Grade 6 Math · Topic 16

Dividing Mixed Numbers

To divide mixed numbers: convert each to an improper fraction first, then apply the Keep, Change, Flip rule and multiply. Simplify and convert back to a mixed number for the final answer.

Lesson alignment: 6.NS.A.1 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Divide mixed numbers by measuring groups

Change each mixed number. Watch it become an improper fraction, then count divisor-size groups along the number line.

Think first: Estimate how many divisor-size groups can fit inside the dividend.

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Divide 2 1/2 ÷ 1 1/4.

First convert to a form that is easier to calculate: 5/2 ÷ 5/4 = 5/2 × 4/5. Now cancel 5s and 2 with 4: 1/1 × 2/1 = 2.

Answer: 2

Worked example 2

Divide 3 1/3 ÷ 1 1/6.

First convert to a form that is easier to calculate: 10/3 ÷ 7/6 = 10/3 × 6/7. Now cancel 3 and 6: 10/1 × 2/7 = 20/7 = 2 6/7.

Answer: 2 6/7

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. 1 1/2 ÷ 3/4 =
    Check

    2

  2. 2 1/4 ÷ 1 1/2 =
    Check

    1 1/2

  3. 3 1/3 ÷ 2 1/2 =
    Check

    1 1/3

  4. 4 1/2 ÷ 1 1/4 =
    Check

    3 3/5

  5. 5 1/2 ÷ 2 3/4 =
    Check

    2

  6. 6 2/3 ÷ 1 1/3 =
    Check

    5

  7. 2 2/5 ÷ 4/5 =
    Check

    3

  8. 7 1/2 ÷ 2 1/4 =
    Check

    3 1/3

Try this situation 1

A length of fabric is 7 1/2 yards. How many 1 1/4-yard pieces can be cut from it?

Show a worked solution

Answer: 6 pieces.

Use Keep-Change-Flip first: the divisor becomes its reciprocal, so 7 1/2 ÷ 1 1/4 = 15/2 ÷ 5/4 = 15/2 × 4/5 = 60/10 = 6.

Try this situation 2

A pitcher holds 4 1/2 cups of lemonade. Each glass holds 3/4 cup. How many full glasses can be filled?

Show a worked solution

Answer: 6 glasses.

Use Keep-Change-Flip first: the divisor becomes its reciprocal, so 4 1/2 ÷ 3/4 = 9/2 × 4/3 = 36/6 = 6.

Fresh questions · saved on this device

Practice this skill

19 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A baker has 6 2/3 cups of flour and needs to divide it into portions of 1 1/3 cups each. How many portions can the baker make?

2. Compute: 2 1/2 ÷ 1/2

3. Compute: 3 1/3 ÷ 1 2/3

4. Compute: 3 1/4 ÷ 1/2

5. Compute: 5 1/4 ÷ 2 1/2. Write your answer as a mixed number.

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Fractions & Decimals quiz ↗Try a full practice test ↗