How to Multiply Numbers Near 100 in Your Head

Level 3 Mental multiplication · Reviewed by The NumThink editorial team · Last reviewed

Short version: Round to 100, multiply, then correct: 98 × 47 = 100 × 47 − 2 × 47 = 4,700 − 94 = 4,606.

This method is the purest example of what NumThink teaches: 98 × 47 looks intimidating until you recognize that 98 is nearly 100. Recognition first, arithmetic second.

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Why it works

A number like 98 is 100 − 2. Substitute: 98 × 47 = (100 − 2) × 47 = 100 × 47 − 2 × 47. Multiplying by 100 is free, and the correction 2 × 47 is small.

Above 100 it flips: 103 × 24 = (100 + 3) × 24 = 2,400 + 72. The method is identical — the sign of the correction is the only thing that changes.

The same idea works near ANY friendly base: 50, 200, 1,000. Round to the base, multiply, correct.

The steps

  1. Spot the friendly structure. Is one factor close to 100 (within about 12)? 98 is 2 below 100.
  2. Multiply via 100. 100 × 47 = 4,700.
  3. Correct the difference. The gap is 2: subtract 2 × 47 = 94. Answer: 4,700 − 94 = 4,606.

Worked examples

easy 99 × 34

Show the thinking

99 = 100 − 1

100 × 34 = 3,400

Subtract 1 × 34: 3,400 − 34 = 3,366.

Answer: 3,366

medium 98 × 47

Show the thinking

98 = 100 − 2

100 × 47 = 4,700

Subtract 2 × 47 = 94: 4,700 − 94 = 4,606.

Answer: 4,606

hard 103 × 24

Show the thinking

103 = 100 + 3

100 × 24 = 2,400

Add 3 × 24 = 72: 2,400 + 72 = 2,472.

Answer: 2,472

When to use it

  • A factor within roughly ±12 of 100 — or of any round base (48 × 62 ≈ 50 × 62 − 2 × 62).
  • Estimation and sanity checks: the rounded product immediately bounds the true answer.

When not to use it

  • Both factors far from any round base — decomposition is the honest tool there.
  • Do not use it when the other factor is huge and the correction becomes the hard part (e.g. 97 × 845): the correction 3 × 845 is almost the whole problem. Prefer compensation on the large factor instead.

Common mistakes

Wrong sign. Subtracting when the number is ABOVE 100. Fix: Below 100 → subtract. Above 100 → add. Say it out loud until it is automatic.
Correcting with the wrong factor. 98 × 47 corrected by 2 × 98. Fix: The gap (2) multiplies the OTHER factor (47). The gap came from 98, so it gets applied to 47.
Check yourself: Estimate first: 98 × 47 must be slightly under 4,700, and 4,606 is. If your answer is far outside that band, re-check the correction.