PrintableCharts

MULTIPLYING BY 11

how to multiply any positive whole number by 11 in your head, digit by digit

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

Free

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Formats
A4 · A3 · A2
What you get
Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject
maths · school · memo · classroom

A digit’s neighbour is the digit to its right. Works for any positive whole number, of any length.

THE TRACHTENBERG SYSTEM

The rule of adding each digit to its neighbour on the right is part of the mental arithmetic system of Jakow Trachtenberg, a mathematician and engineer born in Odesa in 1888. He developed it to keep his mind occupied while held prisoner in a Nazi concentration camp, and later fled to Switzerland. A book on the system came out in English in 1960.

On the sheet

  • A digit’s neighbour is the digit to its right. Works for any positive whole number, of any length.
  • Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
  • Nothing about how it was made: the sheet carries only what the reader needs.

Printing

  • Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
  • All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
  • White background and sparing fills — it prints on a home printer without draining the cartridge.
  • Margins of at least 10 mm: a home printer cannot print to the edge.
  • No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 5 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

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