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

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(17219) (Show Source): You can put this solution on YOUR website!

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since dividing N by 5 gives a remainder of 3, this means that where 'q' is the quotient (which is some whole number). Multiplying everything by 5 gets us

So . If we divide 7N by 5, we then get . In other words, . The remainder is , but it's too big which means that we need to break it up. So .

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

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Answer:

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

Note: Try some examples to give you an idea that it works.
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