Question 7036
 m = r (mod n) means  m =nq+r (mod n) where 0<=r < n. q as quotient, r as
 remainders. And the mod prerseves addition & multiplication.

1.  3+2 (mod 5) = 5 (mod 5) = 0 (mod 5)
2. 15-2(mod 5) = 13 (mod 5) = 3 (mod 5)
3. (3+2)+5(mod 6) = 10 (mod 6) = 4 (mod 6)
4. (12)(3) (mod 5) = 12 (mod 5) * 3 (mod 5) = 2 (mod 5) * 3 (mod 5)
   = 6 (mod 5)= 1 (mod 5).
5. 2(4+11)(mod7) = 30 (mod 7) = 2 (mod 7) 
6. 4cubed(mod12) [Never type cubed or squared any more]
  = 4^3 (mod 12) = 16* 4 (mod 12) = 16 (mod 12) * 4 (mod 12)
  = 4 (mod 12) * 4 (mod 12) = 16 (mod 12) = 4 (mod 12)

7. (624)(589)(mod 9)
  = 624 (mod 9) * 589 (mod 9)
  = (69* 9 + 3) (mod 9) * (65* 9 + 4) (mod 9)
  = 3 (mod 9) * 4 (mod 9)
  = 12 (mod 9)
  = 3 (mod 9)


 Try to use your eyes to calculate small numbers. 
 No calculators , even for the big numbers as (7):
 by reducing the two big numbers separately, you can get the answer right
 away.
 
 If some steps you don't understand, use your brains to think about it.
 Don't suppose mod is hard.


 Kenny