Order of Operations
Grade 5 · Math · Study Guide
Learn the correct sequence for solving math expressions using PEMDAS.
When a math expression has multiple operations, you must follow a specific order: Parentheses first, then Exponents, then Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). This is remembered as PEMDAS.
Multiplication and Division have equal priority — solve whichever comes first when reading left to right. The same applies to Addition and Subtraction. Never skip directly to addition before finishing all multiplication.
Expressions inside parentheses (or brackets) are always solved first, no matter what operations are inside them.
| Step | Operation | Example |
|---|---|---|
| 1st | Parentheses | 2 × (3 + 4) → solve (3+4)=7 first |
| 2nd | Exponents | 2³ → 8 |
| 3rd | Multiplication & Division (left to right) | 6 ÷ 2 × 3 → 3 × 3 = 9 |
| 4th | Addition & Subtraction (left to right) | 10 - 3 + 2 → 7 + 2 = 9 |
| Wrong | Correct | Rule Violated |
|---|---|---|
| 2 + 3 × 4 = 20 | 2 + 3 × 4 = 14 | Multiply before adding |
| 6 ÷ 2 × 3 = 1 | 6 ÷ 2 × 3 = 9 | Left to right for × and ÷ |
| (5 + 3)² = 5² + 3² | (5 + 3)² = 64 | Parentheses before exponents |
Key terms
- PEMDAS
- An acronym for the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
- Expression
- A math statement with numbers and operations but no equals sign.
- Parentheses
- Grouping symbols ( ) that signal operations to be solved first.
- Exponent
- A small raised number showing how many times to multiply a base by itself, e.g., 2³ = 2×2×2 = 8.
Practice questions
What is 3 + 4 × 2?
- 14
- 11
- 10
- 24
Show answer
Answer: 11
Multiply first: 4 × 2 = 8. Then add: 3 + 8 = 11.
What is (6 + 2) × 3?
- 12
- 24
- 14
- 18
Show answer
Answer: 24
Parentheses first: 6 + 2 = 8. Then multiply: 8 × 3 = 24.
10 - 2 × 3 + 1 = ___
Show answer
Answer: 5
Multiply first: 2 × 3 = 6. Then left to right: 10 - 6 = 4, then 4 + 1 = 5.
20 ÷ (2 + 3) = ___
Show answer
Answer: 4
Parentheses first: 2 + 3 = 5. Then divide: 20 ÷ 5 = 4.
What is 2 × 3² ?
- 36
- 18
- 12
- 6
Show answer
Answer: 18
Exponent first: 3² = 9. Then multiply: 2 × 9 = 18.
Fun facts
- The phrase 'Please Excuse My Dear Aunt Sally' is a classic memory trick for PEMDAS!
- Computers follow the order of operations exactly — a tiny mistake in parentheses can make a program crash or return the wrong answer.
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