Question

Write the following ratios in descending order:

$4˸7,5˸14,3˸141˸3$

Answer 1

Given:

$4˸7,5˸14,3˸141˸3$

Convert the ratios to fractions and make their denominator equal to compare.

LCM$(7,14,14,3)$$=42$

$\begin{array}{rcl}\frac{4}{7}& =& \frac{4}{7}\times \frac{6}{6}=\frac{24}{42}\\ \frac{5}{14}& =& \frac{5}{14}\times \frac{3}{3}=\frac{15}{42}\\ \frac{3}{14}& =& \frac{3}{14}\times \frac{3}{3}=\frac{9}{42}\\ \frac{1}{3}& =& \frac{1}{3}\times \frac{14}{14}=\frac{14}{42}\end{array}$

$$\begin{gathered} \Rightarrow \frac{24}{42}>\frac{15}{42}>\frac{14}{42}>\frac{9}{42} \\ \Rightarrow \frac{4}{7}>\frac{5}{14}>\frac{1}{3}>\frac{3}{14} \\ \Rightarrow \left(4˸7\right)>\left(5˸14\right)>\left(1˸3\right)>\left(3˸14\right) \end{gathered}$$

Hence, descending order of $4˸7,5˸14,3˸141˸3$ is $\left(4˸7\right)>\left(5˸14\right)>\left(1˸3\right)>\left(3˸14\right)$