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The Eleven Express
Multiply any two-digit number by 11 in your head, just by adding its two digits. Spot the pattern first. The rule comes after you have found it yourself. This mission is free, with no sign-up.
Multiply these by 11
Look at the first digit and the last digit of each answer, then at the middle digit. What do you notice?
Now predict one yourself
Each answer keeps the outer digits of the number you started with. The gold digits are the outer ones, and the pink digit is the middle one.
You found the rule
Keep the first digit and the last digit apart. Write the sum of the two digits in the gap between them.
It works on bigger numbers too. For 123 × 11, keep the first and last digits and fill each gap with the sum of its two neighbours: 1, then 1 + 2 = 3, then 2 + 3 = 5, then 3. That makes 1353.
The number 11 is just 10 + 1, so a rectangle 11 wide is a block 10 wide with one extra column stuck on. Here is 23 × 11 in tiles. We cut the 11 by 23 rectangle into four parts: a big block (10 by 20), two thin blocks (1 by 20 and 10 by 3) and a tiny block (1 by 3).
Add the four pieces: 200 + 20 + 30 + 3 = 253.
Now look at the two thin blocks. They hold 2 tens and 3 tens, which together make 5 tens. That 5 is 2 + 3, the sum of the two digits, and it sits in the tens place. The big block gives the 2 at the front, and the tiny block gives the 3 at the end. That is the whole trick, drawn in tiles.
The answer is a hundreds, then (a + b) tens, then b units: the first digit, the sum of the digits, and the last digit. For 23, a = 2 and b = 3, so 200 + 50 + 3 = 253. When a + b is 10 or more, the tens piece spills over into the hundreds place, and that is the carry: 78 × 11 = 700 + 150 + 8 = 858.
Eight questions, no calculator
Practice round done
Play the Eleven Mind Reader
Ask someone at home to secretly pick a two-digit number, multiply it by 11 on a calculator, and tell you only the answer. Type their answer below and this page will read their mind. Then try doing it in your head.
This works for answers with three digits, which means a secret number up to 90. The book has a table to practise on, with the hidden numbers to find.
That was Mission 1 of nine
This mission is free and always will be. The other eight multiplication shortcuts are in Book 2: Multiplication Shortcuts, which comes as a printable 45-page book and as online missions like this one.
Multiply by 5 and by 25 · by 9 and by 99 · by 101 and by 1001 · halve and double · two numbers just below 100 · two numbers just above 100 · the Tens Twins
Every mission has the mystery to crack, the reason it works drawn out in tiles and in algebra, Bronze, Silver and Gold practice with a full answer key, a Boss Challenge and a certificate.
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