Lesson 3

How Many Groups?

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Problem 1

Use the tape diagram to find the value of \(\frac12\div\frac13\). Show your reasoning.

A tape diagram. 

Solution

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Problem 2

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."

Solution

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Problem 3

Write a multiplication equation and a division equation to represent each sentence or diagram.

  1. There are 12 fourths in 3.

  2. A tape diagram of 4 equal parts with each part labeled one half. Above the diagram is a brace, labeled 2, that contains all 4 parts.

  3. How many \(\frac 23\)s are in 6?

  4. Fraction bar diagram. 5 equal parts. Each part labeled "the fraction 2 over 5." Total labeled "2."

Solution

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Problem 4

Diego said that the answer to the question “How many groups of \(\frac56\) are in 1?” is \(\frac 65\) or \(1\frac15\). Do you agree with him? Explain or show your reasoning.

Solution

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Problem 5

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 2, Lesson 16.)

Problem 6

Calculate each percentage mentally.

  1. What is 10% of 70?
  2. What is 10% of 110?
  3. What is 25% of 160?
  4. What is 25% of 48?
  5. What is 50% of 90?
  6. What is 50% of 350?
  7. What is 75% of 300?
  8. What is 75% of 48?

Solution

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(From Unit 2, Lesson 23.)