Question

What is a simple way to find 12 mod 7 + 12 mod 7 + 12 mod 7 + 12 mod 7?

Answer 1

12 ≡ 7 + 5 ≡ 5 (mod 7)

so

12 + 12 + 12 + 12 ≡ 4•12 ≡ 4•5 ≡ 20 ≡ 14 + 6 ≡ 6 (mod 7)