The Magic of Multiplying by 11: A Math Trick for Kids

During a rainy holiday in a village, a young boy named Rahin, a sixth grader, was intrigued by his uncle's ability to perform rapid calculations. Rahin challenged his uncle to multiply 34 by 11, which his uncle answered instantly as 374. The uncle explained a simple trick for multiplying two-digit numbers by 11: write the first digit, then the sum of the two digits in the middle, and finally the second digit. For 34, it's 3, (3+4)=7, 4, resulting in 374. Rahin successfully applied this to 61 x 11, getting 671, and verified it with a mobile calculator, delighting in the mathematical discovery.

The uncle then introduced a more complex scenario involving multiplying a five-digit number, 53172, by 11. The technique involves keeping the first and last digits the same and summing adjacent digits sequentially. For 53172, the sums are 5+3=8, 3+1=4, 1+7=8, and 7+2=9. Combining these sums with the original first and last digits yields 584892. Rahin was initially stumped when presented with 6258 x 11, as the sum of 5 and 8 is 13, a two-digit number. The uncle demonstrated a method for handling such cases by using imaginary zeros at the ends and carrying over digits. Adding 5+8=13, Rahin writes down 3 and carries 1. Then, 2+5=7, plus the carried 1, makes 8. Next, 6+2=8. Finally, the leading zero plus 6 is 6, resulting in 68838. Rahin then confidently solved 5619 x 11 using this refined technique, arriving at 61809.