1. **State the problem:** Simplify the given fractions and check the equality $\frac{8}{12} = \frac{2}{2}$.\n\n2. **Simplify each fraction:**\n- $\frac{3}{5}$ is already in simplest form.\n- $\frac{4}{7}$ is already in simplest form.\n- $\frac{8}{72}$ can be simplified by dividing numerator and denominator by 8:\n$$\frac{8}{72} = \frac{\cancel{8}^1}{\cancel{8}^9} = \frac{1}{9}$$\n- $\frac{16}{38}$ can be simplified by dividing numerator and denominator by 2:\n$$\frac{16}{38} = \frac{\cancel{2}^8}{\cancel{2}^{19}} = \frac{8}{19}$$\n- $\frac{8}{12}$ can be simplified by dividing numerator and denominator by 4:\n$$\frac{8}{12} = \frac{\cancel{4}^2}{\cancel{4}^3} = \frac{2}{3}$$\n\n3. **Check the equality:** The problem states $\frac{8}{12} = \frac{2}{2}$. Simplify the right side:\n$$\frac{2}{2} = 1$$\nSince $\frac{8}{12} = \frac{2}{3} \neq 1$, the equality is false.\n\n**Final answer:**\n- $\frac{3}{5}$ and $\frac{4}{7}$ are in simplest form.\n- $\frac{8}{72} = \frac{1}{9}$\n- $\frac{16}{38} = \frac{8}{19}$\n- $\frac{8}{12} = \frac{2}{3}$\n- The equality $\frac{8}{12} = \frac{2}{2}$ is false because $\frac{2}{3} \neq 1$.