Multiply by 11 in your head

To multiply a two-digit number by 11, move its two digits apart and write their sum in the gap.

For 35 × 11, the digits are 3 and 5. Their sum is 8, so the answer reads 3, 8, 5. That is 385.

It works because 11 is 10 + 1. So 35 × 11 is 350 + 35, and adding those two lines is what puts 3 + 5 in the middle.

This rule is for two-digit numbers. Longer numbers use the same idea, with more steps.

The gap holds one digit. When the two digits add to 10 or more, the sum does not fit on its own.

For 78 × 11, the digits give 7, then 15, then 8. Keep the 5 in the middle and carry the 1 into the first digit. The 7 becomes 8, so the answer is 858.

Without the carry the rule would give 7158, which is far too large. 78 is a little under 80, and 80 × 11 is 880, so the answer sits a little under 880.

Now try 57 × 11. The digits are 5 and 7, and they add to 12.

The 12 is already in the gap in the picture. Decide what the first digit becomes.