How does the near-100 method handle one number above 100 and one below, e.g. 107 × 97?

Use signed deviations; opposite signs make the right part negative, so you subtract it.

Deviations +7 and −3:

• Left: 107 + (−3) = 104 → 10400.
• Right: 7 × (−3) = −21.
• Combine: 10400 − 21 = 10379.

Check: 107 × 97 = 10379. ✓ When the two deviations share a sign you append their (positive) product; when they differ, the product is negative and you subtract.