$$ \begin{aligned} \frac{1}{2}a\cdot8 &= \frac{1}{4}a\cdot1&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{2}a\cdot8 &= 4 \cdot \frac{1}{4}a\cdot1&& \text{cancel out the denominators} \\[1 em]16a &= a&& \text{move the $ \color{blue}{ a } $ to the left side} \\[1 em]16a-a &= 0&& \text{simplify left side} \\[1 em]15a &= 0&& \text{ divide both sides by $ 15 $ } \\[1 em]a &= \frac{0}{15}&& \\[1 em]a &= 0&& \\[1 em] \end{aligned} $$

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