Question

Arrange $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$,$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$,$\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$, $\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$6$}\right.$ in ascending order.

Answer 1

step-1

Take the LCM of denominator $2,3,4,6$

it will be $=12$

step-2

Now$\raisebox{1ex}{$1\times 6$}\!\left/ \!\raisebox{-1ex}{$2\times 6$}\right.$ $\raisebox{1ex}{$1\times 4$}\!\left/ \!\raisebox{-1ex}{$3\times 4$}\right.$ $\raisebox{1ex}{$3\times 3$}\!\left/ \!\raisebox{-1ex}{$4\times 3$}\right.$$\raisebox{1ex}{$5\times 2$}\!\left/ \!\raisebox{-1ex}{$6\times 2$}\right.$

$\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$12$}\right.$ $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$12$}\right.$$\raisebox{1ex}{$9$}\!\left/ \!\raisebox{-1ex}{$12$}\right.$ $\raisebox{1ex}{$10$}\!\left/ \!\raisebox{-1ex}{$12$}\right.$

In these fraction the fraction which has a greater the value of numerator has the greatest fraction and the smaller the value of numerator has smallest fraction.

$$\begin{gathered} \raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$12<{\displaystyle \raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$12<{\displaystyle \raisebox{1ex}{$9$}\!\left/ \!\raisebox{-1ex}{$12<{\displaystyle \raisebox{1ex}{$10$}\!\left/ \!\raisebox{-1ex}{$12$}\right.}$}\right.}$}\right.}$}\right. \\ \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3<{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2<{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4<{\displaystyle \raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$12$}\right.}$}\right.}$}\right.}$}\right. \end{gathered}$$