1. Pamela Leutwyler

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

3. 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. 271 395 642 +977 2285 Is the following sum correct?

14. 271 395 642 +977 2285 In theory, the sum of the remainders should equal the remainder when the sum is divided by 9. 1 8 3 5 8 1+8+3+5=17 and 1+7 = 8

15. 271 395 642 +977 2285 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 Shorten the process: 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. 271 395 642 +977 2285 Is the following sum correct? Cast out NINES

17. 271 395 642 +977 2285 Is the following sum correct? Cast out NINES

18. 271 395 642 +977 2285 Is the following sum correct? Cast out NINES

19. 271 395 642 +977 2285 Is the following sum correct? Cast out NINES

20. 271 395 642 +977 2285 Is the following sum correct? Cast out NINES 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.