Grade 6 Math · Topic 15

Dividing Fractions

Dividing by a fraction is the same as multiplying by its reciprocal (its flip). The rule is: Keep, Change, Flip (KCF). Keep the first fraction, change ÷ to ×, flip the second fraction, then multiply.

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

Explore visually

Divide fractions by asking how many groups fit

The number line shows how many divisor-size groups fit inside the dividend.

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 3/4 ÷ 2/5.

Use Keep-Change-Flip: keep the first fraction, change division to multiplication, and flip the second fraction. Then 3/4 × 5/2 = 15/8 = 1 7/8.

Answer: 1 7/8

Worked example 2

Divide 5/6 ÷ 2/3.

Use Keep-Change-Flip first: the divisor becomes its reciprocal, so 5/6 × 3/2. Now cancel 3 and 6: 5/2 × 1/2 = 5/4 = 1 1/4.

Answer: 1 1/4

Try a few on your own

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

  1. 1/2 ÷ 1/4 =
    Check

    2

  2. 3/4 ÷ 1/2 =
    Check

    1 1/2

  3. 2/3 ÷ 4/5 =
    Check

    5/6

  4. 5/8 ÷ 3/4 =
    Check

    5/6

  5. 7/10 ÷ 7/5 =
    Check

    1/2

  6. 9/16 ÷ 3/8 =
    Check

    1 1/2

  7. 4/9 ÷ 2/3 =
    Check

    2/3

  8. 11/12 ÷ 1/6 =
    Check

    5 1/2

Try this situation 1

A piece of ribbon is 3/4 yard long. How many 1/8-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 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6.

Try this situation 2

Three friends share 5/6 of a pizza equally. What fraction of the whole pizza does each get?

Show a worked solution

Answer: 5/18.

Use Keep-Change-Flip first: the divisor becomes its reciprocal, so 5/6 ÷ 3 = 5/6 × 1/3 = 5/18.

Fresh questions · saved on this device

Practice this skill

17 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 rope is 7/8 meter long. It is cut into pieces that are each 1/4 meter long. How many pieces are cut?

2. Divide: 6 ÷ 2/3

3. Divide: 5/6 ÷ 2

4. Divide: 7/8 ÷ 7/12. Write your quotient in simplest form.

5. Divide: 4/5 ÷ 8/10. Write your quotient in simplest form.

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 ↗