$$\frac{203}{1000} = \frac{1}{5}+x$$

$$ \begin{aligned} \frac{203}{1000} &= \frac{1}{5}+x&& \text{multiply ALL terms by } \color{blue}{ 1000 }. \\[1 em]1000\cdot\frac{203}{1000} &= 1000\cdot\frac{1}{5}+1000x&& \text{cancel out the denominators} \\[1 em]203 &= 200+1000x&& \text{ swap the left and right side of the equation } \\[1 em]200+1000x &= 203&& \text{ move 200 to the right } \\[1 em]1000x &= 203-200&& \\[1 em]1000x &= 3&& \text{ divide both sides by $ 1000 $ } \\[1 em]x &= \frac{3}{1000}&& \\[1 em] \end{aligned} $$

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