Aus Online Mathematik Brückenkurs 1

2, 3/5, 5/3 and 7/3 .

It is easier to see the mutual order of the numbers if we write them as decimals.

Because we know that \displaystyle {1}/{5}\;=0.2 and \displaystyle {1}/{3}\;=0.333..., we obtain

\displaystyle \begin{align} & \frac{3}{5}=3\centerdot \frac{3}{5}=3.02=0.6 \\ & \\ & \frac{5}{3}=\frac{3+2}{3}=1+\frac{2}{3}=1.666... \\ & \\ & \frac{7}{3}=\frac{6+1}{3}=2+\frac{1}{3}=2.333... \\ \end{align}

and then we see that.

\displaystyle \begin{align} & \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3} \\ & \\ \end{align}