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

Lesson 6.11Fraction Division Problem Solving

Set B · Version ASecond form · supported practice

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

Learning target I can solve real-world problems by deciding whether the question asks how many groups fit or how much is in one group, writing a fraction division equation, and checking the solution by multiplying.

Why This Matters Agent Torres is closing the biggest case of the year. She has 2/3 of a gallon of fingerprint dust left and each test uses 1/6 of a gallon. Before the evidence expires, she needs to figure out exactly how many tests she can run. Can you write the equation and solve it?

RememberFraction Division Problem Solving

Fraction Division Word Problems. Formula: Total Amount ÷ Group Size = Number of Groups In a word problem, first decide what the question asks: how many groups fit (total ÷ size of each group) or how much is in one group (total ÷ number of groups). The total amount is the dividend and the other number is the divisor. Write the equation, solve it with a model, common denominators, or by multiplying by the reciprocal, then check by multiplying the quotient by the divisor.

  1. Identify the Dividend (total amount being split or shared).
  2. Identify the Divisor (size of each group or part).
  3. Divide: Total ÷ Size = Number of Groups (or Total ÷ Groups = Size per Group)

Words: Model (Modelo)Equation (Ecuación)Solution (Solución)Reasonableness (Razonabilidad)Inverse operations (Operaciones inversas)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    A forensic chemist has 5/6 of a liter of testing solution. Each DNA test requires 1/12 of a liter. She needs to figure out how many tests she can run before the solution runs out. Which equation matches the problem?

    1. A1/12 ÷ 5/6 = t
    2. B5/6 ÷ 1/12 = t
    3. C5/6 × 1/12 = t
    4. D5/6 + 1/12 = t
    Show your work
Part 2Practice the skillshow every step
  1. 2Circle the letter of the best answer. Show how you know.

    What is 2 1/2 ÷ 1/2?

    1. A1 1/4
    2. B2 1/4
    3. C4
    4. D5
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    What is 1 1/2 ÷ 3/4?

    1. A1 1/8
    2. B2
    3. C3/4
    4. D1/2
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    What is 3 1/2 ÷ 1/4?

    1. A3 1/8
    2. B7/8
    3. C13/4
    4. D14
    Show your work
Part 3Apply itreal-world problems
  1. 5Circle the letter of the best answer. Show how you know.

    Three agents share 3/4 pound of casting clay equally. How much clay does each agent get? (3/4 ÷ 3 asks how much is in one share.)

    1. A2 1/4 pounds
    2. B4 pounds
    3. C3 3/4 pounds
    4. D1/4 pound

    Hint Is each share more or less than the 3/4 pound you started with?

    Show your work
  2. 6Circle the letter of the best answer. Show how you know.

    Convert 3 2/5 to an improper fraction.

    1. A6/5
    2. B15/5
    3. C17/5
    4. D32/5
    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.

Explain your thinkingHow do you decide which value is the dividend and which is the divisor in a word problem?

Sentence starter The total amount is the ___ because it is being split into groups. The size of each group is the ___ because we are dividing by that amount.

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 6.11Fraction Division Problem Solving

Set B · Version BSecond form · core practice

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

Learning target I can solve real-world problems by deciding whether the question asks how many groups fit or how much is in one group, writing a fraction division equation, and checking the solution by multiplying.

Why This Matters Agent Torres is closing the biggest case of the year. She has 2/3 of a gallon of fingerprint dust left and each test uses 1/6 of a gallon. Before the evidence expires, she needs to figure out exactly how many tests she can run. Can you write the equation and solve it?

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Room 3 — Sort the Clues: Each safe opens only if you pick the clues that need fraction DIVISION. Sort each clue into the correct lock.

    Groups: Needs Division (how many groups fit?) Needs Multiplication (a part of an amount)
    • A roll of crime-scene tape is 3/5 mile long, cut into 1/10-mile strips. How many strips? (3/5 ÷ 1/10)
    • A footprint trail is 2/3 mile long with markers every 1/12 mile. How many markers? (2/3 ÷ 1/12)
    • Each evidence bag weighs 1/4 pound. The detective grabs 4 bags. What is the total weight? (1/4 × 4)
    • A report is 3/8 page long. Torres reads half of it. How much did she read? (3/8 × 1/2)
  2. 2Write the letter of the matching item on each line.

    Room 4 — Match the Lock: Drag each word problem to the division equation that unlocks it.

    1. A 4/5-yard cord is cut into 1/10-yard fuses for the alarm.
    2. A 1/2-gallon jug of luminol is poured into 1/8-gallon sprayers.
    3. A 3/4-mile escape route is split into 3/8-mile sprints.
    4. A 5/6-liter sample is divided into 1/12-liter test tubes.
    • A4/5 ÷ 1/10 = 8
    • B1/2 ÷ 1/8 = 4
    • C3/4 ÷ 3/8 = 2
    • D5/6 ÷ 1/12 = 10
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A forensic chemist has 5/6 of a liter of testing solution. Each DNA test requires 1/12 of a liter. She needs to figure out how many tests she can run before the solution runs out. 5/6 ÷ 1/12 = ?

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

    A forensic chemist has 5/6 of a liter of testing solution. Each DNA test requires 1/12 of a liter. She needs to figure out how many tests she can run before the solution runs out. Is 10 tests a reasonable answer?

    1. ANo — the answer should be less than 1
    2. BYes — each test uses far less than the total, so the answer should be well above 1
    3. CNo — you cannot divide fractions
    4. DYes — because 10 is a round number
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Room 1 — Evidence Locker: Agent Torres has 7/8 pound of casting clay to lift footprints. Each cast uses 1/8 pound. How many casts can she make to unlock the door?

    1. A1/7
    2. B6
    3. C7
    4. D8
    Rewrite each fraction
    Work it out
    Simplify
  4. 6Circle the letter of the best answer. Show how you know.

    Room 2 — Surveillance Map: A suspect's trail is 5/6 of a mile. Hidden checkpoints are spaced every 1/6 of a mile. How many checkpoints are on the trail?

    1. A1/5
    2. B4
    3. C5
    4. D6
    Rewrite each fraction
    Work it out
    Simplify

Explain your thinkingHow do you decide which value is the dividend and which is the divisor in a word problem?

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