$$ \begin{aligned} \frac{1}{3} &= \frac{5}{6}+p&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot\frac{1}{3} &= 6\cdot\frac{5}{6}+6p&& \text{cancel out the denominators} \\[1 em]2 &= 5+6p&& \text{ swap the left and right side of the equation } \\[1 em]5+6p &= 2&& \text{ move 5 to the right } \\[1 em]6p &= 2-5&& \\[1 em]6p &= -3&& \text{ divide both sides by $ 6 $ } \\[1 em]p &= -\frac{3}{6}&& \\[1 em]p &= -\frac{1}{2}&& \\[1 em] \end{aligned} $$

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