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We removed all cards above 9 so we are working with 1 – 9. By replacing all two digit numbers with a one digit number we are replacing each number with its equivalent in mod 9. In mod9 math, 10 = 1(mod 9). Throughout the activity numbers are added together and changed to their equivalent in mod 9. The positions having values of 1 and 10 are actually both equal to 1. So that is why you can add these positions together. To add in the two cards in the 5 positions you need to first multiply them by 5. This total is then changed to a mod 9 number. In our case you added 6 + 4 + 5 + 3. This is 18 or equal to 9 in mod 9. Then add the 2 and 4 together, multiply by the position to get 30. 30 = 3 mod 9. Add 9 and 3 to get 12 which equals 3 mod 9. |
