The soroban
Parts and values
- Rods. Each rod is one decimal place. The rightmost rod in use is the units, the next one to the left the tens, and so on, exactly as you write numbers.
- Beam. The horizontal bar (the reckoning bar) divides every rod into two parts.
- Heaven bead. The single bead above the beam is worth 5.
- Earth beads. The four beads below the beam are worth 1 each.
- Frame. No part in the arithmetic.
A bead counts only when it touches the beam. So each rod shows one digit:
| Digit | Heaven bead | Earth beads at the beam |
|---|---|---|
| 0 | up (away) | none |
| 1 to 4 | up (away) | 1 to 4 |
| 5 | down (touching) | none |
| 6 to 9 | down (touching) | 1 to 4 |
Four ones and one five are exactly enough for 0 to 9, so every digit has one picture. Older soroban had 5 earth beads and 2 heaven beads; the 1:4 form became the Japanese standard in the first half of the twentieth century.
Unit dots
The beam carries a small dot on every third rod. You choose one dotted rod as the units rod; the dots to its left then fall on the thousands, the millions, and so on, the way commas group digits on paper. In the diagram above the rightmost rod is the units rod and the dot on the second rod marks the thousands, so the soroban shows 20579.
Abax counts rods from the right: the rightmost rod is always the units rod and carries a dot, as does every third rod to its left.
Reading a number
Read left to right, one rod at a time, the way you read written digits. For each rod: is the heaven bead down (5) or not (0); how many earth beads touch the beam (0 to 4); add the two. Leading rods with nothing at the beam are leading zeros.
Setting a number
Start from a clear soroban: every heaven bead up, every earth bead down. Then set the digits from left to right, with the finger the finger rules give:
- Set 3: the thumb pushes three earth beads up.
- Set 7: the index finger brings the heaven bead down and the thumb pushes two earth beads up, in one pinch.
- Set 406: four earth beads up on the hundreds rod, nothing on the tens, heaven bead down and one earth bead up on the units.
These are the first demonstrations of lesson S0 in Abax (3, 7, 50, 406).
Clearing
On a physical soroban you clear by tilting it towards you so every bead drops away from the beam, laying it flat and running the index finger along the top of the beam to push the heaven beads up. In Abax the Clear button (or Escape) does the same with a short sweep from the right.
How many rods
Abax offers 9, 13, 17, 21, 23 and 27 rods. A real soroban always has an odd number of rods; 13 is the usual beginner size and 23 the usual school and exam size. On phones, drills size the soroban to the problem.