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casting out nines

casting out nines. Pamela Leutwyler. 9 goes into 36 four times with remainder 0. 3 + 6 = 9. 9 goes into 36 four times with remainder 0. 3 + 6 = 9. 9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9. 9 goes into 36 four times with remainder 0. 3 + 6 = 9.

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casting out nines

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  1. casting out nines Pamela Leutwyler

  2. 9 goes into 36 four times with remainder 0. 3 + 6 = 9

  3. 9 goes into 36 four times with remainder 0. 3 + 6 = 9 9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9

  4. 9 goes into 36 four times with remainder 0. 3 + 6 = 9 9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9 The sum of the digits of a multiple of 9 is 9 (or a multiple of 9).

  5. 9 goes into 36 four times with remainder 0. 3 + 6 = 9 9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9 The sum of the digits of a multiple of 9 is 9 (or a multiple of 9). 9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2

  6. 9 goes into 36 four times with remainder 0. 3 + 6 = 9 9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9 The sum of the digits of a multiple of 9 is 9 (or a multiple of 9). 9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2 9 goes into 49 five times with remainder 4. 4 + 9 = 13 1 +3 = 4

  7. 9 goes into 36 four times with remainder 0. 3 + 6 = 9 9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9 The sum of the digits of a multiple of 9 is 9 (or a multiple of 9). 9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2 9 goes into 49 five times with remainder 4. 4 + 9 = 13 1 +3 = 4 9 goes into 253 twenty eight times with remainder 1. 2+5+3 = 10 1 +0 = 1

  8. 9 goes into 36 four times with remainder 0. 3 + 6 = 9 9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9 The sum of the digits of a multiple of 9 is 9 (or a multiple of 9). 9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2 9 goes into 49 five times with remainder 4. 4 + 9 = 13 1 +3 = 4 9 goes into 253 twenty eight times with remainder 1. 2+5+3 = 10 1 +0 = 1 The sum of the digits of any whole number = the remainder when that number is divided by 9. If the sum of the digits is > 9, add the digits again.

  9. 9 goes into 36 four times with remainder 0. 3 + 6 = 9 9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9 The sum of the digits of a multiple of 9 is 9 (or a multiple of 9). 9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2 9 goes into 49 five times with remainder 4. 4 + 9 = 13 1 +3 = 4 9 goes into 253 twenty eight times with remainder 1. 2+5+3 = 10 1 +0 = 1 The sum of the digits of any whole number = the remainder when that number is divided by 9. 253 = 2x100 + 5x10 + 3 = 2x(99+1) + 5x(9+1) + 3 = 2x99 + 2x1+ 5x9 + 5x1+3

  10. The sum of the digits of any whole number = the remainder when that number is divided by 9. When dividing by 9, getting a remainder of 9 is the same as getting a remainder of 0.

  11. The sum of the digits of any whole number = the remainder when that number is divided by 9. When dividing by 9, getting a remainder of 9 is the same as getting a remainder of 0. For example: You could say that 9 goes into 27 two times with a remainder of 9 or You could say that 9 goes into 27 three times with a remainder of 0

  12. Casting out nines an algorithm for checking computation

  13. Is the following sum correct?

  14. Is the following sum correct? In theory, the sum of the remainders should equal the remainder when the sum is divided by 9. 1 8 3 5 1+8+3+5=17 and 1+7 = 8 8

  15. Shorten the process: Is the following sum correct? In theory, the sum of the remainders should equal the remainder when the sum is divided by 9. 1 8 3 5 8 All of these numbers are added so there is no need to separate them Also a remainder of 9 is the same as a remainder of 0. Where you see 9, cross it out.

  16. Cast out NINES Is the following sum correct?

  17. Cast out NINES Is the following sum correct?

  18. Cast out NINES Is the following sum correct?

  19. Cast out NINES Is the following sum correct?

  20. Cast out NINES Is the following sum correct? The sum is probably correct. There is 1 chance in 9 that the numbers would match by chance. If the numbers do not match then you have found an error.

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