Preparing the boardThe board is clear. Press play, or step through with the arrow keys. Once you have watched it, try it from memory.
123 Set 123 on the rods, lining its ones digit up with the unit point.
WhyThe board holds one running total and nothing else. Every term after this one is worked into these same rods, which is why a soroban never needs scratch paper — and why the board is the thing you learn to picture.
置く Set the number
+5 −1 Lower the heaven bead (+5) and take 1 earth bead back down on the hundreds rod.
Add 456 Digits go on from the highest place down, the opposite of written arithmetic. That is what lets a soroban keep pace with a number being read aloud: you can start before you have heard the end of it.
WhyAdding 4 needs 4 earth beads but only 3 are free, so the five bead stands in for them. It puts on 5, which overshoots by 1, and that 1 comes straight back off: +5 − 1 = +4.
五の合成 Five-complement addition
+5 Lower the heaven bead (+5) on the tens rod.
WhyThe heaven bead is worth exactly 5 and is still free, so 5 goes on in one motion.
そのまま入れる Direct addition
+5 +1 Lower the heaven bead (+5) and push 1 earth bead up on the ones rod.
Why6 is 5 + 1. The heaven bead is worth exactly 5 and is still free, so it carries the 5 and 1 earth bead carries the rest.
そのまま入れる Direct addition
−5 −2 Raise the heaven bead (−5) and pull 2 earth beads down on the tens rod.
Subtract 78 Digits go on from the highest place down, the opposite of written arithmetic. That is what lets a soroban keep pace with a number being read aloud: you can start before you have heard the end of it.
Why7 is 5 + 2. The heaven bead gives back its 5 and 2 earth beads give back the rest.
そのまま払う Direct subtraction
−5 −3 Raise the heaven bead (−5) and pull 3 earth beads down on the ones rod.
Why8 is 5 + 3. The heaven bead gives back its 5 and 3 earth beads give back the rest.
そのまま払う Direct subtraction
Answer 501
A free 3D Japanese abacus that works any addition, subtraction, multiplication or division bead by bead, and explains why each move is the one the method calls for. Type a problem or pick a practice level, watch it worked, try it from memory, then do it in your head from a flash. The methods are the ones taught in Japanese soroban schools.
The soroban (算盤) is the Japanese abacus. Each rod is one decimal place and holds one upper bead worth 5 and four lower beads worth 1 each, so a single rod shows any digit from 0 to 9. Dots on the beam mark the unit rods, where a number’s ones digit is lined up. It descends from the Chinese suanpan and took its present one-and-four form in the 20th century.
Each number goes on from its highest digit down, into one running total on the rods. When a rod has too few beads for a move, a complement stands in: the five bead covers 1 to 4 (五の合成 and 五の分解, five-complement addition and subtraction), and a full rod carries ten to the rod on its left or borrows ten from it (十の繰り上がり and 十の繰り下がり). The app names the technique behind every move.
This app teaches 両落とし (ryō-otoshi): neither factor is set on the rods. Both are held in mind, and each single-digit product is added straight into the answer. Where it goes follows one rule: count places from the ones place as 0, and a digit in place k times a digit in place j lands with its ones digit k + j rods left of the answer’s ones rod. Because the board shows nothing but the answer, the same work carries over to mental arithmetic.
Division uses 片落とし (kata-otoshi) with 確商 (kakushō): the divisor is held in mind and only the dividend is set. Each quotient digit is settled in your head first, as the largest multiple of the divisor that still fits, then set to the left of the dividend, and its products are subtracted where they fall. Nothing is placed and then taken back, a habit that would not survive the move to mental arithmetic. A division that does not come out exactly runs to the number of decimal places you choose.
Anzan (暗算) is calculating on a soroban you picture rather than touch, and it is the goal of soroban training. Every problem can be worked in three stages: Watch, where each bead moves with its reason; From memory, where you work it yourself and reveal a step only when stuck; and Flash, where the problem is shown for a moment and you answer from your head, as in flash anzan (フラッシュ暗算).
It is free, with nothing to install and no sign-up. It runs in a modern browser on a computer, tablet or phone, in English or Japanese.