Digit reduction is a self-limiting process. Add digits together repeatedly and, barring an exception, you'll always end up somewhere between 1 and 9 — there's no way for the reduction rule to output a 47 or a 132, because the rule keeps folding any multi-digit result back down.
The exception is the handful of numbers most schools agree to stop reducing early: 11, 22, and 33. These are treated as complete in themselves, said to carry an intensified version of their single-digit counterpart (2, 4, and 6 respectively) rather than being reduced down to them.