To simplify ratios, we have to divide each part of the ratio by a common factor. The common factor for the first ratio is 3, and the common factor for the second ratio is 9.
![\begin{gathered} 12\colon21\Rightarrow(12)/(3)\colon(21)/(3)\Rightarrow4\colon7 \\ 9\colon18\Rightarrow(9)/(9)\colon(18)/(9)\Rightarrow1\colon2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/1s2flftbtw8kol54ba1bo8ok70cs90uige.png)
Therefore, the first simplified ratio is 4:7 and the second simplified ratio is 1:2.