1. Express the following according to the 24 -hour clock: \( \begin{array}{lll}\text { (a) } 10: 15 \mathrm{a} . \mathrm{m} & \text { (b) } 9: 05 \mathrm{a} . \mathrm{m} & \text { (c) } 10: 00 \mathrm{a} . \mathrm{m}\end{array} \) \( \begin{array}{lll}\text { (e) } 6: 20 \mathrm{p} . \mathrm{m} & \text { (f) } 9: 45 \mathrm{p} . \mathrm{m} & \text { (g) } 11: 10 \mathrm{p} . \mathrm{m} \\ \text { (i) } 12: 15 \mathrm{p} . \mathrm{m} & \text { (j) } 12: 35 \mathrm{a} . \mathrm{m} & \end{array} \)

Sure! Here are the times expressed in the 24-hour clock format: \[ \begin{array}{lll} \text{(a) } 10:15 \, \text{a.m.} & \rightarrow & 10\:15 \\ \text{(b) } 9:05 \, \text{a.m.} & \rightarrow & 09\:05 \\ \text{(c) } 10:00 \, \text{a.m.} & \rightarrow & 10\:00 \\ \text{(e) } 6:20 \, \text{p.m.} & \rightarrow & 18\:20 \\ \text{(f) } 9:45 \, \text{p.m.} & \rightarrow & 21\:45 \\ \text{(g) } 11:10 \, \text{p.m.} & \rightarrow & 23\:10 \\ \text{(i) } 12:15 \, \text{p.m.} & \rightarrow & 12\:15 \\ \text{(j) } 12:35 \, \text{a.m.} & \rightarrow & 00\:35 \\ \end{array} \] **Explanation:** - **For a.m. times (before noon):** The 24-hour clock is the same as the 12-hour clock, except that times are often written with a leading zero for hours between 1 a.m. and 9 a.m. - **For p.m. times (afternoon and evening):** Add 12 to the hour component. - *Example:* - 6:20 p.m. → 18:20 - 9:45 p.m. → 21:45 - **Special Cases:** - 12:00 a.m. is written as 00:00. - 12:00 p.m. remains 12:00. - *Example:* - 12:15 p.m. → 12:15 - 12:35 a.m. → 00:35 I hope this helps!