Grade 6 Math · Topic 45

The Distributive Property

The distributive property lets you multiply a number outside parentheses by each term inside. It is the bridge between multiplication and addition/subtraction — and the key to simplifying many algebraic expressions.

Lesson alignment: 6.EE.A.4 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Expand with a distributive area model

Split each equal row into an x-part and unit squares. Count the pieces in both ways.

Think first: How many x-parts and unit squares do you predict across all equal rows?

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

Use the distributive property: 4(x + 3).

Start by writing the calculation clearly: 4 · x + 4 · 3 = 4x + 12.

Answer: 4x + 12

Worked example 2

Use the distributive property: 5(2y - 7).

Start by writing the calculation clearly: 5 · 2y - 5 · 7 = 10y - 35.

Answer: 10y - 35

Try a few on your own

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

  1. 3(x + 5)
    Check

    3x+15

  2. 6(y - 2)
    Check

    6y-12

  3. 2(4a + 3)
    Check

    8a+6

  4. 7(x + 2y)
    Check

    7x+14y

  5. 4(3x - 1)
    Check

    12x-4

  6. 5(2 + 3b)
    Check

    10+15b

  7. -2(x + 4)
    Check

    -2x-8

  8. 8(2x - y + 3)
    Check

    16x-8y+24

Try this situation 1

A gym has 5 rooms; each has x treadmills and 3 bikes. Write the total number of machines as a simplified expression.

Show a worked solution

Answer: 5x + 15.

Start by writing the calculation clearly: 5(x + 3) = 5x + 15.

Try this situation 2

Mia bought 4 bags. Each bag has 3 apples and 5 oranges. Use the distributive property to find total fruits.

Show a worked solution

Answer: 32 fruits.

Start by writing the calculation clearly: 4(3 + 5) = 4(3) + 4(5) = 12 + 20 = 32.

Fresh questions · saved on this device

Practice this skill

45 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. Which expression is equivalent to 6(k - 5)?

2. The expression 6x - 3(2x + 4) is equivalent to which of the following?

3. Which expression is equivalent to 7(m - 4)?

4. Which expression is equivalent to 4(3x - 2) + 6x?

5. Which of the following expressions is equivalent to 4(x + 7)?

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 ↗