SOLUTION: when N is divided by 5, the remainder is 3. what is the remainder when 7N is divided by 5?

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Question 252512: when N is divided by 5, the remainder is 3. what is the remainder when 7N is divided by 5?
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(9135) About Me  (Show Source):
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!
Since dividing N by 5 gives a remainder of 3, this means that N%2F5=q%2B3%2F5 where 'q' is the quotient (which is some whole number). Multiplying everything by 5 gets us N=5q%2B3


So 7N=7%285q%2B3%29=35q%2B21. If we divide 7N by 5, we then get 7N%2F5=%2835q%2B21%29%2F5=%2835q%29%2F5%2B21%2F5=7q%2B21%2F5. In other words, 7N%2F5=7q%2B21%2F5. The remainder is 21%2F5, but it's too big which means that we need to break it up. So 21%2F5=%2820%2B1%29%2F5=20%2F5%2B1%2F5=4%2B1%2F5.

Since the fractional portion is 1%2F5, this tells us that the remainder is 1.

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Answer:

So the remainder of dividing 7N by 5 is 1.


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