Grade 6 Math · Topic 44

Order of Operations

To make sure everyone gets the same answer, math has agreed-upon rules called the order of operations. Follow them in order: Parentheses, Exponents, Multiply/Divide (left to right), and Add/Subtract (left to right). The handy mnemonic is PEMDAS.

Lesson alignment: 6.EE.A.1 · 6.EE.A.2.c · Take your time. You can return to this lesson whenever you need it.

Explore visually

Build a power from equal factors

Change the base or exponent. The expanded product shows exactly what the exponent counts.

Think first: Predict what will change when you adjust one value, then use the model to check your idea.

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.

Grade 6 core skill · 6.EE.A.1

Read an exponent as equal factors

An exponent tells how many times the base is used as a factor. It does not tell you to multiply the base by the exponent.

Example: 3²

Base: 3 · Exponent: 2 · Expanded form: 3 × 3

3² = 3 × 3 = 9

Now use order of operations: 5 + 3² = 5 + 9 = 14. Evaluate the power before adding.

Common mix-up: 3² is not 3 × 2. The small raised 2 counts the number of threes being multiplied.

Quick check: Evaluate 2 + 4²

First, 4² = 4 × 4 = 16. Then 2 + 16 = 18.

Follow the worked examples

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

Worked example 1

Simplify 3 + 4 × 2.

Follow the order of operations carefully. Multiply before adding: 3 + (4 × 2) = 3 + 8 = 11.

Answer: 11

Worked example 2

Simplify (6 + 2)² ÷ 4 - 3.

Parentheses: 8² ÷ 4 - 3. Exponent: 64 ÷ 4 - 3. Now divide: 16 - 3. Now subtract: 13.

Answer: 13

Try a few on your own

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

  1. 5 + 3 × 4
    Check

    17

  2. (8 - 3) × 2
    Check

    10

  3. 24 ÷ 6 + 1
    Check

    5

  4. 2³ + 5
    Check

    13

  5. 3 + 2 × 5 - 4
    Check

    9

  6. (4 + 6) ÷ 2 + 3
    Check

    8

  7. 6² - 4 × 5
    Check

    16

  8. 2(3 + 4) - 2²
    Check

    10

Try this situation 1

Evaluate 20 - 3 × (2 + 4).

Show a worked solution

Answer: 2.

Parentheses: 20 - 3 × 6. Now multiply: 20 - 18. Now subtract: 2.

Try this situation 2

A teacher orders 4 packs of pencils at $3 each and 2 packs of erasers at $5 each. Use one expression to find the total.

Show a worked solution

Answer: $22.

Start by writing the calculation clearly: 4(3) + 2(5) = 12 + 10 = 22.

Fresh questions · saved on this device

Practice this skill

97 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. What does the exponent mean in 4³?

2. What is 3²?

3. Evaluate 2 + 4².

4. Which expression is the expanded form of 5³?

5. Which operation comes first in 6 × 2² + 1?

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 ↗