Question

Arrange the following ratios in ascending order of magnitude:

$2:3,17:21,11:14\mathrm{and}5:7$.

Answer 1

Step1: Making the denominator same of each ratio.

The given ratios can be written in fraction form as $\frac{2}{3},\frac{17}{21},\frac{11}{14}\mathrm{and}\frac{5}{7}$.

The L.C.M. of 3, 21, 14 and 7 is 42.

Make the denominator of each ratio as 42 by multiplying and dividing by a suitable factor.

$\begin{array}{rcl}\frac{2\times 14}{3\times 14}& =& \frac{28}{42}\\ \frac{17\times 2}{21\times 2}& =& \frac{34}{42}\\ \frac{11\times 3}{14\times 3}& =& \frac{33}{42}\\ \frac{5\times 6}{7\times 6}& =& \frac{30}{42}\end{array}$

Step2: Comparison between ratios by comparing the numerators

$$\begin{gathered} \mathrm{Since}28<30<33<34\Rightarrow \frac{28}{42}<\frac{30}{42}<\frac{33}{42}<\frac{34}{42} \\ \Rightarrow \frac{2}{3}<\frac{5}{7}<\frac{11}{14}<\frac{17}{21} \end{gathered}$$

Final Answer: The ratios in ascending order is $2:3,5:7,11:14,17:21$.