How does rounding-and-adjusting (compensation) speed up an addition like 497 + 286?

Round one number to something friendly, add, then undo the rounding.

Turn a hard sum into an easy one plus a small correction:

497 + 286 → round 497 up to 500: 500 + 286 = 786 → you added 3 too many, so subtract 3 → 783.

Check: 497 + 286 = 783. ✓ The trick is to add back or take away exactly the amount you rounded by. Round the number that's closest to a round value.