NewCompetition — train in the real contest format: 200 questions in 8 minutes, categories A to I.See how it works
K
Kani
Cosmic Abacus
🔟

Big friends practice: the 10-complement rules

The carry, done the abacus way: when a digit will not fit on its rod, take ten from the rod to its left and give back the difference.

  • 4 rows × 2 digits, add & subtract
  • About 8 min
  • Free, no account

Sample problems

Real problems from this drill, with answers. Nothing to install, no account, no email — work them on paper, on a physical abacus, or in your head.

  1. 1
    98
    − 93
    + 48
    − 44
    ?
  2. 2
    36
    + 46
    + 89
    − 69
    ?
  3. 3
    85
    − 68
    + 47
    − 46
    ?
  4. 4
    65
    + 62
    + 72
    + 49
    ?
  5. 5
    43
    − 39
    + 26
    + 46
    ?
  6. 6
    78
    + 20
    − 95
    + 53
    ?
  7. 7
    65
    + 74
    − 39
    + 75
    ?
  8. 8
    93
    + 56
    − 58
    + 28
    ?
  9. 9
    44
    − 13
    + 56
    − 19
    ?
  10. 10
    44
    − 26
    + 38
    − 51
    ?
Full answer key
  1. 98 − 93 + 48 − 44 = 9
  2. 36 + 46 + 89 − 69 = 102
  3. 85 − 68 + 47 − 46 = 18
  4. 65 + 62 + 72 + 49 = 248
  5. 43 − 39 + 26 + 46 = 76
  6. 78 + 20 − 95 + 53 = 56
  7. 65 + 74 − 39 + 75 = 175
  8. 93 + 56 − 58 + 28 = 119
  9. 44 − 13 + 56 − 19 = 68
  10. 44 − 26 + 38 − 51 = 5

Practise it now

The same drill, live in your browser, with a virtual soroban and instant marking.

🔟

Loads a full interactive drill right here on the page. It never asks who you are.

No signup. Nothing saved unless you ask.

About this drill

Big friends are the pairs that add to ten: 1–9, 2–8, 3–7, 4–6, 5–5. To add 7 to a rod showing 6, you cannot — so you add one bead on the rod to the left (worth ten) and remove three on the right, because 7 is 10 minus 3. On paper this is called carrying. On the abacus it is a single two-handed gesture, and it is the last mechanical rule the method needs.

These drills stack four two-digit numbers with mixed signs, which is where big friends and small friends start appearing in the same problem. That combination is the real difficulty of this level — not either rule alone, but switching between them without pausing.

How to practise it

  1. 1Memorise the five pairs to ten before starting.
  2. 2Left hand on the tens rod, right hand on the units rod.
  3. 3Add the ten first, then remove the complement — always that order.
  4. 4Watch for problems needing both a small and a big friend in one row.
Where this sits

Level 4 — Elementary B

Big friends — the 10-complement rules — on 2-digit problems.

Teaches: 10-complement (big friends) technique, 2-digit operations

Find your level with the free placement exam →

Questions

Is a big friend the same as carrying?
It produces the same result, but the procedure is different. Written carrying defers the ten to a later step; the abacus moves it immediately, so there is never anything held in reserve.
Why do both hands move?
Because two rods change at once. Training both hands from the start is what keeps speed up later — one-handed abacus work hits a ceiling fast.
My child mixes up small and big friends.
Normal at this stage. The cue is which bead is blocked: if the five-bead can solve it, it is a small friend; if the whole rod is full, it is a big friend.
How many digits should we practise on?
Two is right for learning the rule. Widen to three only after the two-rod carry is automatic, or the child ends up managing place value instead of the technique.