Kani Math
Cosmic Abacus
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Multi-digit multiplication practice (3 × 2)

Six partial products, no scratch paper, nothing written down — the point at which abacus multiplication overtakes the written algorithm outright.

  • 3-digit × 2-digit multiplication
  • About 12 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
    166 × 99
    ?
  2. 2
    105 × 76
    ?
  3. 3
    539 × 56
    ?
  4. 4
    524 × 20
    ?
  5. 5
    495 × 95
    ?
  6. 6
    689 × 78
    ?
  7. 7
    440 × 28
    ?
  8. 8
    387 × 70
    ?
  9. 9
    124 × 97
    ?
  10. 10
    390 × 42
    ?
Full answer key
  1. 166 × 99 = 16434
  2. 105 × 76 = 7980
  3. 539 × 56 = 30184
  4. 524 × 20 = 10480
  5. 495 × 95 = 47025
  6. 689 × 78 = 53742
  7. 440 × 28 = 12320
  8. 387 × 70 = 27090
  9. 124 × 97 = 12028
  10. 390 × 42 = 16380

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
  • ✓Guided lessons that teach the technique, not just drills
  • ✓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, with parent and teacher views
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Practise it now

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

This problem type runs in the full app rather than the inline drill:

Open in the app ↗

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

About this drill

A three-by-two multiplication produces six partial products that all have to land in the right place and accumulate correctly. Written down this needs two rows and a careful alignment; on the soroban it is one continuous sequence of adds, and the answer is simply what is left on the rods when the sequence ends.

This is also where visualization pays off most dramatically. A learner who can hold a six-rod image can do these mentally in a few seconds, which is not achievable with any written or memorised shortcut. The drills below run the same problems on beads first, then flash them for mental work.

How to practise it

  1. 1Confirm 2×1 multiplication is fully automatic before starting.
  2. 2Fix the reference rod before the first move and do not shift it.
  3. 3Take the multiplier digits in a consistent order, every single time.
  4. 4Only attempt these mentally once the bead version is error-free.
Where this sits

Level 8 — Higher B

Multi-digit multiplication with full mental visualization.

Teaches: Multi-digit multiplication, advanced mental abacus operations

Find your level with the free placement exam →

Questions

How many rods does 3 × 2 need?
Five for the answer plus three for the multiplicand, so eight or more. Anything narrower forces a mid-problem reset, which is where errors come from.
Is this faster than a calculator?
For a trained learner, comparable up to about this size — the abacus wins on setup time, the calculator wins as digits grow. Speed is not really the argument; the mental capability it builds is.
Can this be done mentally?
Yes, and it is the standard target at this level. It requires a stable six- to eight-rod mental image, which is why three-digit addition comes first.
What about decimals?
The same procedure — only the reference rod moves. Decimal placement is taught as an extension once whole-number multiplication is reliable.
Learn the techniqueAbacus multiplicationWalk through it on the beads →