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×11 Magic

📘What it is

A magical way to multiply any number by 11! Place digits side by side and add neighbors — done!

🛠️How it works

23×11: 2_3, put 2+3=5 in between → 253. Magic? No, math!

🔢A worked example

11 × 35 in a second: keep the outer digits (3 and 5) and put their sum in the middle (3 + 5 = 8) → 385. Another: 11 × 72 = 7_(7+2)_2 = 792.

🎓A closer look

The rule: the outer digits of the number stay in place, and between them you write the sum of each pair of neighbouring digits. In 48×11 the edges are 4 and 8, and the middle is 4+8=12 — since it exceeds nine, the 1 carries to the left: 4+1=5, then 2, then 8 → 528. Three-digit numbers work the same way: 234×11 = 2, 2+3, 3+4, 4 → 2574.

The trick works because 11 = 10 + 1: the number is added to itself shifted one place, so every digit ends up summed with its neighbour. Once a child sees this, the rule is understood rather than memorised. Multiplying by 11 also turns up in percentages (10% + 1%) and quick estimates.

  • Age: 8-9; confident addition is all that is required.
  • Common mistake: forgetting the carry when a neighbour sum exceeds 9.
  • Practice tip: start with digit pairs that sum below 10 (25, 34, 52), then move on to carrying cases.

💡Why it helps

The Trachtenberg system — while others use calculators, you calculate in your head!

❓Frequently asked questions

It is a Trachtenberg trick that teaches you to multiply any number by 11 almost instantly: you add neighbouring digits and place the result between the outer digits. For example, 35 x 11 — add 3 and 5, put 8 in the middle, and you get 385.
No, it complements it. The child still knows column multiplication from school, and this trick simply adds a faster way to do the same calculation in their head.
A child who is confident with addition, roughly from age 8-9, can pick this lesson up easily, because it relies only on adding digits.
Yes, on MentalMath the x11 Magic lesson and every other lesson are completely free and open without any registration.

Other methods

🧮 Abacus (Soroban) — the foundation of mental arithmetic 🔟 Friend of 10 🤝 Big Friends 👬 Big Brother 🌉 Bridge to 10 9️⃣ ×9 Technique 🕛 ×12 Technique 🕉️ Vedic Math (100) 🔱 Vedic Math (1000) ✖️ Urdhva-Tiryagbhyam — vertical and crosswise multiplication 🔲 Squaring a number — the fast way ➗ Division
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