How to calculate a Modulo? I really can't get my head around this "modulo" thing. 
Can someone show me a general step-by-step procedure on how I would be able to find out the 5 modulo 10, or 10 modulo 5. 
Also, what does this mean: 1/17 = 113 modulo 120 ? 
Because when I calculate(using a calculator) 113 modulo 120, the result is 113. But what is the 1/17 standing for then? 
THANK YOU! 

Modulo is counting when knowing only a limited amount of numbers. E.g. modulo three, instead of counting 
$$0,1,2,3,4,5,6,7,8,9,10,11,...$$
you count
$$
\underset{\color{lightgray}0}0,
\underset{\color{lightgray}1}1,
\underset{\color{lightgray}2}2,\;\;
\underset{\color{lightgray}3}0,
\underset{\color{lightgray}4}1,
\underset{\color{lightgray}5}2,\;\;
\underset{\color{lightgray}6}0,
\underset{\color{lightgray}7}1,
\underset{\color{lightgray}8}2,\;\;
\underset{\color{lightgray}9}0,
\underset{\color{lightgray}{10}}1,
\underset{\color{lightgray}{11}}2,...$$
As you can see, you will end up at zero whenever the actual number is divisible by three. So finding the nearest multiples of three will help you to find its value moldulo three.
Example. $362$ is close to $360=3\times 120$. Since it is two larger than $360$, it is equivalent to $2$ modulo three. As explained in the other answers you could have found this using division with rest.
The "$1/17$ modulo $120$" is just a short form of the question "what number $x\in\{1,...,119\}$ do I have to multiply by $17$ so that the result $17x$ is equivalent to $1$ modulo $120$?". In this case, it is $113$.
