Soroban for grown-ups — Unit 3: Small friends (complements of 5)

What the small friends are

Each rod has four lower beads worth 1 and one upper bead worth 5. To add 4 to a rod that already shows 3 there is only one free lower bead, so a direct move is impossible. The soroban solves this with the upper bead: add 5, then take away the 1 that was too much. 1 and 4 are partners that make 5, and so are 2 and 3. These pairs are called small friends, or complements of 5.

Subtraction runs the same idea backward. To take 4 from 7, remove the upper bead and give back 1. With practice you stop thinking "5 minus 1"; the hand simply makes the move.

The eight moves

There are eight small-friend moves: +4 is +5 −1, +3 is +5 −2, +2 is +5 −3, +1 is +5 −4, and −4 is −5 +1, −3 is −5 +2, −2 is −5 +3, −1 is −5 +4. Each is used only when the direct move is not possible on that rod. On longer numbers you still work from the left, so 1,234 + 4,321 is four small-friend moves, one on each rod.

Practice in this unit

You watch the moves, do a few with the next bead lit, then a set on your own and three sums in your head. For more, choose Small friends in Practice and do the same sums against the clock.