Simplify $\frac{1}{5}\cdot \frac{8}{7}\div \frac{12}{20}$.
Dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the expression as $\frac{1}{5} \cdot \frac{8}{7} \cdot \frac{20}{12}$. When multiplying fractions, we multiply the numerators and the denominators. So we have $\frac{1 \cdot 8 \cdot 20}{5 \cdot 7 \cdot 12}$. That reduces to $\frac{160}{420}$ And dividing the numerator and denominator by 20 we get $\frac{8}{21}$. Right, so $\frac{1}{5}\cdot \frac{8}{7}\div \frac{12}{20} = \frac{8}{21}$.

