7 min readUpdated 22 September 2026
Set 4 on the ones rod of a soroban. Now add 3.
You can't — not directly. All four earth beads are already up, and there is nothing left to push. The rod shows 4 and the answer needs to be 7. This is the moment the abacus stops being a counting toy and becomes a method, because the way out is the first real abacus formula: the Small Friend.
4
Tap the beads to try it
Prefer to watch? Episode 7 of our video series walks through the Small Friend formula in under four minutes.
What "Small Friend" means
Two numbers are Small Friends if they add up to 5. There are only two pairs:
- 1 and 4
- 2 and 3
The rule: when you can't add a number directly with the earth beads, add 5 with the heaven bead and take away its Small Friend.
- To add 4: push the heaven bead down (+5), then push 1 earth bead down (−1). Because +4 = +5 −1.
- To add 3: +5, then −2.
- To add 2: +5, then −3.
- To add 1: +5, then −4.
Say it the way abacus teachers do: "Plus three is plus five, minus two."
Worked example: 4 + 3
- The rod shows 4 (four earth beads up).
- Push the heaven bead down: that is +5. The rod now reads 9 — too much, on purpose.
- Push two earth beads down: that is −2 (the Small Friend of 3).
- The rod shows 7. Done.
7
Tap the beads to try it
Subtraction with Small Friends
The same idea works in reverse. Set 7 (heaven bead plus two earth beads) and subtract 4. You can't take four earth beads away — only two are up. So:
- To subtract 4: push the heaven bead up (−5), then push 1 earth bead up (+1). Because −4 = −5 +1.
- To subtract 3: −5, then +2.
- To subtract 2: −5, then +3.
- To subtract 1: −5, then +4.
Worked: 7 − 4. Heaven bead up (7 → 2), one earth bead up (2 → 3). The rod shows 3.
3
Tap the beads to try it
Why not just memorise 4 + 3 = 7?
A child will eventually know 4 + 3 = 7 cold. The point of the formula is what it trains underneath: the habit of breaking a number into a convenient part and a leftover. That habit is exactly what mental arithmetic is made of, and it is why abacus learners later find Big Friend carrying — and much larger numbers — natural rather than frightening.
It also means there is nothing to memorise except two pairs. Four rules for addition, four for subtraction, all generated from "1 and 4, 2 and 3".
How Abacus Kids teaches it
In the app's Learning Path this is Level 2, chapters 6 and 7 — one chapter for adding, one for subtracting — after four chapters of direct bead moves so the child already knows when a move is impossible. Chapter 5 is a short animated introduction to why the formulas exist at all.
Practice problems are generated fresh every time, and in Step by Step mode the app shows the formula hint and bead-direction arrows at the exact moment the child needs them.
Next: when 5 isn't enough either
Small Friends solve running out of earth beads. But set 8 and try to add 5: now the whole rod is full, and the only way forward is the next rod over. That is the job of the Big Friend formulas.
Practise Small Friends on a real abacus
Chapters 1–3 of Level 2 are free, and the formula chapters are part of Premium. Start with the free lessons and see how your child takes to it.
