5600334395f542c6e4bacf4c0402b82)
Solution
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Problem 3
Use a standard inch ruler to answer each question. Then, write a multiplication equation and a division equation that answer the question.
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How many \(\frac12\)s are in 7?
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How many \(\frac38\)s are in 6?
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How many \(\frac{5}{16}\)s are in \(1\frac78\)?
![Image of a ruler. Top, inches. Scale 0 to 8, by 1's. Bottom, centimeters. Scale 0 to 20, by 1's.](https://cms-im.s3.amazonaws.com/14BwkpxRxUhg3riUmFM2uTJs?response-content-disposition=inline%3B%20filename%3D%226-6.4.PP.Image.09.png%22%3B%20filename%2A%3DUTF-8%27%276-6.4.PP.Image.09.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T035645Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=40538d9469da242b0392bedb0297be1c77c50be63eb8df71f1ef526be7d7643e)
Solution
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Problem 4
Use the tape diagram to answer the question: How many \(\frac25\)s are in \(1\frac12\)? Show your reasoning.
![A tape diagram of two equal parts on a square grid. Each part is composed of 5 squares. A brace from the beginning of the diagram to the middle of the eighth square is labeled "one and one half."](https://cms-im.s3.amazonaws.com/CRCeQksF1t3w9YoXEFN6T6Mu?response-content-disposition=inline%3B%20filename%3D%226-6.4.PP.Image.13.png%22%3B%20filename%2A%3DUTF-8%27%276-6.4.PP.Image.13.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T035645Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8ac069345053e8a1e8849e17ce0eb676e05ea1065e0daed877ce8bff748d0865)
Solution
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Problem 5
Write a multiplication equation and a division equation to represent each sentence or diagram.
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There are 12 fourths in 3.
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How many \(\frac 23\)s are in 6?
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Solution
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(From Unit 4, Lesson 4.)Problem 6
At a farmer’s market, two vendors sell fresh milk. One vendor sells 2 liters for $3.80, and another vendor sells 1.5 liters for $2.70. Which is the better deal? Explain your reasoning.
Solution
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(From Unit 3, Lesson 5.)Problem 7
A recipe uses 5 cups of flour for every 2 cups of sugar.
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How much sugar is used for 1 cup of flour?
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How much flour is used for 1 cup of sugar?
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How much flour is used with 7 cups of sugar?
- How much sugar is used with 6 cups of flour?
Solution
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(From Unit 3, Lesson 6.)