×11 in 3 Seconds: Pull Apart, Add the Middle

Step by step

1. 11 notebooks × $34. Total in 3 seconds?
   Eleven notebooks cost thirty-four dollars each. Can you find the total in three seconds?
2. $374. First, the school way
   It's three hundred seventy-four dollars. Let's see the school way first.
3. 34 × 1 = 34 · 34 × 10 = 340 · 34 + 340 = 374
   Write thirty-four times eleven. Thirty-four times one is thirty-four. Thirty-four times ten is three hundred forty. Add them, and you get three hundred seventy-four.
4. The trick: pull apart, add the middle
   Now the trick. In China, kids learn it as a rhyme: pull apart, add the middle. Pull the three and the four apart.
5. 3 + 4 = 7 → 3 7 4
   Three plus four is seven. Drop the seven in the middle. Three, seven, four: three hundred seventy-four!
6. × 11 = × 10 + × 1 → 340 + 34
   Why does it work? Times eleven is times ten, plus times one. So it's three hundred forty plus thirty-four.
7. End: 4 · Front: 3 · Middle: 3 + 4
   Line them up. The four stays at the end. The three stays at the front. And in the middle, the three and the four get added!
8. 57 × 11: 5 + 7 = 12
   But what if the middle adds up to ten or more? Try fifty-seven times eleven. Five plus seven is twelve.
9. Keep 2, carry 1: 5 + 1 = 6 → 627
   Keep the two in the middle, and carry the one to the front. Five plus one is six. Six, two, seven: six hundred twenty-seven!
10. Pull apart, sum in the middle, carry if 10+
    So, to multiply a two-digit number by eleven: pull the digits apart, and put their sum in the middle. If the sum is ten or more, carry the one.