Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.2Division Expressions with Fractions and Mixed Numbers

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can explain what dividing a fraction by a fraction means, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

Why This Matters Agent Rivera is dividing a 3/4-pound evidence bag into portions that each weigh 1/8 pound. She needs to know exactly how many portions she can make for testing. Can you solve the case?

RememberDivision Expressions with Fractions and Mixed Numbers

Dividing Fractions by Fractions. Formula: a/b ÷ c/d = a/b × d/c When you divide a fraction by a fraction, you keep the first fraction, change ÷ to ×, and flip the second fraction (the divisor) to its reciprocal. Then multiply and simplify.

  1. Name the question: 3/4 ÷ 1/8 asks how many 1/8s fit in 3/4.
  2. Use common denominators: 3/4 = 6/8, and 6 eighths ÷ 1 eighth =
  3. Shortcut: multiply by the reciprocal of the divisor, 3/4 × 8/1 = 24/4 = 6, then check by multiplying: 6 × 1/8 = 6/8 = 3/4

Words: Dividend (Dividendo)Divisor (Divisor)Reciprocal (Recíproco)Quotient (Cociente)Simplify (Simplificar)

Part 1Practice the skillshow every step
  1. 1Circle the letter of the best answer. Show how you know.

    What is 6 ÷ 1/2?

    1. A1/12
    2. B3
    3. C6 1/2
    4. D12
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    What is 6 ÷ 1/3?

    1. A2
    2. B3
    3. C1/18
    4. D18
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    What is 3 ÷ 1/5?

    1. A3/5
    2. B5/3
    3. C8
    4. D15
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    What is 10 ÷ 1/4?

    1. A2.5
    2. B1/40
    3. C14
    4. D40
    Show your work
Part 2Apply itreal-world problems
  1. 5Circle the letter of the best answer. Show how you know.

    The lab printer fills 2/5 of a box of evidence labels in 1/2 hour. At that rate, how much of a box does it fill in ONE hour?

    1. A1/5 box
    2. B1 1/4 boxes
    3. C4/5 box
    4. D9/10 box

    Hint How many half-hours are in one hour?

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Problem1/2 ÷ 1/4
    2. 2Divide straight across(1 ÷ 1) / (2 ÷ 4) = 1/(1/2)
    3. 3Answer= 2

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint You cannot divide fractions by dividing the numerators and denominators straight across.

    Correct work
    Correct answer:

Explain your thinkingWhy does 5/6 ÷ 1/12 = 10? How does the bar model show this?

Sentence starter 5/6 ÷ 1/12 = 10 because 5/6 is the same as ___ twelfths, and ___ twelfths divided by 1 twelfth = ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.2Division Expressions with Fractions and Mixed Numbers

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can explain what dividing a fraction by a fraction means, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

Why This Matters Agent Rivera is dividing a 3/4-pound evidence bag into portions that each weigh 1/8 pound. She needs to know exactly how many portions she can make for testing. Can you solve the case?

Part 1Practice the skillshow every step
  1. 1Circle the letter of the best answer. Show how you know.

    What is (3/4) ÷ (1/2)?

    1. A1/2
    2. B2/3
    3. C3/2
    4. D3/8
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
  2. 2Circle the letter of the best answer. Show how you know.

    What is (2/3) ÷ (4/9)?

    1. A2/3
    2. B3/2
    3. C8/27
    4. D9/4
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
  3. 3Circle the letter of the best answer. Show how you know.

    What is (5/6) ÷ (5/12)?

    1. A1/2
    2. B2
    3. C12/5
    4. D25/72
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A carpenter has a board that is 5/6 of a foot long. She needs to cut pieces that are each 1/12 of a foot. She wants to know how many pieces she can cut from the board. 5/6 ÷ 1/12 = ?

    1. A2
    2. B5/72
    3. C10
    4. D12
    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    A carpenter has a board that is 5/6 of a foot long. She needs to cut pieces that are each 1/12 of a foot. She wants to know how many pieces she can cut from the board. Rewrite 5/6 with a denominator of 12.

    1. A5/12
    2. B6/12
    3. C10/12
    4. D11/12
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
  3. 6Circle the letter of the best answer. Show how you know.

    A carpenter has a board that is 5/6 of a foot long. She needs to cut pieces that are each 1/12 of a foot. She wants to know how many pieces she can cut from the board. If each piece were 1/6 of a foot, how many pieces?

    1. A5
    2. B6
    3. C10
    4. D30
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units

Explain your thinkingWhy does 5/6 ÷ 1/12 = 10? How does the bar model show this?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help