Answer: The largest ratio is (d) 1 : 3.
Step-by-step explanation: We are given to select the larges ratio among the given options.
The first ratio is
[tex]\dfrac{5}{36}.[/tex]
The second ratio is
[tex]2:9=\dfrac{2}{9}=\dfrac{2\times 4}{9\times 4}=\dfrac{8}{36}.[/tex]
The third ratio is
[tex]3\textup{ to }18=\dfrac{3}{18}=\dfrac{3\times 2}{18\times 2}=\dfrac{6}{36}.[/tex]
The fourth ratio is
[tex]1:3=\dfrac{1}{3}=\dfrac{1\times 12}{3\times 12}=\dfrac{12}{36}.[/tex]
Arranging all the ratios in ascending order, we have
[tex]\dfrac{5}{36},~\dfrac{6}{36},~\dfrac{8}{36},~\dfrac{12}{36}\\\\\\\Rightarrow \dfrac{5}{36},~\dfrac{3}{18},~\dfrac{2}{9},~\dfrac{1}{3}.[/tex]
Thus, the largest ratio is (d) 1 : 3.
