111×11

111×11 is a simple multiplication problem. The product of 111 and 11 is 1221. This can be calculated by hand or with a calculator.

To perform the multiplication manually, one method is to use the standard algorithm. Write 111 above 11 and multiply 111 by the units digit of 11, which is 1. This gives 111. Then, multiply 111 by the tens digit of 11, which is also 1, and shift the result one place to the left, giving 1110. Finally, add these two results: 111 + 1110 = 1221.

Another interesting observation relates to multiplying numbers composed of ones. When multiplying a number consisting of 'n' ones by 11, the result can often be observed to follow a pattern, especially for small values of 'n'. For n=3, as in 111, the pattern is visible. The digits of the result are formed by summing adjacent digits of the multiplicand, with carry-overs handled as usual. In this case, 111 × 11 can be seen as (100 + 10 + 1) × 11 = 1100 + 110 + 11 = 1221. The digits 1, 1+1, and 1 form the basis of the result.

The number 1221 is a palindrome, meaning it reads the same forwards and backward. This palindromic property is a characteristic of the product of 111 and 11.

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