1. The problem asks us to simplify the fractions $\frac{8}{24}$ and $\frac{16}{56}$ to their lowest terms. 2. To simplify a fraction, we divide the numerator and denominator by their greatest common divisor (GCD). 3. For $\frac{8}{24}$, find the GCD of 8 and 24. $$\text{GCD}(8,24) = 8$$ 4. Divide numerator and denominator by 8: $$\frac{8}{24} = \frac{\cancel{8}^1}{\cancel{24}^3} = \frac{1}{3}$$ 5. For $\frac{16}{56}$, find the GCD of 16 and 56. $$\text{GCD}(16,56) = 8$$ 6. Divide numerator and denominator by 8: $$\frac{16}{56} = \frac{\cancel{16}^2}{\cancel{56}^7} = \frac{2}{7}$$ 7. Therefore, the simplified fractions are: $$\frac{8}{24} = \frac{1}{3}$$ $$\frac{16}{56} = \frac{2}{7}$$