R1 · Lesson 5: Order of Operations (PEMDAS)

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Why this matters for Grade 6: Standard 6.EE.1 asks you to write and evaluate numerical expressions involving whole-number exponents. Standard 6.EE.2 has you evaluate algebraic expressions. Both require you to follow the correct order — if you add before you multiply, you get a completely different (wrong) answer.

Learn It

PEMDAS — The Order of Operations

When an expression has more than one operation, use PEMDAS to decide which to do first:

Parentheses
first

Exponents
next

MDultiply &
Divide (left→right)

ASdd &
Subtract (left→right)

Example 1: 3 + 4 × 2

No parentheses or exponents → multiply first
3 + 4 × 2 = 3 + 8 = 11

Wrong way (left to right without rules): 3+4=7, then 7×2=14 — that is not correct.

Example 2: (3 + 4) × 2

Parentheses first
(3 + 4) × 2 = 7 × 2 = 14

The parentheses changed the answer from 11 to 14!

Example 3: 2³ + 5

Exponent first: 2³ = 2×2×2 = 8
2³ + 5 = 8 + 5 = 13

Example 4: 20 − 6 ÷ 2

Division before subtraction
20 − 6 ÷ 2 = 20 − 3 = 17

Example 5: 4 + 3 × (6 − 2)

Step 1 — Parentheses: (6−2) = 4
4 + 3 × (6 − 2) → 4 + 3 × 4
Step 2 — Multiply: 3×4 = 12
4 + 3 × 4 → 4 + 12
Step 3 — Add
4 + 12 = 16

Try It · Guided

Work These Together

1. Evaluate: 3 + 4 × 2

Hint

Multiply first: 4×2=8. Then add: 3+8=11.

2. Which expression equals 14?

Hint

(3+4)×2: parentheses first → 7×2=14.

Practice · On Your Own

You Try

3. Evaluate: 2³ + 5

Hint

2³ = 2×2×2 = 8. Then 8+5=13.

4. Evaluate: 20 − 6 ÷ 2

Hint

Division before subtraction: 6÷2=3. Then 20−3=17.

5. Evaluate: 4 + 3 × (6 − 2)

Hint

Parentheses first: 6−2=4. Then multiply: 3×4=12. Then add: 4+12=16.

★

Exit Ticket

Show What You Know

6. Evaluate: 5 + 3² × 2

Hint

Exponent first: 3²=9. Then multiply: 9×2=18. Then add: 5+18=23.

7. Which value does (8 − 2) × 3 + 1 equal?

Hint

Parentheses: 8−2=6. Multiply: 6×3=18. Add: 18+1=19.

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