Abacus addition and subtraction

The golden rules

1. Set the first number, with its last digit on your ones rod.
2. Work through the second number from left to right, one digit at a time.
3. Add or take away each digit on the rod that matches its place.
4. The board now shows the answer. Nothing to write down.

Every digit uses one of the moves below. Which one depends only on what the rod shows right now.

Just move them

If there are enough free earth beads, simply push that many up with your thumb (adding) or down with your index finger (taking away).

Taking away works the same way in reverse: 3 − 2 is two earth beads down with the index finger.

The 5-bead

Adding or taking away exactly 5 is one movement of the heaven bead.

Numbers 6 to 9

6, 7, 8 and 9 are 5 plus a bit. Move the heaven bead and the extra earth beads together, as one pinch.

When the beads run out

Sometimes the move you need is not physically there. The rod shows 4 and you want to add 1, but all four earth beads are already up. Or the rod shows 3 and you want to add 7, but a rod cannot hold 10.

That is where complements come in. Pairs that make 5 — little friends — handle the first case. Pairs that make 10 — big friends — handle carrying and borrowing. They are the core of the soroban method and each has its own guide.

Which move do I use?

Find what the rod shows now in the left column, and the digit you are adding or taking away along the top.

• DDirect: just move the beads
• 5The 5-bead on its own
• C5 and a bit, together
• LFLittle friend (5 complement)
• BFBig friend (carry or borrow)

• DDirect: just move the beads
• 5The 5-bead on its own
• C5 and a bit, together
• LFLittle friend (5 complement)
• BFBig friend (carry or borrow)

Checking your answer

Addition and subtraction check each other. After adding a number, take it away again: if you land back where you started, you were right. It is also excellent practice, because taking away usually feels less automatic than adding until you have done a lot of it.

A teaching order that works

Introduce one new idea at a time, in this order:

1. 1 + 2 — earth beads up with the thumb.
2. 3 − 2 — earth beads down with the index finger.
3. 2 + 5 — the heaven bead down.
4. 7 − 5 — the heaven bead up.
5. 2 + 6 — heaven and earth together.
6. 8 − 6 — the same, in reverse.
7. 4 + 1 — the first little friend.
8. 5 − 1 — a little friend taking away.
9. 3 + 7 — the first big friend, carrying.
10. 10 − 7 — a big friend, borrowing.