6.NOS.1 Group 2 · Challenge

Practice Set · Part 1

Division Expressions with Fractions and Mixed Numbers

Pick up where we left off

Name: Date: Group:

Where we left off

Our goal: I can divide a fraction by a fraction and divide with mixed numbers by multiplying by the reciprocal, explain why the method works, and use it on a problem I have not seen before.

The big idea: Multiply by the reciprocal to divide fractions, and read a fraction part of the answer as part of one more group.

Model to copy — Example · The answer is not whole

  1. Lena has 3/4 cup of flour. One batch of muffins needs 2/3 cup. How many batches can she make?
  2. Write the division. Then Keep, Change, Flip: 3/4 ÷ 2/3 → 3/4 × 3/2
  3. Multiply the tops. Multiply the bottoms: 3/4 × 3/2 = 9/8
  4. Write the answer as a mixed number: 9/8 = 11/8
  5. Say what 11/8 means for Lena: 1 batch + 1/8 of a batch
  6. 3/4 ÷ 2/3 = 11/8. Lena can make 1 full batch and 1/8 of another batch.

Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

  1. 1

    Same stepsFinish what the group started. Use the model above, step for step.

    Try it together — then prove it: Find 1/2 ÷ 1/4. Then explain why the answer is bigger than 1/2. Keep, Change, Flip. Then multiply. (1/2 × 4/1 = 4/2) Simplify. What is 1/2 ÷ 1/4? (4/2 = 2) Why is the answer bigger than 1/2? (The answer counts 1/4 pieces. Each piece is smaller than 1/2, so 2 of them fit.)
    Show your work
  2. 2

    Warm restartWhat is 6 ÷ 1/2?

    1. A1/12
    2. B3
    3. C6 1/2
    4. D12

    How do you know?

  3. 3

    Warm restartWhat is 6 ÷ 1/3?

    1. A2
    2. B3
    3. C6/3
    4. D18

    How do you know?

  4. 4

    Warm restartWhat is 3 ÷ 1/5?

    1. A3/5
    2. B5/3
    3. C8
    4. D15

    How do you know?

6.2 Small Group · Group 2 · Practice SetPart 1 of 4
6.NOS.1 Group 2 · Challenge

Practice Set · Part 2

Division Expressions with Fractions and Mixed Numbers

Keep going

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

  1. 5

    Think it through5/6 ÷ 1/12 = ?

    1. A2
    2. B5/72
    3. C10
    4. D12

    Why is that the answer?

  2. 6

    Think it throughRewrite 5/6 with a denominator of 12.

    1. A5/12
    2. B6/12
    3. C10/12
    4. D11/12

    How do you know? Give a second reason as well.

  3. 7

    Think it throughIf each piece were 1/6 of a foot, how many pieces?

    1. A5
    2. B6
    3. C10
    4. D30

    Explain your thinking. What would have to change for a different choice to be right?

  4. 8

    Back to the modelWhy does 5/6 ÷ 1/12 = 10? How does the bar model show this?

6.2 Small Group · Group 2 · Practice SetPart 2 of 4
6.NOS.1 Group 2 · Challenge

Practice Set · Part 3

Division Expressions with Fractions and Mixed Numbers

Words and reasoning

Word bank · Banco de palabras

Dividend (Dividendo)Divisor (Divisor)Reciprocal (Recíproco)Quotient (Cociente)Simplify (Simplificar)Mixed number (Número mixto)Improper fraction (Fracción impropia)

Use the words

Fill each blank with a word from the bank.

Explain the thinking

  1. 9

    Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

    The mistake: A common mistake in Divide Fractions is flipping the wrong fraction: students flip the dividend (the first fraction) instead of the divisor (the second fraction).
  2. 10

    Say moreWhy do we multiply by the reciprocal when we divide one fraction by another?

  3. 11

    Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Agent Reyes has 5/6 pound of fingerprint powder in the evidence locker. Each sample tube for the crime lab holds 1/12 pound.

    Show your work
6.2 Small Group · Group 2 · Practice SetPart 3 of 4
6.NOS.1 Group 2 · Challenge

Practice Set · Part 4

Division Expressions with Fractions and Mixed Numbers

Show what you know

Last check

These two come from Lesson 6.1. If they are shaky, that is the lesson to revisit — not this one.

  1. 12

    Show what you knowExplain your thinking — What is 5/6 ÷ 1/12?

    1. A5/72
    2. B5/6
    3. C10
    4. D72/5

    Explain your choice.

  2. 13

    From Lesson 6.1Explain your thinking — What does 5 ÷ 1/4 mean, and what is the quotient?

    1. AHow many 1/4-size pieces fit into 5; quotient is 20
    2. B1/4 of 5; quotient is 5/4
    3. C5 groups of 1/4; quotient is 5/4
    4. D5 minus 1/4; quotient is 4 3/4

    How do you know?

  3. 14

    From Lesson 6.1If each section were 1/2 yard instead, how many sections?

    1. A3
    2. B12
    3. C18
    4. D24

    How do you know?

Be honest — this tells your teacher what to do next

I can…Not yetGetting thereGot it
I can divide a fraction by a fraction and divide with mixed numbers by multiplying by the reciprocal, explain why the method works, and use it on a problem I have not seen before.
I can explain why it works: Multiply by the reciprocal to divide fractions, and read a fraction part of the answer as part of one more…
I can justify my answer to a skeptic and connect it to a second strategy or representation.

One question I want to ask my group next time