## Basic College Mathematics (9th Edition)

The multiplication shortcut is simply dividing a numerator and a denominator by their common factor. Example: $\frac{3}{5} \cdot \frac{35}{7} = \frac{3}{1} \cdot \frac{7}{7}$. Here we divided the numerator $35$ and the denominator $5$ by their common factor $5$. Next, we divide the numerator $7$ and the denominator $7$ by their common factor $7$: $\frac{3}{1} \cdot \frac{7}{7} = \frac{3}{1} \cdot \frac{1}{1}$. There is further simplification possible, so the answer is $\frac{3}{5} \cdot \frac{35}{7} = \frac{3}{1} \cdot \frac{7}{7} = \frac{3}{1} \cdot \frac{1}{1} = 3$.