Question

write the steps you will follow to show that a number is divisible by 11 after taking the sum of an original number and reversed number​

Answer 1

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You've probably already noticed a pattern with some multiples of 11. The two digit numbers are easy to recognize: 11, 22, 33, 44, and so on. But once you get to larger numbers, it's difficult to recognize them at a glance. Fortunately, there are a couple of rules you can learn that work with numbers of any size, that don't require any math skills besides simple addition and subtraction:

1. Write the number with spaces in digits. For example, if you want to know whether 10,516 is divisible by 11, write the number between like this:

1 0 5 1 6 subtraction.

2. Write a + sign in front of the first digit. For example:

+1 0 5 1 6

3. Write a - sign in front of the next digit. Your paper should now look like this:[1]

+1 - 0 5 1 6

4. Keep alternating the + and - signs for all digits. Add a + sign in front of the third digit, then a - sign in front of the fourth, and so on until you reach the end:[2]

5. Add and subtract the digits. Now treat this like any arithmetic problem, adding and subtracting the digits together:[3]

+1 - 0 + 5 - 1 + 6

= 11

6. Check your answer. These simple rules tell you whether the original number is divisible by 11:[4]

If your answer is divisible by 11 (0, 11, 22, etc.), the original number is also divisible by 11. Keep in mind that 0 is a multiple of 11, since 11 * 0 = 0.

If your answer is not a multiple of 11, the original number is not divisible by 11.

The answer was 11, which is a multiple of 11.

Therefore, the original number 10,516 is divisible by 11.