Сравните значения выражений: 1/5+1/3 и 1/6+1/2.

Ответ:

\[\frac{1}{5} + \frac{1}{3}\ \ \ и\ \ \ \frac{1}{6} + \frac{1}{2}\]

\[\frac{1^{\backslash 3}\ }{5} + \frac{1^{\backslash 5}}{3} = \frac{3 + 5}{15} = \frac{8}{15}\]

\[\frac{1}{6} + \frac{1^{\backslash 3}}{2} = \frac{1 + 3}{6} = \frac{4}{6} = \frac{2}{3} = \frac{10}{15}\]

\[\frac{8}{15} < \frac{10}{15}\]

\[\Longrightarrow \frac{1}{5} + \frac{1}{3} < \frac{1}{6} + \frac{1}{2}.\]