54 mod 4

[Bella]

Professor Loh told us 27 + 27 (mod 4) = 3 + 3, which equals 6. The calculator says 27 + 27 (mod 4) = 2. Why?

[studiouszebra]

See I don't have module 5 but I know some mod.
27 mod 4 = 3:
because
27 = 6 * 4 + 3

and
54 = 13 * 4 + 2
now
54 = 27 + 27 = (6 * 4 + 3) + (6 * 4 + 3)
54 = (6 * 4 ) + (6 * 4 ) + (3 + 3)
54 = (6 * 4 ) + (6 * 4 ) + 4 + 2
54 = 4( 12 + 1) + 2

54 = 13 * 4 + 2
And I don't know Professor said that but I thought this would work.
Sorry if I misunderstood.

[pulleybear]

@Bella Both are actually correct. I believe Professor Loh first found 27 (mod 4) to be 3, and then doubled this to get 6. Professor Loh is emphasizing the simplification step, which makes working with larger numbers easier. And if we simplify this further, 6 is 2 (mod 4). So your calculator is not wrong; 27 + 27 is 2 (mod 4). But noting Professor Loh's strategy will help you solve these types of problems more efficiently