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Stage 19 of 20

Mixed Operations & Order

Real problems mix operations. Learn the order of operations (PEMDAS) and practice switching between skills rapidly — the hallmark of mental math mastery.

What You'll Learn

  • Apply order of operations: parentheses, multiply/divide, add/subtract
  • Switch between operations without losing track
  • Solve multi-step problems entirely mentally

Explanation

PEMDAS: Parentheses first, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right).

Example: 3 + 4 × 2 = 3 + 8 = 11 (multiply first). Not (3 + 4) × 2 = 14.

Break complex problems into chunks. For 24 + 18 ÷ 3: first 18 ÷ 3 = 6, then 24 + 6 = 30.

Parentheses override everything: (24 + 18) ÷ 3 = 42 ÷ 3 = 14.

Pro Tips

  • • Underline or mentally circle operations to do first.
  • • Estimate the final answer before computing — catch order mistakes early.
  • • Practice with two-step problems before attempting three or more steps.

Practice Exercises

Work through each problem mentally. Click "Show Answer" when you're ready to check.

  1. 1. 3 + 4 × 2 = ?
  2. 2. 20 − 6 ÷ 2 = ?
  3. 3. (5 + 3) × 4 = ?
  4. 4. 18 ÷ 3 + 7 = ?
  5. 5. 10 + 2 × 6 = ?
  6. 6. (12 − 4) × 2 = ?
  7. 7. 30 ÷ 5 + 9 = ?
  8. 8. 8 × 3 − 10 = ?
  9. 9. (20 + 5) ÷ 5 = ?
  10. 10. 15 − 3 × 4 = ?