Order of Operations (PEMDAS)
Grade 6 · Math · Study Guide
Master the rules for evaluating mathematical expressions in the correct order.
When a math expression has more than one operation, you need rules to make sure everyone gets the same answer. Those rules are called the order of operations. The memory trick PEMDAS stands for: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
Step 1: Evaluate everything inside Parentheses (or brackets) first. Step 2: Evaluate Exponents (powers and square roots). Step 3: Multiplication and Division — from left to right. Step 4: Addition and Subtraction — from left to right.
The 'left to right' rule is critical for steps 3 and 4. Multiplication and division have equal priority, so you just work left to right — you don't always multiply before you divide. Same with addition and subtraction.
For example: 3 + 4 × 2² − (6 ÷ 3). Step 1 (parentheses): 6÷3 = 2, giving 3 + 4 × 2² − 2. Step 2 (exponents): 2²=4, giving 3 + 4 × 4 − 2. Step 3 (multiplication): 4×4=16, giving 3 + 16 − 2. Step 4 (addition/subtraction left to right): 3+16=19, 19−2=17. Answer: 17.
| Step | Operation | Rule |
|---|---|---|
| 1st | Parentheses ( ) | Work inside grouping symbols first |
| 2nd | Exponents ^ | Evaluate powers and roots |
| 3rd | Multiplication × and Division ÷ | Left to right — equal priority |
| 4th | Addition + and Subtraction − | Left to right — equal priority |
Key terms
- PEMDAS
- Order of operations acronym: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
- Order of Operations
- Rules determining the sequence in which operations are performed in an expression
- Exponent
- A number telling how many times to multiply the base by itself — e.g. 3⁴ = 3×3×3×3
- Parentheses
- Grouping symbols that indicate operations to be performed first
Flashcards
- PEMDAS
- Parentheses → Exponents → Multiplication/Division → Addition/Subtraction
- P — Parentheses
- Evaluate everything inside ( ) or [ ] first, innermost to outermost
- E — Exponents
- Evaluate powers like 3² = 9 or 2⁴ = 16
- M/D — left to right
- Multiply and divide in left-to-right order — equal priority, no preference
- A/S — left to right
- Add and subtract in left-to-right order — equal priority
- 3 + 4 × 2 = ?
- 11, not 14 — multiply first: 4×2=8, then add 3 → 11
Practice questions
Evaluate: 5 + 3 × 4
- 17
- 32
- 20
- 24
Show answer
Answer: 17
Multiply first: 3×4=12. Then add: 5+12=17. Not 32 (that would be wrong left-to-right).
Evaluate: (8 + 2) × 3 − 5
- 25
- 29
- 13
- 19
Show answer
Answer: 25
Parentheses first: 8+2=10. Then multiply: 10×3=30. Then subtract: 30−5=25.
In PEMDAS, multiplication always comes before division.
Show answer
Answer: False
Multiplication and division have EQUAL priority — you do whichever comes first reading left to right.
In PEMDAS, the 'E' stands for ___.
Show answer
Answer: exponents
PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Evaluate: 24 ÷ 4 + 2² × 3
- 18
- 12
- 54
- 42
Show answer
Answer: 18
Exponents: 2²=4. Division: 24÷4=6. Multiplication: 4×3=12. Addition: 6+12=18.
Fun facts
- Different countries use different memory tricks: in Canada it's BEDMAS (Brackets, Exponents, Division, Multiplication, Addition, Subtraction) — same rules, different order for D and M!
- Calculators that don't follow order of operations (like basic 4-function calculators) give wrong answers — scientific calculators are programmed with PEMDAS built in.
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