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Addition Compensation: Round, Add, Then Correct

Level 2 Mental addition · Reviewed by The NumThink editorial team · Last reviewed

Short version: 297 + 468: round 297 to 300, add (768), then subtract the 3 you borrowed: 765.

This page is part of the NumThink Mental addition course. Read why the method works, watch it run on worked examples, then drill it in the practice box below until it feels automatic.

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Why it works

Adding 300 is trivial; adding 297 is not. Compensation just moves the difficulty: borrow 3 to make the friendly number, add, then give the 3 back.

It is the addition twin of round-and-correct multiplication — the same recognize-a-friendly-neighbor skill.

The steps

  1. Spot the near-friendly number. 297 is 3 away from 300.
  2. Round and add. 300 + 468 = 768.
  3. Correct back. You added 3 too much: 768 − 3 = 765.

Worked examples

Easy 59 + 27

Show the thinking

59 → 60 (+1)

60 + 27 = 87

87 − 1 = 86.

Answer: 86

Medium 297 + 468

Show the thinking

297 → 300 (+3)

300 + 468 = 768

768 − 3 = 765.

Answer: 765

Hard 1,996 + 2,458

Show the thinking

1,996 → 2,000 (+4)

2,000 + 2,458 = 4,458

4,458 − 4 = 4,454.

Answer: 4,454

When to use it

  • One number is a hair away from a round number (…97, …98, …01, …02).
  • Both numbers near round bases: round both, add, correct both: 297 + 498 → 300 + 500 − 3 − 2 = 795.

When NOT to use it

  • Numbers already friendly — compensation is wasted motion on 300 + 468.
  • Both numbers awkward (289 + 477): left-to-right addition is more reliable than double-borrowing.

Common mistakes

Forgetting the correction. Answering 768 for 297 + 468. Fix: The correction is the whole point — repeat it as a pair: "borrowed 3, give back 3".
Wrong direction. Subtracting after rounding DOWN instead of adding back. Fix: Rounded up → subtract. Rounded down → add. The correction always undoes the rounding.
Check yourself: Estimate: 297 + 468 must sit just under 300 + 468 = 768 — and 765 does.