Question

polygon k is a scaled copy of polygon j.
polygon j
polygon k
what scale factor takes polygon j to polygon k?
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Explanation:

Step1: Convert mixed number to improper fraction

$1\frac{1}{5}=\frac{1\times5 + 1}{5}=\frac{6}{5}$, $1\frac{3}{5}=\frac{1\times5+3}{5}=\frac{8}{5}$

Step2: Calculate the scale factor

The scale factor $k$ is the ratio of the corresponding side lengths of the scaled - copy (polygon $K$) to the original polygon (polygon $J$). Let's use the side lengths $3$ (from polygon $J$) and $1\frac{1}{5}=\frac{6}{5}$ (from polygon $K$).
$k=\frac{\frac{6}{5}}{3}=\frac{6}{5}\times\frac{1}{3}=\frac{2}{5}$

We can check with another pair of sides. Using side length $4$ (from polygon $J$) and $1\frac{3}{5}=\frac{8}{5}$ (from polygon $K$)
$k = \frac{\frac{8}{5}}{4}=\frac{8}{5}\times\frac{1}{4}=\frac{2}{5}$

Answer:

$\frac{2}{5}$