Complements are the key to speed on the soroban. They are simply pairs of numbers that "complete" 5 or 10.
Friends of 5
Two pairs complete five: (1 and 4) and (2 and 3). We use them when earth beads aren’t enough. Example: to add 4 when there aren’t enough beads, add the heaven bead (5) and subtract the complement 1.
Friends of 10
Pairs that complete ten: (1 and 9), (2 and 8), (3 and 7), (4 and 6), (5 and 5). We use them when carrying to the next column. Example: 8 + 5 → carry 1 and subtract the ten-complement 5.
General rule
- For addition when beads are short: +digit = +10 − its complement.
- For subtraction when beads are short: −digit = −10 + its complement.
Apply these rules hands-on in the addition and subtraction lessons on the interactive abacus.