$$ \begin{aligned} \frac{4}{16}+x+100 &= 0&& \text{multiply ALL terms by } \color{blue}{ 16 }. \\[1 em]16\cdot\frac{4}{16}+16x+16\cdot100 &= 16\cdot0&& \text{cancel out the denominators} \\[1 em]4+16x+1600 &= 0&& \text{simplify left side} \\[1 em]16x+1604 &= 0&& \text{ move the constants to the right } \\[1 em]16x &= -1604&& \text{ divide both sides by $ 16 $ } \\[1 em]x &= -\frac{1604}{16}&& \\[1 em]x &= -\frac{401}{4}&& \\[1 em] \end{aligned} $$

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