Learn abacus — step by step

The Sorobak abacus is a frame with rods and sliding beads. Instead of writing a number, you show it with beads. Each rod has one upper bead and four lower beads, separated by a horizontal counting bar.

A bead counts only when it is moved toward the bar. On the ones rod, the upper bead is worth 5 and each lower bead is worth 1. Add the values of the beads at the bar to read the digit. Beads away from the bar add nothing.

For now, use just the ones rod. Later, the rod immediately to its left will show tens: one lower bead there means 10. To clear a rod, move the upper bead up and all lower beads down, away from the bar.

The bar is your reference point. Upper beads count when they move down; lower beads count when they move up.

Try this example

To show 6, combine a value of 5 from the upper bead with 1 from a lower bead.

1. 0Start at zero: all beads are away from the bar.
2. 5Move the upper bead down to the bar: 5.
3. 6Move one lower bead up: 5 + 1 = 6.

One rod can show every digit from 0 to 9. For 0, leave all beads away from the bar. For 1, 2, 3 and 4, move that many lower beads up and leave the upper bead away.

For 5, use the upper bead alone. For 6, 7, 8 and 9, keep that bead at the bar and add one, two, three or four lower beads. Count values, not just beads: two beads can mean 6 when one is an upper bead.

Select a number below to inspect its bead pattern. Then return to Your turn and practise all ten digits.

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7 is 5 + 2: the upper bead and two lower beads touch the bar.

1. 0Clear the rod to 0.
2. 5Bring the upper bead to the bar for 5.
3. 7Bring two lower beads to the bar: 5 + 2 = 7.

Move beads along their own rod. Lower beads form a group next to the bar: if you bring the third lower bead up, the two above it move with it. On this screen, tapping a lower bead moves the whole connected group as needed.

To add a lower bead, move it up toward the bar. To remove one, move it down. The upper bead works in the opposite direction: down adds 5, up removes 5. You cannot move a bead across the bar or onto another rod.

Correct move: starting at 2, bring one more lower bead up to make 3. Incorrect move: bringing the upper bead down makes 7, not 3. Read the number after a move and use Try again whenever you need a fresh start.

On a physical abacus, the right thumb usually pushes lower beads up; the index finger moves them down and moves the upper bead in either direction.

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Start with 2, add one lower bead to make 3, then move that bead away to return to 2.

1. 2Start with two lower beads at the bar: 2.
2. 3Move the next lower bead up: 3.
3. 2Move the lowest active lower bead down: back to 2.

Addition means increasing the value on the abacus. Set the first number, then bring enough available beads toward the bar to add the second number. Leave the first number in place as you work.

Begin with sums that have enough free beads: 1 + 2, 2 + 2, or 5 + 3. Adding 5 uses the upper bead, so 2 + 5 means leaving two lower beads up and bringing the upper bead down.

Only move the beads needed for the amount you are adding. If there are not enough free lower beads and the upper bead is available, use the friends of 5 technique in lesson 6.

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For 1 + 2, start with 1 and bring two more lower beads up. Three lower beads now count, so the answer is 3.

1. 1Set the first number: 1.
2. 3Add two lower beads: 1 + 2 = 3.

Subtraction means decreasing the value on the abacus. Set the starting number, then move counted beads away from the bar. Read the beads that remain at the bar to find the answer.

For 4 − 2, move two lower beads down. For 8 − 5, move the upper bead up and leave the three lower beads alone. These are direct subtractions because the value you need to remove is already available in active beads.

Do not move a bead toward the bar when you mean to remove its value. Friends of 5 will help later when the lower beads you need are not available.

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For 4 − 2, begin with four lower beads at the bar. Move two away; the two remaining beads show 2.

1. 4Set the starting number: 4.
2. 2Move two lower beads down: 4 − 2 = 2.

Friends of 5 are pairs that add up to 5: 1 and 4, or 2 and 3. A number’s friend tells you what is missing to make 5. For example, 3 needs 2, so adding 3 can be done as +5 −2.

Use this exchange when there are not enough free lower beads and the upper bead is available. In 4 + 3, all four lower beads are already at the bar. Add 5 with the upper bead, then remove 2 lower beads. The result is 7.

For subtraction, reverse the exchange: to subtract a number, remove 5 and add its friend. In 6 − 3, remove the upper bead’s 5 to leave 1, then add 2 lower beads to reach 3. Use direct moves whenever the needed beads are available.

Add using +5 − the friend. Subtract using −5 + the friend. The temporary number between moves is only a step on the way to the answer.

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

Try this example

4 + 3 = 4 + 5 − 2 = 7. Watch how an exchange lets you add without needing a fifth lower bead.

1. 4Start with four lower beads: 4.
2. 9Add 5 by bringing the upper bead down: temporarily 9.
3. 7Remove two lower beads: 9 − 2 = 7.

Friends of 10 are pairs such as 1 and 9, 2 and 8, or 4 and 6. When an addition reaches 10 or more, one rod is not enough. The rod on the right shows ones; the rod immediately to its left shows tens. One lower bead on the tens rod is worth 10.

To add using a friend of 10, add one ten on the left and subtract the friend from the ones on the right. For 8 + 4, use +10 −6. First show 18, then remove 1 and 5 from the ones rod to finish at 12: one ten and two ones.

For subtraction across a ten, borrow by removing one ten and adding the friend on the ones rod. For 13 − 4, use −10 +6: 13 becomes 3, then 8, then 9. These exercises guide each separate bead move so you can see the exchange.

A rod holds a digit from 0 to 9. Carrying changes the next rod’s value; beads themselves never jump between rods.

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

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8 + 4 = 8 + 10 − 6 = 12. Here, removing 6 is two moves: remove a lower bead worth 1, then the upper bead worth 5.

1. 8Set 8 on the ones rod; leave the tens at 0.
2. 18Add one lower bead on the tens rod: temporarily 18.
3. 17Remove one lower bead from the ones rod: 17.
4. 12Remove the upper bead from the ones rod: 12.