Kani Math
Cosmic Abacus
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Three-digit addition drills

Three digits and chained carries — where a carry into the tens can push another one straight into the hundreds.

  • 5 rows × 3 digits, addition
  • 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
    132
    + 105
    + 230
    + 639
    + 121
    ?
  2. 2
    146
    + 914
    + 150
    + 650
    + 600
    ?
  3. 3
    800
    + 766
    + 520
    + 621
    + 330
    ?
  4. 4
    555
    + 301
    + 548
    + 309
    + 598
    ?
  5. 5
    496
    + 557
    + 958
    + 347
    + 628
    ?
  6. 6
    456
    + 345
    + 725
    + 379
    + 276
    ?
  7. 7
    619
    + 244
    + 862
    + 386
    + 438
    ?
  8. 8
    327
    + 801
    + 320
    + 248
    + 395
    ?
  9. 9
    130
    + 686
    + 465
    + 819
    + 497
    ?
  10. 10
    858
    + 719
    + 271
    + 248
    + 237
    ?
Full answer key
  1. 132 + 105 + 230 + 639 + 121 = 1227
  2. 146 + 914 + 150 + 650 + 600 = 2460
  3. 800 + 766 + 520 + 621 + 330 = 3037
  4. 555 + 301 + 548 + 309 + 598 = 2311
  5. 496 + 557 + 958 + 347 + 628 = 2986
  6. 456 + 345 + 725 + 379 + 276 = 2181
  7. 619 + 244 + 862 + 386 + 438 = 2549
  8. 327 + 801 + 320 + 248 + 395 = 2091
  9. 130 + 686 + 465 + 819 + 497 = 2597
  10. 858 + 719 + 271 + 248 + 237 = 2333

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.

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About this drill

At three digits the interesting failure mode appears: the chained carry. Adding to a rod showing 9 pushes a carry left, and if that rod also shows 9 the carry keeps travelling. Learners who have only practised isolated carries stall here, because they have been treating the carry as an event rather than as something that can cascade.

This is also the practical width for everyday arithmetic — prices, distances, scores. Getting fluent at three digits is the point where mental arithmetic stops being a party trick and starts being genuinely useful outside practice sessions.

How to practise it

  1. 1Use at least four rods so a carry off the hundreds has somewhere to go.
  2. 2Add each row right to left: units, tens, hundreds.
  3. 3When a carry cascades, follow it all the way before the next row.
  4. 4Read all three rods as one number at the end.

Questions

How many rods do I need?
Four is the practical minimum: three for the numbers and one spare for a carry out of the hundreds. Most virtual and physical abacuses have far more.
What is a chained carry?
A carry that lands on a rod already showing 9, forcing another carry immediately. Three-digit work is where it starts happening regularly.
Should this be done mentally?
Eventually, yes — three digits is the standard starting width for mental abacus work. Get it error-free on beads first.
Is this too hard for a seven-year-old?
Not if the two-digit carry is already automatic. Level here is about technique already mastered, not about age.
Learn the techniqueBig friends (10-complements)Walk through it on the beads →