English

Counting Up: Subtract by Measuring the Gap

Level 1 Mental subtraction · Reviewed by The NumThink editorial team · Last reviewed

Short version: 645 − 297: count up 297 → 300 (3) → 600 (300) → 645 (45). The gap is 3 + 300 + 45 = 348.

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

Try it now

No signup · instant feedback

Why it works

Subtraction IS the gap between two numbers — so instead of grinding out columns and borrows, measure the gap directly along friendly milestones (300, 600).

This is exactly how shopkeepers give change, and it is the most reliable mental subtraction method for numbers that are far apart or end awkwardly.

The steps

  1. Jump to the nearest round number. 297 → 300: that is 3.
  2. Jump in big friendly chunks. 300 → 600: that is 300.
  3. Finish with the remainder. 600 → 645: that is 45.
  4. Add the jumps. 3 + 300 + 45 = 348.

Worked examples

Easy 52 − 38

Show the thinking

38 → 40 (2)

40 → 50 (10)

50 → 52 (2)

2 + 10 + 2 = 14.

Answer: 14

Medium 645 − 297

Show the thinking

297 → 300 (3)

300 → 600 (300)

600 → 645 (45)

3 + 300 + 45 = 348.

Answer: 348

Hard 1,243 − 986

Show the thinking

986 → 1,000 (14)

1,000 → 1,200 (200)

1,200 → 1,243 (43)

14 + 200 + 43 = 257.

Answer: 257

When to use it

  • The number being subtracted ends awkwardly (…97, …86) — borrow-fests on paper.
  • Any subtraction where the two numbers are close: the gap is small, so count it.

When NOT to use it

  • Numbers where no borrowing would occur anyway (845 − 623) — just subtract left-to-right.
  • The gap is huge (902 − 11): counting up wastes steps; left-to-right is faster.

Common mistakes

Skipping a milestone. Going 986 → 1,243 directly and losing the count. Fix: Always land on round milestones — 1,000, 1,200 — then the last small hop.
Forgetting to add the jumps. Remembering the jumps but not summing them. Fix: Say each jump with its size, then total once at the end.
Check yourself: The jumps must reconstruct the original number: 297 + 348 = 645 ✓ — a free built-in check.