2 3 + ( 6 7 − 9 7 ) ⋅ ( 2 5 − 16 21 : 4 7 ) {\displaystyle {\frac {2}{3}}+\left({\frac {6}{7}}-{\frac {9}{7}}\right)\cdot \left({\frac {2}{5}}-{\frac {16}{21}}:{\frac {4}{7}}\right)}
6 7 − 9 7 = 6 − 9 7 = − 3 7 {\displaystyle {\frac {6}{7}}-{\frac {9}{7}}={\frac {6-9}{7}}=-{\frac {3}{7}}}
2 5 − 16 21 : 4 7 {\displaystyle {\frac {2}{5}}-{\frac {16}{21}}:{\frac {4}{7}}}
2 5 − 16 21 : 4 7 = 2 5 − 16 21 ⋅ 7 4 = 2 5 − 16 ⋅ 7 21 ⋅ 4 {\displaystyle {\frac {2}{5}}-{\frac {16}{21}}:{\frac {4}{7}}={\frac {2}{5}}-{\frac {16}{21}}\cdot {\frac {7}{4}}={\frac {2}{5}}-{\frac {16\cdot 7}{21\cdot 4}}}
2 5 − 16 4 ⋅ 7 21 ⋅ 4 1 = 2 5 − 4 ⋅ 7 1 21 3 ⋅ 1 = 2 5 − 4 3 {\displaystyle {\frac {2}{5}}-{\frac {{\cancelto {4}{16}}\cdot 7}{21\cdot {\cancelto {1}{4}}}}={\frac {2}{5}}-{\frac {4\cdot {\cancelto {1}{7}}}{{\cancelto {3}{21}}\cdot 1}}={\frac {2}{5}}-{\frac {4}{3}}}
( Vorgang: 2 5 − _ 4 3 ) {\displaystyle \textstyle \left(^{\text{Vorgang: }}{\frac {2}{5}}{\underline {\xcancel {-}}}{\frac {4}{3}}\right)\quad } = 2 ⋅ 3 − 4 ⋅ 5 5 ⋅ 3 = 6 − 20 15 = − 14 15 {\displaystyle ={\frac {2\cdot 3-4\cdot 5}{5\cdot 3}}={\frac {6-20}{15}}=-{\frac {14}{15}}}
2 3 + ( 6 7 − 9 7 ) − 3 7 ⋅ ( 2 5 − 16 21 : 4 7 ) − 14 15 = {\displaystyle {\frac {2}{3}}+{\cancelto {-{\frac {3}{7}}}{\left({\frac {6}{7}}-{\frac {9}{7}}\right)}}\cdot {\cancelto {-{\frac {14}{15}}}{\left({\frac {2}{5}}-{\frac {16}{21}}:{\frac {4}{7}}\right)}}=}
2 3 + ( − 3 7 ) ⋅ ( − 14 15 ) {\displaystyle {\frac {2}{3}}+\left(-{\frac {3}{7}}\right)\cdot \left(-{\frac {14}{15}}\right)}
2 3 + 3 1 ⋅ 14 2 7 1 ⋅ 15 5 {\displaystyle {\frac {2}{3}}+{\frac {{\cancelto {1}{3}}\cdot {\cancelto {2}{14}}}{{\cancelto {1}{7}}\cdot {\cancelto {5}{15}}}}} (hier erst kürzen) = 2 3 + 1 ⋅ 2 1 ⋅ 5 = 2 3 + 2 5 = {\displaystyle ^{\text{(hier erst kürzen)}}={\frac {2}{3}}+{\frac {1\cdot 2}{1\cdot 5}}={\frac {2}{3}}+{\frac {2}{5}}=}
2 ⋅ 5 + 2 ⋅ 3 3 ⋅ 5 = 16 15 {\displaystyle {\frac {2\cdot 5+2\cdot 3}{3\cdot 5}}={\frac {16}{15}}}
