“Friends of 5” and “friends of 10” are two of the most important ideas in Soroban. They are the complement pairs that allow children to add and subtract efficiently when the exact beads they want are not available in the current position.
These ideas can sound abstract at first, but they become much easier when taught with movement and repetition. Once children understand them, many calculations that seemed awkward suddenly become smooth.
What “friends” means in Soroban
In Soroban language, “friends” are number pairs that work together to make a larger target. Friends of 5 are pairs such as 1 and 4, 2 and 3. Friends of 10 include pairs such as 1 and 9, 2 and 8, and 4 and 6.
These pairs matter because Soroban often asks you to change one set of beads into another equivalent value quickly. Instead of thinking only about the answer, the child learns to think about the easiest bead movement.
How friends of 5 work
Friends of 5 are usually introduced first because they relate directly to the upper bead worth five. For example, if you want to add 4 but only one lower bead is available, you can add 5 and subtract 1. The pair 4 and 1 becomes useful immediately.
This is why the idea is not just memorization. It is a movement strategy. Children should see and feel what happens on the abacus while they say the pair out loud.
- 1 and 4 make 5
- 2 and 3 make 5
- 4 can be thought of as +5 -1
How friends of 10 work
Friends of 10 become important when one rod does not have enough lower value available and the next place value must be involved. For example, adding 8 may be easier as +10 -2.
At first, children may find this strange because they see one number but are asked to think with a pair. Repetition helps. With time, the complement becomes automatic and calculation becomes much faster.
- 1 and 9 make 10
- 2 and 8 make 10
- 3 and 7 make 10
- 4 and 6 make 10
- 5 and 5 make 10
How to teach these ideas without confusion
Teach one pair family at a time. Do not mix all complements into one long lesson. Let the child say the pair, move the beads, and repeat the pattern several times.
It also helps to combine explanation with visual Soroban lessons and short follow-up training drills. Seeing, saying, and doing the same rule together makes it stick.
Common beginner mistakes
A common mistake is teaching the pairs as flashcards only. The child may recite them correctly but still freeze during actual calculation because the physical movement is not connected to the number pair.
Another mistake is moving on before the child recognizes the pairs quickly. Complements do not need months of work, but they do need enough repetition to feel natural.
Conclusion
Friends of 5 and friends of 10 are the bridge between basic bead control and fluent Soroban calculation. They help children think flexibly, move beads efficiently, and solve problems with less hesitation.
When taught with movement, speech, and repetition, these rules become much easier than they first appear.
FAQ
Do children need to memorize all friends of 10 at once?
No. It is better to teach and practice them gradually so the child connects each pair to actual bead movement.
Why are friends of 5 taught before friends of 10?
Because they are usually easier to see on a single rod and connect directly to the upper bead worth five.
What if my child can say the pairs but cannot use them?
That usually means the concept has been memorized verbally but not practiced enough physically. More guided bead movement is needed.
Are these complement rules important for Anzan later?
Yes. Strong complement knowledge helps children calculate more smoothly on the Soroban and later visualize those moves during mental calculation.