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Adding and taking away

Little friends: the 5 complements

When there is no room for a small number, add 5 and give its little friend back — in one movement.

Updated · 2 min read

The pairs

Two numbers are little friends when they add up to 5. There are only two pairs to learn:

Little friends: pairs that make 5
NumberIts friendTogether
141 + 4 = 5
232 + 3 = 5
323 + 2 = 5
414 + 1 = 5

Why you need them

Say the rod shows 4 and you want to add 1. All four earth beads are already up against the beam, so there is no bead left to push. The answer is to add a whole 5 with the heaven bead and take away the extra 4 — because 1 and 4 are friends, +5 −4 is the same as +1.

The trick only works if you know the pairs instantly. Learn them as partners, not as sums to work out.

Adding with a little friend

Rule: to add a number when the earth beads are full, bring the heaven bead down and push its friend's worth of earth beads down, together.

Worked example: 4 + 1 = 5

Move 1: Set 4. No room for 1. Put 5 on and take its friend 4 back off — one motion.04
Move 1. Set 4. No room for 1. Put 5 on and take its friend 4 back off — one motion. ☝️ index finger
Finished board: 505
Answer: 5

Worked example: 3 + 2 = 5

Move 1: Set 3. No room for 2. Put 5 on and take its friend 3 back off — one motion.03
Move 1. Set 3. No room for 2. Put 5 on and take its friend 3 back off — one motion. ☝️ index finger
Finished board: 505
Answer: 5

Taking away with a little friend

Rule: to take a number away when there are not enough earth beads up, push the heaven bead up and push its friend's worth of earth beads up, together.

Worked example: 5 − 1 = 4

Move 1: Set 5. No little beads to take 1. Take 5 off and put its friend 4 back — one motion.05
Move 1. Set 5. No little beads to take 1. Take 5 off and put its friend 4 back — one motion. 👍 thumb + ☝️ index finger, together
Finished board: 404
Answer: 4

Worked example: 7 − 3 = 4

Move 1: Set 7. No little beads to take 3. Take 5 off and put its friend 2 back — one motion.07
Move 1. Set 7. No little beads to take 3. Take 5 off and put its friend 2 back — one motion. 👍 thumb + ☝️ index finger, together
Finished board: 404
Answer: 4

Learn them as pairs, not sums

The goal is for "4" to make you think "1" without any arithmetic. Quick ways to drill it:

  • Call and answer. You say a number from 1 to 4; your child says its friend. Then swap.
  • Hand pairs. Hold up fingers on one hand; the empty fingers are the friend.
  • Short daily sets. A handful of little-friend sums every day beats one long session.

Chart: which additions need a little friend?

Every cell marked LF needs a little friend. Notice they only appear when the rod shows 1 to 4 and the result would be 5 to 9.

Which move to use when adding
Rod shows+1+2+3+4+5+6+7+8+9
0DDDD5CCCC
1DDDLF5CCCBF
2DDLFLF5CCBFBF
3DLFLFLF5CBFBFBF
4LFLFLFLF5BFBFBFBF
5DDDDBFBFBFBFBF
6DDDBFBFBFBFBFBF
7DDBFBFBFBFBFBFBF
8DBFBFBFBFBFBFBFBF
9BFBFBFBFBFBFBFBFBF
  • DDirect: just move the beads
  • 5The 5-bead on its own
  • C5 and a bit, together
  • LFLittle friend (5 complement)
  • BFBig friend (carry or borrow)

Ready to try it?

Practise Little Friends →

Printable practice: Level 4 worksheet

Common questions

What is a 5 complement on the abacus?

It is the number that makes 5 with another: 1 and 4, or 2 and 3. You use it when there are not enough earth beads to add or take away directly.

Why are they called little friends?

It is a friendly name used when teaching children: the two numbers work as partners to make 5. Pairs that make 10 are called big friends.

Why not just count the beads one by one?

Counting is slow and becomes impossible when the rod is full. Using the friend turns every case into one fixed, quick movement, which is the whole point of the soroban method.