Free printable chart

Small friends and big friends chart

Every complement rule the soroban uses, on one page you can print and put on the wall. Small friends make five, big friends make ten, and both friends use the two in one move.

Show the friend pair

Small friends — adding

When there are not enough earth beads free, add the heaven bead and take the friend away.

Small friends — adding
You want	So you do	Because
+1	+5 − 4	1 + 4 = 5
+2	+5 − 3	2 + 3 = 5
+3	+5 − 2	3 + 2 = 5
+4	+5 − 1	4 + 1 = 5

Small friends — subtracting

The same pairs in reverse: take the heaven bead off and put the friend back.

Small friends — subtracting
You want	So you do	Because
−1	−5 + 4	1 + 4 = 5
−2	−5 + 3	2 + 3 = 5
−3	−5 + 2	3 + 2 = 5
−4	−5 + 1	4 + 1 = 5

Big friends — adding

When this rod cannot take the number, even with the heaven bead, add one bead on the rod to the left and take the friend off this one.

Big friends — adding
You want	So you do	Because
+1	+10 − 9	1 + 9 = 10
+2	+10 − 8	2 + 8 = 10
+3	+10 − 7	3 + 7 = 10
+4	+10 − 6	4 + 6 = 10
+5	+10 − 5	5 + 5 = 10
+6	+10 − 4	6 + 4 = 10
+7	+10 − 3	7 + 3 = 10
+8	+10 − 2	8 + 2 = 10
+9	+10 − 1	9 + 1 = 10

Big friends — subtracting

When this rod does not hold enough to take the number away, take one bead off the rod to the left, then add the friend back on this one.

Big friends — subtracting
You want	So you do	Because
−1	−10 + 9	1 + 9 = 10
−2	−10 + 8	2 + 8 = 10
−3	−10 + 7	3 + 7 = 10
−4	−10 + 6	4 + 6 = 10
−5	−10 + 5	5 + 5 = 10
−6	−10 + 4	6 + 4 = 10
−7	−10 + 3	7 + 3 = 10
−8	−10 + 2	8 + 2 = 10
−9	−10 + 1	9 + 1 = 10

Both friends in one move

Sometimes both friends fire at once.

Both friends in one move
You want	So you do	Because
+6	+10 − 5 + 1	6 + 4 = 10, 4 + 1 = 5
+7	+10 − 5 + 2	7 + 3 = 10, 3 + 2 = 5
+8	+10 − 5 + 3	8 + 2 = 10, 2 + 3 = 5
+9	+10 − 5 + 4	9 + 1 = 10, 1 + 4 = 5
−6	−10 + 5 − 1	6 + 4 = 10, 4 + 1 = 5
−7	−10 + 5 − 2	7 + 3 = 10, 3 + 2 = 5
−8	−10 + 5 − 3	8 + 2 = 10, 2 + 3 = 5
−9	−10 + 5 − 4	9 + 1 = 10, 1 + 4 = 5

How to use this chart

Print it and keep it beside the abacus for the first few weeks. A child looks up a rule two or three times, then stops needing it — the point is to make the substitution automatic in the fingers, not to memorise a table.

Every rule here is the same idea: the bead you want is not free, so you use a bigger bead and give back the difference. That single substitution is what turns the abacus from a counting device into a calculating one, and it is why abacus training transfers to mental arithmetic at all.

Practise small friends →Practise big friends →Try it on the free abacus →How to use an abacus →Printable soroban flash cards →

Common questions

What is a small friend on the abacus?

A small friend is the number that pairs with yours to make 5 — 1 with 4, 2 with 3. It matters when the rod has too few free earth beads for your number and the heaven bead is still up: to add 4 to a rod showing 2, push the heaven bead down for 5 and take the small friend 1 straight back off. The addition table above lists all four rules. Elementary A is where this is taught.

What is a big friend on the abacus?

A big friend is the number that pairs with yours to make 10 — 3 with 7, 4 with 6, up to 9 with 1. You use it when the rod cannot take the digit at all: add 10 as one bead on the rod to the left, then take the big friend off the rod you are on. That carry is Elementary B, the level after small friends.

Do the same pairs work for subtraction?

Yes — the same pairs, run backwards. To subtract 4 when the rod has too few earth beads, take 5 off and add the small friend 1 back. To subtract 7, borrow 10 from the rod on the left and add the big friend 3 here. The chart prints all five tables — small and big friends, adding and subtracting, and both friends in one move — so nothing has to be reversed in your head.

Do I have to memorise the complements?

The pairs, yes; the table, no. The two small-friend pairs (1 and 4, 2 and 3) and the five big-friend pairs should come back instantly, because a pause mid-sum costs more than a wrong digit. The rows are not learned by heart: a child looks one up two or three times and the substitution moves into the fingers. That is what the chart is for — a lookup for the first weeks, not a revision list.

See all questions →

Kani Math is mental math practice for kids, free to start, with an optional Premium plan.

Get it on the App Store and Google Play, or practice on the web at kani-math.com.