Free sample activity · Grades 6–8

Order of Operations Practice

These questions use whole-number expressions with explicit multiplication signs. Multiplication and division share precedence, as do addition and subtraction; work from left to right within each pair.

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How to use this activity

Allow five to ten minutes. Write each intermediate step. Complete grouped expressions first and evaluate exponents before multiplication or division.

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Multiplication before addition

What is 6 + 3 × 4?

18 36 24
Answer: A.

Multiply 3 × 4 first to get 12, then add 6. The result is 18.

Parentheses

What is (6 + 3) × 4?

18 36 30
Answer: B.

The parentheses group 6 + 3, which equals 9. Then 9 × 4 = 36.

Equal precedence

What is 24 ÷ 6 × 2?

2 12 8
Answer: C.

Division and multiplication have equal precedence. Work left to right: 24 ÷ 6 = 4, then 4 × 2 = 8.

Subtraction and addition

What is 15 - 7 + 2?

10 6 4
Answer: A.

Addition and subtraction have equal precedence. Work left to right: 15 - 7 = 8, then 8 + 2 = 10.

Exponents

What is 2³ + 5?

11 13 18
Answer: B.

The exponent means 2 × 2 × 2 = 8. Add 5 after evaluating the power: 8 + 5 = 13.

Several steps

What is 18 ÷ (3 + 3) + 2 × 4?

20 32 11
Answer: C.

First 3 + 3 = 6. Then 18 ÷ 6 = 3 and 2 × 4 = 8. Finally, 3 + 8 = 11.

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  1. Multiplication before addition

    What is 6 + 3 × 4?

    Answer: 18

    Multiply 3 × 4 first to get 12, then add 6. The result is 18.

  2. Parentheses

    What is (6 + 3) × 4?

    Answer: 36

    The parentheses group 6 + 3, which equals 9. Then 9 × 4 = 36.

  3. Equal precedence

    What is 24 ÷ 6 × 2?

    Answer: 8

    Division and multiplication have equal precedence. Work left to right: 24 ÷ 6 = 4, then 4 × 2 = 8.

  4. Subtraction and addition

    What is 15 - 7 + 2?

    Answer: 10

    Addition and subtraction have equal precedence. Work left to right: 15 - 7 = 8, then 8 + 2 = 10.

  5. Exponents

    What is 2³ + 5?

    Answer: 13

    The exponent means 2 × 2 × 2 = 8. Add 5 after evaluating the power: 8 + 5 = 13.

  6. Several steps

    What is 18 ÷ (3 + 3) + 2 × 4?

    Answer: 11

    First 3 + 3 = 6. Then 18 ÷ 6 = 3 and 2 × 4 = 8. Finally, 3 + 8 = 11.

Take it one step further

Write two expressions using the same numbers and operations but different parentheses. Explain why their values differ.

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