Answer: The correct option is
(C) n = fraction 1 over 2.
Step-by-step explanation: We are to find the simplified form of the fraction 4 over 5 n minus fraction 1 over 5 equals fraction 2 over 5 n.
From the given information, we can write the equation as follows:
\(\dfrac{4}{5}n-\dfrac{1}{5}=\dfrac{2}{5}n.\)
Solving the above equation, we get
\(\dfrac{4}{5}n-\dfrac{1}{5}=\dfrac{2}{5}n\\\\\\\Rightarrow \dfrac{4}{5}n-\dfrac{2}{5}n=\dfrac{1}{5}\\\\\\\Rightarrow \dfrac{4-2}{5}n=\dfrac{1}{5}\\\\\\\Rightarrow \dfrac{2}{5}n=\dfrac{1}{5}\\\\\\\Rightarrow n=\dfrac{5}{2\times 5}\\\\\\\Rightarrow n=\dfrac{1}{2}.\)
Thus, the required simplified form is \(n=\dfrac{1}{2}.\)
Option (C) is CORRECT.
