Multiply 72 × 11 without pen and paper

Question

Multiplying by 11 has a shortcut so fast it looks like a party trick. Solve it in your head. What is 72 	imes 11? Aim: under 5 seconds.

Accepted Answer

For a two-digit number times 11, keep the outer digits and drop their sum in the middle: 72 	imes 11 = 7\ \underbrace{(7+2)}{9}\ 2 = 792. So the answer reads off directly as \mathbf{792}. Sanity check the long way: 72 	imes 10 = 720, plus one more 72 gives 720 + 72 = 792. Matches. The only wrinkle is when the two digits add to 10 or more, then you carry into the left digit. Here 7+2=9, so no carry and the digits sit cleanly. Takeaway. Times-11 on a two-digit number is "split the digits, insert their sum." Carry only when the inner sum reaches 10.

Multiply 72 × 11 without pen and paper

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