Question
Find the fourth proportional to $\frac{1}{3}, \frac{1}{4}, \frac{1}{5}$
✓
Answer
Let fourth proportional to $\frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ be $x$
then $\frac{1}{3}: \frac{1}{4}:: \frac{1}{5}: x$
$\Rightarrow \frac{1}{3} \times x=\frac{1}{4} \times \frac{1}{5}$
$\Rightarrow x=\frac{1}{4} \times \frac{1}{5} \times \frac{3}{1}=\frac{3}{20}$.
then $\frac{1}{3}: \frac{1}{4}:: \frac{1}{5}: x$
$\Rightarrow \frac{1}{3} \times x=\frac{1}{4} \times \frac{1}{5}$
$\Rightarrow x=\frac{1}{4} \times \frac{1}{5} \times \frac{3}{1}=\frac{3}{20}$.
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