Grade 6 Math · Topic 22

Dividing Decimals by Decimals

Division is much easier when the divisor is a whole number. So when dividing by a decimal, shift both decimal points the same number of places to the right until the divisor is a whole number. Then divide normally.

Lesson alignment: 6.NS.B.3 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Make a decimal divisor a whole number

Multiply both numbers by the same power of 10. The quotient does not change.

Think first: What power of 10 will make the divisor a whole number, and what must happen to 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 5.6 ÷ 0.7.

Make the divisor a whole number first. Move both decimals 1 place right: 56 ÷ 7 = 8.

Answer: 8

Worked example 2

Divide 9.45 ÷ 0.15.

Make the divisor a whole number first. Move both decimals 2 places right: 945 ÷ 15 = 63.

Answer: 63

Try a few on your own

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

  1. 4.8 ÷ 0.6 =
    Check

    8

  2. 3.5 ÷ 0.5 =
    Check

    7

  3. 7.2 ÷ 0.9 =
    Check

    8

  4. 6.4 ÷ 0.8 =
    Check

    8

  5. 1.44 ÷ 0.12 =
    Check

    12

  6. 2.25 ÷ 0.15 =
    Check

    15

  7. 8.4 ÷ 0.4 =
    Check

    21

  8. 10.08 ÷ 0.24 =
    Check

    42

Try this situation 1

A ribbon is 4.5 meters long. It is cut into pieces 0.25 meter long. How many pieces are made?

Show a worked solution

Answer: 18 pieces.

Start by writing the calculation clearly: 4.5 ÷ 0.25. Move decimals 2 places: 450 ÷ 25 = 18.

Try this situation 2

Gas costs $3.20 per gallon. How many gallons can be bought with $16?

Show a worked solution

Answer: 5 gallons.

Start by writing the calculation clearly: 16 ÷ 3.20 = 1600 ÷ 320 = 5.

Fresh questions · saved on this device

Practice this skill

18 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 roll of fabric is 18.9 meters long. Each scarf needs 1.5 meters of fabric. How many complete scarves can be made?

2. What is 9.6 ÷ 0.32?

3. A rope is 15.75 meters long. You need to cut it into pieces that are 0.35 meters long. How many pieces will you get?

4. A water tank holds 14.4 gallons. You fill containers that hold 0.9 gallons each. How many containers can you fill completely?

5. What is 2.4 ÷ 0.6?

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 ↗