Yes you are correct! :)
Step 1. Simplify \(\frac{1}{15} * \frac{-10}{13}\) to \(- \frac{1}{15}* \frac{10}{13}\)
\(\frac{1}{15} * \frac{10}{13}\)
Step 2. Apply this rule \(\frac{a}{b} * \frac{c}{d} = \frac{ac}{db}\)
\(\frac{1*10}{15*13}\)
Step 3. Simplify \(1*10\) to \(10\)
\(\frac{10}{15*13}\)
Step 4. Simplify \(15*13\) to \(195\)
\(\frac{10}{195}\)
Step 5. Simplify
\(\frac{2}{39}\)
Done! :) Your answer is \(\frac{2}{39}\)