The Mental Math Dojo
You already know the ×11 trick. Twenty-five times eleven: drop 2 + 5 between the digits and you get 275, instantly, with no working. It feels like a cheat code.
Now do 87 × 11.
Guess first — commit before you look
87 × 11. Same trick. What comes out?
No paper. Run the rule the way you remember it and pick the answer it gives you.
The workbench
Six shortcuts. Six ways to break one.
Every trick here is an identity you already know, wearing a disguise. Drive the numbers yourself and watch the shortcut and the algebra move together — then push each one until it fails, because that is the part nobody teaches.
The shortcut
The algebra underneath
Verdict
Where this bites
Arithmetic you can do in your head is a lie detector
Not because you'll ever need to beat a spreadsheet. Because the moment a number lands in front of you, you get one chance to notice it can't be right — and that chance closes when the meeting moves on.
In the room
"Retention is up 8 points." Points or percent? From 3% to 11%, or from 3% to 3.24%? Those are different companies. 1% as a unit is what lets you ask the question before the slide changes.
The vendor quote
$4.20 a seat, 1,800 seats. Double and halve: 4.2 × 1,800 → 8.4 × 900 → 16.8 × 450 → 33.6 × 225 … or just 42 × 180 = 7,560. So when the quote says $9,400, you ask what the extra $1,840 is for.
The board deck
A growth number that survived three decks because nobody multiplied it out. Near-round products and ×5, ×25, ×50 turn a two-second sanity check into something you can do while someone is still talking.
The shortcut you inherited
"Drop two zeros" works on 300 and quietly lies about 340. Every trick in here has a boundary, and the ones you can't derive are the ones that will fail you in front of an audience.