5 13 − 2 13 {\displaystyle \ {\frac {5}{13}}-{\frac {2}{13}}\ } = 5 − 2 13 = 3 13 {\displaystyle ={\frac {5-2}{13}}={\frac {3}{13}}\qquad }
5 4 + 2 3 {\displaystyle \ {\frac {5}{4}}+{\frac {2}{3}}\ } = {\displaystyle =} = 5 ⋅ 3 + 2 ⋅ 4 3 ⋅ 4 = 15 + 8 12 = 23 12 {\displaystyle ={\frac {5\cdot 3+2\cdot 4}{3\cdot 4}}={\frac {15+8}{12}}={\frac {23}{12}}}
5 4 ⋅ 3 7 {\displaystyle {\frac {5}{4}}\cdot {\frac {3}{7}}} = 5 ⋅ 3 4 ⋅ 7 = 15 28 {\displaystyle ={\frac {5\cdot 3}{4\cdot 7}}={\frac {15}{28}}}
5 4 : 3 7 {\displaystyle \ {\frac {5}{4}}:{\frac {3}{7}}\ } = 5 4 ⋅ 7 3 = 5 ⋅ 7 4 ⋅ 3 = 35 12 {\displaystyle \ ={\frac {5}{4}}\cdot {\frac {7}{3}}={\frac {5\cdot 7}{4\cdot 3}}={\frac {35}{12}}\qquad } ( 7 3 {\displaystyle \textstyle {\frac {7}{3}}} ist der Kehrwert von 3 7 {\displaystyle \textstyle {\frac {3}{7}}} )
