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

Lesson 6.11Fraction Division Problem Solving

Start hereWords, worked example, and sentence starters

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?

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
ModelSpanish: Modelo A picture or math way to show a problem so you can solve it. A bar model showing 3/4 split into 1/8-size pieces, or the equation 3/4 ÷ 1/8 = 6
EquationSpanish: Ecuación A math sentence with an equal sign showing both sides are the same. 3/4 ÷ 1/8 = 6 — the left side (division) equals the right side (answer)
SolutionSpanish: Solución A number that makes the equation or inequality true. In 3/4 ÷ 1/8 = 6, the solution is 6 portions
ReasonablenessSpanish: Razonabilidad Checking if your answer makes sense. 3 ÷ 1/4 = 12. Is 12 reasonable? Yes, because 1/4 is small so many pieces fit into 3.
Inverse operationsSpanish: Operaciones inversas Two math actions that undo each other, like × and ÷. If 3/4 ÷ 1/8 = 6, then 6 × 1/8 = 6/8 = 3/4. Multiplication checks division.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Agent Torres has 2/3 gallon of dust and each test uses 1/6 gallon. I ask: how many tests fit?

  1. The total 2/3 is the dividend. The size of each test 1/6 is the divisor. My equation is 2/3 ÷ 1/6.
  2. In sixths, 2/3 = 4/6, and 4 sixths ÷ 1 sixth = 4. Multiplying by the reciprocal gives the same answer: 2/3 × 6/1 = 12/3 = 4.
  3. So she can run 4 tests. I check by multiplying back: 4 × 1/6 = 4/6 = 2/3. It matches the total, so the answer is reasonable.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A ribbon is 3/4 yard and each bow uses 1/4 yard. The total 3/4 is the dividend; 1/4 is the divisor.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • 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.

Word bank ModelEquationSolutionReasonablenessInverse operationsdividenddivisortotalgroupsplitequation

Watch out!A common mistake

A common mistake in Fraction Division Problem Solving is reversing which fraction is the dividend and which is the divisor when setting up the equation from a word problem. For example: a pitcher holds 3/4 cup of punch, and each serving is 1/8 cup

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

Lesson 6.11Fraction Division Problem Solving

Level 0Most support · every hint printed

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?

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Agent Torres has 2/3 gallon of dust and each test uses 1/6 gallon. I ask: how many tests fit?

  1. The total 2/3 is the dividend. The size of each test 1/6 is the divisor. My equation is 2/3 ÷ 1/6.
  2. In sixths, 2/3 = 4/6, and 4 sixths ÷ 1 sixth = 4. Multiplying by the reciprocal gives the same answer: 2/3 × 6/1 = 12/3 = 4.
  3. So she can run 4 tests. I check by multiplying back: 4 × 1/6 = 4/6 = 2/3. It matches the total, so the answer is reasonable.
Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort each word problem: should you DIVIDE or MULTIPLY to solve it?

    Groups: Division Problem Multiplication Problem
    • How many 1/3-cup scoops fit into 2 cups? (2 ÷ 1/3)
    • A ribbon is 3/4 yard. Each piece is 1/8 yard. How many pieces? (3/4 ÷ 1/8)
    • You run 1/2 mile, 3 times. How far total? (1/2 × 3)
    • A recipe uses 2/3 cup. You make half a recipe. How much? (2/3 × 1/2)
    Steps to try
    1. Re-read each story: does it ask 'how many fit?' or 'how much is a part of the amount?'
    2. 'How many groups or pieces fit' → division. 'A fraction OF an amount' → multiplication.
    3. First card: 1/3-cup scoops filling 2 cups asks how many scoops FIT — decide which lock that clue belongs in.
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A ribbon is 4/5 of a yard long. Each bow uses 1/10 of a yard. Which equation finds how many bows can be made?

    1. A1/10 ÷ 4/5
    2. B4/5 ÷ 1/10
    3. C4/5 × 1/10
    4. D4/5 + 1/10
    Steps to try
    1. Name the roles: 4/5 yard is ALL the ribbon; 1/10 yard is what one bow uses.
    2. 'How many bows' means total ÷ group size — and the total always comes before the ÷ sign.
    3. Decide which number is being cut up. Put that one first, then check each choice's order and operation.
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    A detective has 1/2 gallon of solution. Each test uses 1/8 gallon. How many tests can be run?

    1. A1/16
    2. B1/4
    3. C4
    4. D16
    Steps to try
    1. The total is 1/2 gallon; each test drains 1/8 gallon — you're counting tests.
    2. Rewrite 1/2 as eighths so both amounts match, or the reciprocal shortcut with 8/1.
    3. Multiply top and bottom of 1/2 by 4 to get eighths, then count how many 1/8-tests that covers.
    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  3. 4Circle the letter of the best answer. Show how you know.

    A trail is 3/4 mile long. A jogger runs laps of 1/4 mile each. How many laps does the jogger complete?

    1. A1/3 lap
    2. B3 laps
    3. C3/16 lap
    4. D4 laps
    Steps to try
    1. The trail is 3/4 mile total, and every lap covers exactly 1/4 mile.
    2. Both numbers are fourths — count how many 1/4s stack up to reach 3/4.
    3. Stack laps one at a time: 1/4, then 2/4, then… stop when you reach 3/4 and count your laps.
    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