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×12 Technique

📘What it is

The fast way to multiply by 12! Double the digit and add its neighbor. Simple!

🛠️How it works

24×12: double each digit and add left neighbor → 288!

🔢A worked example

Compute 12 × 14: multiply 14 by 10 (140) and 14 by 2 (28), then add → 168. In Trachtenberg's method you double each digit and add the right neighbour.

🎓A closer look

The whole rule fits in one sentence: double each digit and add its right-hand neighbour, moving right to left with an imaginary zero in front of the number. 23×12: ones 3×2=6; tens 2×2+3=7; leading 0×2+2=2 → 276. With carrying: in 36×12, first 6×2=12 — write 2, carry 1; then 3×2+6+1=13 — write 3, carry 1; finally 0×2+3+1=4 → 432.

Doubling supplies the ×2 part and the neighbour supplies the ×10 part — together exactly ×12. This is the most used rule of the Trachtenberg family: clocks, dozens and measurement units come up daily, so fast ×12 pays off in real life.

  • Age: 9-10; doubling must already be effortless.
  • Common mistake: doubling the neighbour instead of the digit itself.
  • Practice tip: as preparation, practise rapidly doubling the numbers from 1 to 50.

💡Why it helps

12 appears in clocks, months, and measurement systems. Fast multiplication helps in daily life!

❓Frequently asked questions

It is a Trachtenberg method that teaches fast multiplication by 12: you double each digit and add its neighbour. This makes mental calculation much simpler.
No, it does not. The child keeps using the school method, and this technique simply adds a quicker route.
A child who knows multiplication and addition, roughly from age 9-10, can master this lesson.
First practise doubling each digit and adding its neighbour on small numbers, then move on to larger ones. On MentalMath this lesson is free and can be practised without limits.

Other methods

🧮 Abacus (Soroban) — the foundation of mental arithmetic 🔟 Friend of 10 🤝 Big Friends 👬 Big Brother 🌉 Bridge to 10 ✨ ×11 Magic 9️⃣ ×9 Technique 🕉️ Vedic Math (100) 🔱 Vedic Math (1000) ✖️ Urdhva-Tiryagbhyam — vertical and crosswise multiplication 🔲 Squaring a number — the fast way ➗ Division
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