Question

Check whether the given ratios are equal i.e., they are in proportion. If yes, then write them in the proper form $4:12\mathrm{and}9:27$

Answer 1

We have,

$4:12\mathrm{and}9:27$

$\begin{array}{rcl}4:12& =& \frac{4}{12}\\ & =& \frac{4÷4}{12÷4}[\mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}4]\\ & =& \frac{1}{3}\\ & =& 1:3\end{array}$

$\begin{array}{rcl}9:27& =& \frac{9}{27}\\ & =& \frac{9÷9}{27÷9}[\mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}9]\\ & =& \frac{1}{3}\\ & =& 1:3\end{array}$

We get, $4:12=9:27$

Thus, the given ratios are equal i.e. they are in proportion and proper form is $4:12::9:27$.