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

Lesson 6.10Divide 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 with mixed numbers means, rewrite them as improper fractions, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

Why This Matters Agent Chen is mapping a suspect's route. The total distance is 3 1/2 miles, and each segment between landmarks is 1/4 mile. She needs to know how many segments are on the route to place surveillance cameras at every landmark.

RememberDivide Mixed Numbers

Dividing Mixed Numbers A mixed number, like 3 1/2, has a whole part and a fraction part. Before you can divide, you change each mixed number into an improper fraction (top heavier than bottom). Then ask how many of the divisor fit — with common denominators or by multiplying by the reciprocal — and check by multiplying the quotient by the divisor.

  1. Convert each mixed number to an improper fraction: 3 1/2 = 7/2.
  2. Name the question and divide: 7/2 ÷ 1/4 asks how many 1/4s fit in 7/2. With common denominators, 7/2 = 14/4, and 14 fourths ÷ 1 fourth = 14, or multiply by the reciprocal: 7/2 × 4/1 = 28/2 =
  3. Simplify, then check by multiplying: 14 × 1/4 = 14/4 = 3 1/2

Words: Mixed Number (Número mixto)Improper Fraction (Fracción impropia)Convert (Convertir)Simplify (Simplificar)Reciprocal (Recíproco)

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

    What is 2/3 ÷ 1/3?

    1. A1/2
    2. B2/9
    3. C2
    4. D6
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    What is 1/2 ÷ 1/4?

    1. A1/8
    2. B1/2
    3. C2
    4. D4
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    What is 3/4 ÷ 1/8?

    1. A3/32
    2. B6
    3. C8/3
    4. D24
    Show your work
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A 4 1/2-cup jar of fingerprint gel fills exactly 1 1/2 test kits. How much gel is in ONE kit? (4 1/2 ÷ 1 1/2 asks how much is in one whole kit.)

    1. A6 3/4 cups
    2. B1/3 cup
    3. C3 cups
    4. D4 1/3 cups

    Hint The jar fills MORE than one kit, so one kit holds less than 4 1/2 cups.

    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    What is the reciprocal of 3/5?

    1. A1/3
    2. B3/5
    3. C5/5
    4. D5/3
    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. 6Circle the letter of the best answer. Show how you know.

    A detective has a rope that is 5 1/4 feet long. She needs to cut it into pieces that are each 3/4 of a foot for tying evidence tags. How many pieces can she cut? Write 5 1/4 as an improper fraction.

    1. A9/4
    2. B20/4
    3. C21/4
    4. D51/4
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
    1. 1Whole over 13 becomes 3/1.
    2. 2KeepThe first fraction does not move.
    3. 3Change · Flip÷ becomes ×; flip the second fraction.
    4. 4CheckDividing by a piece smaller than 1 gives a BIGGER answer.

Explain your thinkingWhy is converting to an improper fraction the first step when dividing mixed numbers?

Sentence starter Before dividing, I convert 2 1/2 to ___ because it is easier to ___ with improper fractions.

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 6.10Divide 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 with mixed numbers means, rewrite them as improper fractions, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

Why This Matters Agent Chen is mapping a suspect's route. The total distance is 3 1/2 miles, and each segment between landmarks is 1/4 mile. She needs to know how many segments are on the route to place surveillance cameras at every landmark.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Mission 4: Match each suspect's case-file number (a mixed number) to its decoded improper fraction.

    1. 5 1/4
    2. 2 3/5
    3. 3 1/6
    4. 4 2/3
    • A21/4
    • B13/5
    • C19/6
    • D14/3
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A detective has a rope that is 5 1/4 feet long. She needs to cut it into pieces that are each 3/4 of a foot for tying evidence tags. How many pieces can she cut? 5 1/4 ÷ 3/4 = ?

    1. A3 3/4
    2. B4
    3. C6
    4. D7
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    A detective has a rope that is 5 1/4 feet long. She needs to cut it into pieces that are each 3/4 of a foot for tying evidence tags. How many pieces can she cut? Check the answer: how long are 7 pieces of 3/4 foot?

    1. A3/4 foot
    2. B5 1/4 feet
    3. C5 3/4 feet
    4. D7 feet
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Mission 1: The stakeout shift is 4 1/2 hours long. Each agent covers a 1 1/2-hour watch. How many agent watches fill one shift?

    1. A2 1/2
    2. B3
    3. C4 1/2
    4. D6
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Mission 2: A surveillance route is 3 miles long, split into 1 1/2-mile patrol sections. How many sections are on the route?

    1. A1 1/2
    2. B2
    3. C3
    4. D4 1/2
    Show your work
  5. 6Circle the letter of the best answer. Show how you know.

    Mission 3: There are 7 1/2 feet of caution tape to seal a crime scene. Each doorway needs 2 1/2 feet. How many doorways can be sealed?

    1. A2 1/2
    2. B3
    3. C5
    4. D10
    Show your work

Explain your thinkingWhy is converting to an improper fraction the first step when dividing mixed numbers?

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