Simplify $15 \cdot \frac{7}{10} \cdot \frac{1}{9}$.
To simplify a product of fractions, I can use the rule that multiplying fractions is the same as multiplying the numerators and multiplying the denominators. So, $15 \cdot \frac{7}{10} \cdot \frac{1}{9} = \frac{15 \cdot 7}{10 \cdot 9}$. Now, I can simplify the fraction by canceling out any common factors in the numerator and denominator. I notice that 15 and 10 have a common factor of 5, so I can divide both by 5 to get 3 and 2. This gives me $\frac{3 \cdot 7}{2 \cdot 9} = \frac{21}{18}$. Finally, I can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 3. This gives me $\frac{21}{18} = \frac{7}{6}$. This is the simplest form of the fraction, so I'm done. 