Choose a two-digit positive whole number. Add its digits, subtract that sum from the original number, then add the digits of what remains.
47 → 4 + 7 = 11 → 47 − 11 = 36 → 3 + 6 = 9
The main lesson uses base ten and inputs 10–99. The final two lessons explore larger numbers and other bases. No sign-in is needed; this file works offline. Lesson links become shareable after you host the file.
A graph dot represents an allowed whole-number input. Lines between dots, where shown, are visual guides.
This interactive lesson needs JavaScript. Its core proof is (10a + b) − (a + b) = 9a. For a = 1 through 9, the results 9, 18, …, 81 each have digit sum 9.