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avatar+199 

When n is divided by 5, the remainder is 1. What is the remainder when 3n is divided by 5? Can I have the explanation + solution

 Oct 6, 2019
 #1
avatar+199 
+1

It's pretty obvious that the remainder is 3 but what is the math behind it

 Oct 6, 2019
 #2
avatar+196 
+1

Let m be a multiple of 5.

 

n is one more than a multiple of 5, so n=m+1

3n=3(m+1)=3m+3

3m will always be a multiple of 5 because m is a multiple of 5, so the remainder is 3.

 Oct 6, 2019
 #3
avatar+2417 
0

You can also do some modulus, but Im too lazy for dat

CalculatorUser  Oct 6, 2019
 #4
avatar+105700 
+1

\(\frac{n}{5}=k+\frac{1}{5}\qquad \text{k is an integer}\\ n=5k+1\\ 3n=15k+3\\ \frac{3n}{5}=3k\quad Remainder\;3 \)

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 Oct 7, 2019

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