12. Do the following problems in clock arithmetic mod 8, if possible. If not possible, state so.

 

a) 5 + 7 = 4, from the table

b) 2 - 6 = 4, reading the addition table backwards.

c) 4 x 5 = 4 from the table.

d) 7 / 3 = 5 by reading the multiplication table backwards.

e) 5 / 4 cannot be done. There is no multiple of 4 which is equal to 5. All of the multiples of 4 are either 0 or 4 in clock arithmetic modulo 8

f) 5x5x5x5 = (5x5)x(5x5). From the table, 5x5 = 1, so this becomes 1x1 = 1.