Question

Write the following ratios in ascending order:

$3˸5,5˸6,7˸87˸10$

Answer 1

Given:

$3˸5,5˸6,7˸87˸10$

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

LCM$(5,6,8,10)$$=120$

$\begin{array}{rcl}\frac{3}{5}& =& \frac{3}{5}\times \frac{24}{24}=\frac{72}{120}\\ \frac{5}{6}& =& \frac{5}{6}\times \frac{20}{20}=\frac{100}{120}\\ \frac{7}{8}& =& \frac{7}{8}\times \frac{15}{15}=\frac{105}{120}\\ \frac{7}{10}& =& \frac{7}{10}\times \frac{12}{12}=\frac{84}{120}\end{array}$

$$\begin{gathered} \Rightarrow \frac{72}{129}<\frac{84}{120}<\frac{100}{120}<\frac{105}{120} \\ \Rightarrow \frac{3}{5}<\frac{7}{10}<\frac{5}{6}<\frac{7}{8} \\ \Rightarrow \left(3˸5\right)<\left(7˸10\right)<\left(5˸6\right)<\left(7˸8\right) \end{gathered}$$

Hence, ascending order of $3˸5,5˸6,7˸87˸10$ is $\left(3˸5\right)<\left(7˸10\right)<\left(5˸6\right)<\left(7˸8\right)$