Kani Math
Cosmic Abacus
Launch App →
🔟

Big friends practice: the 10-complement rules

The carry, done the abacus way: when a digit will not fit on its rod, add ten on the rod to its left and take the difference off this one.

  • 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
    96
    + 5
    − 58
    + 65
    ?
  2. 2
    70
    − 44
    + 73
    + 33
    ?
  3. 3
    42
    + 65
    − 10
    + 44
    ?
  4. 4
    80
    − 55
    + 83
    + 89
    ?
  5. 5
    93
    − 79
    + 35
    + 82
    ?
  6. 6
    42
    + 73
    − 81
    + 96
    ?
  7. 7
    6
    + 83
    + 88
    − 99
    ?
  8. 8
    79
    + 18
    + 62
    − 91
    ?
  9. 9
    75
    + 33
    + 74
    − 28
    ?
  10. 10
    72
    + 25
    + 4
    − 91
    ?
Full answer key
  1. 96 + 5 − 58 + 65 = 108
  2. 70 − 44 + 73 + 33 = 132
  3. 42 + 65 − 10 + 44 = 141
  4. 80 − 55 + 83 + 89 = 197
  5. 93 − 79 + 35 + 82 = 131
  6. 42 + 73 − 81 + 96 = 130
  7. 6 + 83 + 88 − 99 = 78
  8. 79 + 18 + 62 − 91 = 68
  9. 75 + 33 + 74 − 28 = 154
  10. 72 + 25 + 4 − 91 = 10

This page is one drill. The app is the whole programme.

Kani Math is a full mental-arithmetic course, not a single exercise. Free to start, no signup, and it runs on the web, Android and iPhone.

  • ✓Nine levels, from the first bead to division
  • ✓Four timed sprints and two practice exams, with leaderboards
  • ✓Flash, listening and abacus drills at a speed you set
  • ✓Versus matches against friends or the computer
  • ✓Say your answers out loud — the app listens and marks them
  • ✓Streaks, coins and badges, a teacher view, and a parent dashboard with Premium
Nine levels, one skill at a time.
Math Sprint — solve against the clock.
A weekly progress view for parents.

Want to stay here? The demo further down runs right on this page.

Launch App →Try the demo ↓
Get the app
Download on theApp StoreGet it onGoogle PlayIn your browserLaunch App

Practise it now

A live drill of the same shape, 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.

Explore the free virtual abacus →How to use an abacus →Mental Math Drill →

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 4, 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.

One case is kept for later. On a rod showing 6, adding 7 means taking 3 off, but only one earth bead is raised, so the 3 comes off as a small friend inside the carry: plus ten on the left, five-bead up, two earth beads up. That is both friends at once, 6 + 7 = 13, and it is taught at Intermediate A. The drills on this level leave it out; the walkthrough at kani-math.com/learn/big-friends looks ahead to it frame by frame.

Knowing which sums those are tells you what this level does not ask yet. When the complement to remove is 4 or less, count the earth beads standing under the five-bead: if the complement is larger than that count, the move needs both friends and waits for Intermediate A. 6 + 7, 6 + 8 and 7 + 6 are such moves, while 8 + 7 is a plain big friend, because a rod showing 8 has exactly the three earth beads that come off. A complement of 5 is never a problem either: that is just the five-bead going back up. A child still unsure which bead carries which value should spend a session at kani-math.com/abacus/how-to-use before drilling any of this.

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. 4Small friends still turn up in other rows; a small friend inside a carry waits for Intermediate A.
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 whether the answer still fits on the rod. If it does but the earth beads you need are not free, the five-bead solves it: a small friend. If adding would take the rod past 9, or taking away would take it below 0, a ten has to move on the rod to the left: 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.
My child can do 9 + 3 but gets stuck on 6 + 7.
That is expected: 6 + 7 is not a big-friend move. In 9 + 3 the complement to remove is 7, and a rod showing 9 has the five-bead and four earth beads, so 7 lifts off directly. In 6 + 7 the complement is 3, and a rod showing 6 has only one earth bead raised, so the 3 comes off as a small friend inside the carry: both friends, which Intermediate A teaches. Let it wait until big friends are automatic. It is worked step by step at kani-math.com/learn/big-friends.
Our speed dropped since starting this level. Is that normal?
Yes, and at this point a drop is the correct sign. Until now every blocked digit had a one-rod answer; here some of them need two rods and both hands, so the child is doing more work per row than on the previous level. Accuracy is the metric that matters for now — a column worked slowly and correctly beats a fast one with a carry missed somewhere in the middle, because a wrong answer gives no clue about which row went wrong. Speed comes back once the two-rod gesture stops being two separate decisions.
Learn the techniqueBig friends (10-complements)Walk through it on the beads →