Friends of 5 and friends of 10 — understood through the beads

In soroban addition and subtraction, the biggest stumbling block is Friends of 5 and Friends of 10. A "friend" is the number that makes 5 (or 10) when you add it. When there are not enough beads, you use that friend to calculate.

Friends of 5 —— when there are not enough 1-beads

Friends of 5: 1 and 4 / 2 and 3

When there are not enough one-beads, add the 5-bead and take off the friend.

→

3 + 4: not enough one-beads → bring down the five-bead and clear the 5-partner of 4, 1

→

7 − 3: not enough one-beads → add the 5-partner of 3, 2, then take off the 5-bead

Friends of 10 —— carrying and borrowing

Friends of 10: 1 and 9 / 2 and 8 / 3 and 7 / 4 and 6 / 5 and 5

When that place cannot take any more, take off the friend of 10 and add 1 to the next place.

→

8 + 5: clear the 10-partner of 5, 5 (5 and 5 make 10), then add 1 to the tens → 13

→

13 − 6: take the 1 off the tens and add the 10-partner of 6, 4 → 7

How to remember it

Learn it with your fingers: repeating until your hands move before your head does is the shortcut
Say it out loud: saying "the friend of 4 is 1" out loud as you flick makes it stick faster
Keep to the order: friends of 5 → no carrying → friends of 10 → carrying. Skipping a step makes it easy to get stuck later

In this app, starting from 20th Kyu (answers up to 5), in order questions come in exactly this order. When you get one wrong, a diagram shows which friend tripped you up.

🧮 Try it for yourself

Compared with only reading, moving your hands is far quicker to learn. Soroban Kingdom's levels 20–16 are free forever, with no sign-up, on any phone or computer.

When you get one wrong, the bead move that most likely went wrong (worked out from the answer) is shown in a diagram.

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