What Is the Compensation Technique?
Compensation is a mental math strategy where you temporarily adjust a number to make calculation easier, then correct the result afterward. If a number is close to a round number (like 298 ≈ 300), round it, compute with the friendly number, then add or subtract the difference. This is one of the most powerful and widely applicable mental math techniques.
Why Compensation Works
Our brains process round numbers far faster than irregular ones. Adding 300 + 156 requires one simple step; adding 298 + 156 requires managing carries and awkward digits. By compensating, you trade a tiny adjustment at the end for a dramatically simpler main calculation. This technique works for addition, subtraction, and even multiplication.
Addition Compensation
Identify which number is closest to a round value. Round it up or down, perform the operation, then reverse the rounding. For 298 + 156: round 298 → 300, compute 300 + 156 = 456, compensate by subtracting 2 → 454. The compensation amount is always the difference between the original and rounded number.
Subtraction Compensation
The same logic applies in reverse. For 503 - 197: round 197 → 200, compute 503 - 200 = 303, compensate by adding 3 → 306. You subtracted 3 too many, so you add 3 back. Practice identifying which number to round — usually pick the one furthest from a round number for maximum simplification.
Practice Examples
Example 1: 298 + 156 = ?
- Round 298 to 300
- 300 + 156 = 456
- Subtract 2 (you added 2 extra): 456 - 2 = 454
Answer: 454
Example 2: 503 - 197 = ?
- Round 197 to 200
- 503 - 200 = 303
- Add back 3 (you subtracted 3 too many): 303 + 3 = 306
Answer: 306
Example 3: 49 + 38 = ?
- Round 49 to 50: 50 + 38 = 88
- Subtract 1: 88 - 1 = 87
Answer: 87