9
that I think perfectly encapsulates the justification for my essay; “The stock market is filled with people who know the price of everything but the value of nothing”
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Division by 11
Here are four ways for different types of numbers:
1. If the sum of every other digit, starting with the first, is equal to the sum of every other digit starting with the second, then the number is evenly divisible by 11. Try 13057. 1+0+7 = 3+5, therefore it should divide evenly by 11. And indeed it does: 13057 / 11 = 1187. 2. If all the digits are the same and there's an even number of digits, then the number is evenly divisible by 11. 333,333 - Yes. 3,333,333 - No. 3. If the number is a 3 digit number with different digits, add the two outside digits. If the difference between the sum and the middle digit is 11 then 11 divides evenly into the 3 digit number. If the sum is the same as the middle digit, then 11 will also divide evenly into the number. Try 484. 4 + 4 = 8 which equals the middle digit so 11 divides into 484 evenly. How about 913? 9 + 3 = 12 and 12 - 1 = 11 so 913 is evenly divisible by 11. 4. If the digits are different, count them from the right and then add the numbers in the odd positions and the even positions. Subtract the smaller number from the larger. If the difference is evenly divisible by 11, so is your original number. Take the number 181,907. The numbers 8,9, and 7 are in the odd positions. They sum to 24. The numbers 1,1, and 0 are in the even positions. They sum to 2. Subtract 2 from 24 to get 22. 22 divides by 11 into 2, so 181,907 is evenly divisible by 11.
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