3 + 5
- Ones rod: 3 + 5. Direct move: the beads for 5 are free, so push them to the beam. The abacus now shows 8.
Action
+ 5
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Answer: 3 + 5 = 8 · Check: 8 − 5 = 3.
Addition and Subtraction on the Abacus, Step by Step
Adding means pushing beads to the beam; taking away means moving them off. This guide shows you how to teach both, from 3 + 5 to 43 − 18, one rule at a time.
Three kinds of move
Every addition or subtraction on a soroban is one of three kinds of move. Teach them in this order and practise each one before moving on.
| Move | When you use it | Examples |
|---|---|---|
| Direct | The beads you need are free to move | 3 + 5, 8 − 6 |
| Small friends (make 5) | The move would cross the 5 bead on one rod | 4 + 3 is +5 −2; 6 − 2 is −5 +3 |
| Big friends (make 10) | The rod would go past 9, or below 0 | 7 + 5 is +10 −5; 12 − 5 is −10 +5 |
The beginner tutorial shows the addition moves bead by bead, and the friend tables list every pair.
Direct moves
Start here. When the beads are free, the move is exactly what the sum says.
8 − 6
- Ones rod: 8 − 6. Direct move: take 6 away from the beam. The abacus now shows 2.
Action
− 6
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Answer: 8 − 6 = 2 · Check: 2 + 6 = 8.
Small friends (make 5)
Use small friends when the move would cross the 5 bead on a single rod. The pairs are 1 and 4, and 2 and 3.
4 + 3
- Ones rod: 4 + 3. 3 can't go on directly. Small friends: +3 is done as +5 −2. The abacus now shows 7.
Action
+ 3
= +5 −2
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Answer: 4 + 3 = 7 · Check: 7 − 3 = 4.
6 − 2
- Ones rod: 6 − 2. 2 can't come off directly. Small friends: −2 is done as −5 +3. The abacus now shows 4.
Action
− 2
= −5 +3
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Answer: 6 − 2 = 4 · Check: 4 + 2 = 6.
Big friends and borrowing (make 10)
Use big friends when a rod would go past 9 (carrying) or below 0 (borrowing). The pairs are 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5.
7 + 5
- Ones rod: 7 + 5. 7 + 5 is more than 9. Big friends: +5 is done as +10 −5. Take away 5 on this rod and add 1 on the tens rod. The abacus now shows 12.
Action
+ 5
= +10 −5
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Answer: 7 + 5 = 12 · Check: 12 − 5 = 7.
12 − 5
- Ones rod: 2 − 5. This rod has only 2, less than 5. Big friends: −5 is done as −10 +5. Take 1 from the tens rod and add 5 on this rod. The abacus now shows 7.
Action
− 5
= −10 +5
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Answer: 12 − 5 = 7 · Check: 7 + 5 = 12.
Two-digit sums, rod by rod
Work from the left, biggest place first. Each rod uses one of the same three moves, and sometimes one move needs another inside it.
47 + 38
- Tens rod: 4 + 3. 3 can't go on directly. Small friends: +3 is done as +5 −2. The abacus now shows 77.
- Ones rod: 7 + 8. 7 + 8 is more than 9. Big friends: +8 is done as +10 −2. Take away 2 on this rod and add 1 on the tens rod. The abacus now shows 85.
Action
+ 3
= +5 −2
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Action
+ 8
= +10 −2
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Answer: 47 + 38 = 85 · Check: 85 − 38 = 47.
43 − 18
- Tens rod: 4 − 1. Direct move: take 1 away from the beam. The abacus now shows 33.
- Ones rod: 3 − 8. This rod has only 3, less than 8. Big friends: −8 is done as −10 +2. Take 1 from the tens rod and add 2 on this rod. Adding 2 here is itself a small-friend move: +2 is done as +5 −3. The abacus now shows 25.
Action
− 1
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Action
− 8
= −10 +2
Green outline and arrow = a bead that moved. Faded beads are away from the bar.
Answer: 43 − 18 = 25 · Check: 25 + 18 = 43.
Try a guided sum
The tool walks you through one sum, a rod at a time. Your child says what each rod shows after the move; the hint explains which friend to use, and the abacus updates as you go.
0
Practise + and −
Ten questions at a time. Work each one on the abacus or on paper, then check. A wrong answer shows the right one and how to check it. Only answers right the first time count towards your learning journey.
Common mistakes
- Starting from the ones rod. Abacus users work from the left. It matches how numbers are read and prepares for mental calculation.
- Guessing the friend. Say the rule out loud before moving: "plus 3 is plus 5 minus 2".
- Forgetting the carry. With big friends, the 1 on the next rod is part of the same move. Do both before going on.
- Borrowing from the wrong rod. Always take the 1 from the rod directly to the left.
- Not clearing the abacus. Start every sum with all the beads away from the beam.
Tips for parents
- Teach one kind of move at a time: direct moves, then small friends, then big friends.
- Keep a real abacus beside the screen, so your child feels the beads move.
- Ask your child to say the rule before moving any beads.
- Practise + and − with the same pair together: +3 and −3 use the same friends.
- Keep it short. Ten correct sums is a good day's work.
Next: multiplication on the abacus. For paper practice, make an addition worksheet or a subtraction worksheet.