Write each of these ratios in its simplest form: \( \begin{array}{ll}\text { (a) } 3: 12=1: 4 & \text { (b) } 4: 30 \\ \text { (d) } 9: 21= & \text { (e) } 8: 64 \\ \text { (g) } 6: 22 & \text { (h) } 11: 99\end{array} \)

To simplify each of the given ratios, we divide both parts of the ratio by their greatest common divisor (GCD). (a) \( 3:12 \) The GCD of 3 and 12 is 3. \[ \frac{3}{3} : \frac{12}{3} = 1:4 \] (b) \( 4:30 \) The GCD of 4 and 30 is 2. \[ \frac{4}{2} : \frac{30}{2} = 2:15 \] (d) \( 9:21 \) The GCD of 9 and 21 is 3. \[ \frac{9}{3} : \frac{21}{3} = 3:7 \] (e) \( 8:64 \) The GCD of 8 and 64 is 8. \[ \frac{8}{8} : \frac{64}{8} = 1:8 \] (g) \( 6:22 \) The GCD of 6 and 22 is 2. \[ \frac{6}{2} : \frac{22}{2} = 3:11 \] (h) \( 11:99 \) The GCD of 11 and 99 is 11. \[ \frac{11}{11} : \frac{99}{11} = 1:9 \] In summary, the simplified forms of the ratios are: - (a) \( 1:4 \) - (b) \( 2:15 \) - (d) \( 3:7 \) - (e) \( 1:8 \) - (g) \( 3:11 \) - (h) \( 1:9 \)