SOLUTION: The remainder when an integer r is divided by 13 is 7. What is the remainder when 3r is divided by 13?

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Question 883075: The remainder when an integer r is divided by 13 is 7. What is the remainder when 3r is divided by 13?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
r/13 = q + 7/13
r = 13q + 7
3r = 3*(13q + 7)
3r = 3*(13q) + 3*(7)
3r = 39q + 21
3r/13 = (39q + 21)/13
3r/13 = 39q/13 + 21/13
3r/13 = 39q/13 + 21/13
3r/13 = 3q + 21/13
3r/13 = 3q + (13+8)/13
3r/13 = 3q + 13/13 + 8/13
3r/13 = 3q + 1 + 8/13

So the remainder is 8