Grade 6 Math · Topic 49

Solving One-Step Equations: Multiplication and Division

For one-step equations involving multiplication or division, undo with the opposite operation. To solve ax = b, divide both sides by a. To solve (x)/(a) = b, multiply both sides by a. Then check.

Lesson alignment: 6.EE.B.7 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Solve multiplication and division equations

Equal groups connect the equation to the inverse operation that isolates x.

Think first: How can equal groups show the inverse operation that isolates x?

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

Solve 7x = 56.

To keep the equation balanced, divide both sides by 7: x = 56 ÷ 7 = 8. Check: 7(8) = 56. ✓

Answer: x = 8

Worked example 2

Solve (m)/6 = 9.

Multiply both sides by 6: m = 9 × 6 = 54. Check: 54/6 = 9. ✓

Answer: m = 54

Try a few on your own

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

  1. 4x = 28
    Check

    x=7

  2. 6y = 42
    Check

    y=7

  3. (x)/3 = 7
    Check

    x=21

  4. (n)/5 = 8
    Check

    n=40

  5. 9a = 81
    Check

    a=9

  6. 12b = 60
    Check

    b=5

  7. (p)/4 = 11
    Check

    p=44

  8. 15x = 90
    Check

    x=6

Try this situation 1

A box of 8 pencils costs $24. How much is each pencil? Write and solve an equation.

Show a worked solution

Answer: $3 each.

Start by writing the calculation clearly: 8x = 24 ⇒ x = 3.

Try this situation 2

A cake is split equally among 5 people; each gets 4 ounces. How heavy was the whole cake?

Show a worked solution

Answer: 20 ounces.

Start by writing the calculation clearly: (c)/5 = 4 ⇒ c = 20.

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

Your practice results stay in this browser and appear in the course progress report.

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. Solve: (x)/6 = 12. Which step comes first?

2. Solve: 6x = 54

3. Solve: (x)/8 = 5

4. Solve: 9x = 81. Which equation shows the correct first step?

5. Solve: 3x = 15

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 Expressions, Equations & Inequalities quiz ↗Try a full practice test ↗