Find the sub-duplicate ratio of (i) \[\mathbf{9}:\text{ }\mathbf{16}\] (ii) \[{\scriptscriptstyle 1\!/\!{ }_4}:\text{ }\mathbf{1}/\mathbf{9}\]

(i) \[\mathbf{9}:\text{ }\mathbf{16}\]

We know that

Sub-duplicate ratio of \[9:\text{ }16\text{ }=\text{ }\surd 9:\text{ }\surd 16\text{ }=\text{ }3:\text{ }4\]

(ii) \[{\scriptscriptstyle 1\!/\!{ }_4}:\text{ }1/9\]

We know that

Sub-duplicate ratio of \[{\scriptscriptstyle 1\!/\!{ }_4}:\text{ }1/9\text{ }=\text{ }\surd 1/4:\text{ }\surd 1/9\]

So we get

\[\begin{array}{*{35}{l}}

=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}:\text{ }1/3  \\

=\text{ }3:\text{ }2  \\

\end{array}\]