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The Abacus

Move the beads with your finger, or tap them here on the screen. Every step you are shown is worked out from the real rules of the soroban, so what you practise here is exactly what you do on the abacus in your hand.

Start learning

Tap any bead. A bead only counts when it touches the middle bar.

Learn the abacus, step by step

Seven levels, from picking it up for the first time to working without looking. Start at Level 1 even if you think you know it — the early lessons are what make the later ones easy.

1

Meet the abacus

What the beads are and how to read them.

The beads and the bar Know what each bead is worth and when it counts. Making 0 to 9 Set any single digit on one rod without thinking about it. Reading bigger numbers Read and set two- and three-digit numbers.
2

Straight adding and taking away

Moving beads directly, with no tricks needed yet.

Adding and taking away 1 to 4 Move the 1-beads with confidence. Adding and taking away 5 Use the 5-bead on its own. Adding and taking away 6 to 9 Move the 5-bead and the 1-beads together in one go.
3

Small friends

The pairs that make 5 — the first real technique.

Why we need small friends See the problem the technique solves. Small friends — adding Add 1, 2, 3 and 4 using the 5-bead. Small friends — taking away Subtract 1, 2, 3 and 4 using the 5-bead.
4

Big friends

The pairs that make 10, and carrying to the next rod.

Why we need big friends Understand carrying on the abacus. Big friends — adding Carry to the next rod smoothly. Big friends — taking away Borrow from the next rod smoothly.
5

Combinations

When a big friend needs a small friend to finish the job.

Combination — adding Handle the case where a big friend is not enough on its own. Combination — taking away The same idea, for subtraction.
6

Bigger numbers and speed

Multi-digit work, long columns, and flash practice.

Two and three digit numbers Work rod by rod without losing your place. Long columns Keep accuracy over ten numbers in a row. Flash practice Start picturing the abacus instead of touching it.
7

Times and share

A first look at multiplication and division on the beads.

Multiplying by parts Turn a multiplication into additions you already know. Dividing by taking away See division as repeated subtraction on the beads.

All the formulas on one card

Every technique in one place — the small friends that make 5, the big friends that make 10, and the combinations that need both. Print this and keep it beside you until you no longer need it.

Small friends — adding

Pairs that make 5. Use one when the 1-beads you need are not free, but the 5-bead is.

  • +4 = +5 − 1
  • +3 = +5 − 2
  • +2 = +5 − 3
  • +1 = +5 − 4

Small friends — taking away

The same pairs, worked backwards.

  • −4 = −5 + 1
  • −3 = −5 + 2
  • −2 = −5 + 3
  • −1 = −5 + 4

Big friends — adding

Pairs that make 10. Add one bead on the next rod to the left, then take the partner off this rod.

  • +9 = +10 − 1
  • +8 = +10 − 2
  • +7 = +10 − 3
  • +6 = +10 − 4
  • +5 = +10 − 5
  • +4 = +10 − 6
  • +3 = +10 − 7
  • +2 = +10 − 8
  • +1 = +10 − 9

Big friends — taking away

Take one bead off the rod to the left, then put the partner back on this rod.

  • −9 = −10 + 1
  • −8 = −10 + 2
  • −7 = −10 + 3
  • −6 = −10 + 4
  • −5 = −10 + 5
  • −4 = −10 + 6
  • −3 = −10 + 7
  • −2 = −10 + 8
  • −1 = −10 + 9

Combination — adding

Used when the big-friend step cannot be taken off directly, so a small friend is needed as well.

  • +9 = +10 − 5 + 4
  • +8 = +10 − 5 + 3
  • +7 = +10 − 5 + 2
  • +6 = +10 − 5 + 1

Combination — taking away

The mirror image, for subtraction.

  • −9 = −10 + 5 − 4
  • −8 = −10 + 5 − 3
  • −7 = −10 + 5 − 2
  • −6 = −10 + 5 − 1