1. **State the problem:** Simplify the expression $\frac{8r}{10rw}$. 2. **Recall the formula and rules:** When simplifying fractions, divide numerator and denominator by their greatest common factor (GCF). Also, cancel common variables in numerator and denominator. 3. **Find the GCF of the coefficients:** The GCF of 8 and 10 is 2. 4. **Divide numerator and denominator by 2:** $$\frac{8r}{10rw} = \frac{8 \div 2 \cdot r}{10 \div 2 \cdot r w} = \frac{4r}{5rw}$$ 5. **Cancel the common variable $r$ in numerator and denominator:** $$\frac{4\cancel{r}}{5\cancel{r}w} = \frac{4}{5w}$$ 6. **Final simplified expression:** $$\frac{4}{5w}$$ This means the original expression simplifies to $\frac{4}{5w}$ by dividing coefficients by their GCF and canceling the common variable $r$.