MULTIPLYING VIA THE MIDDLE

how to multiply 47 × 53 in your head, and any pair equally far from a round number

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.

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

The middle is the number exactly halfway between the two, that is, half their sum. The trick works for any two numbers with an even sum and is easiest when the middle is a round number.

THE LARGEST PRODUCT IS IN THE MIDDLE

Among pairs with the same sum, the product grows as the numbers close in on the middle, and it is largest when they are equal: then nothing is subtracted from the square of the middle. For a sum of 100 the products are 40 × 60 = 2400, 45 × 55 = 2475, 48 × 52 = 2496, 49 × 51 = 2499, 50 × 50 = 2500. That is why, of all rectangles with the same perimeter, the square has the largest area.

On the sheet

The middle is the number exactly halfway between the two, that is, half their sum. The trick works for any two numbers with an even sum and is easiest when the middle is a round number.
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.

MULTIPLYING VIA THE MIDDLE

THE LARGEST PRODUCT IS IN THE MIDDLE

On the sheet

Printing

More like this

BARBELL MATHS

BASE RATES

BENFORD’S LAW

THE BIRTHDAY PARADOX