Betrachte ${\displaystyle \frac{1}{2}}\backslash dfrac\{1\}\{2\}$: ${\displaystyle \frac{1+6}{2+2}}={\displaystyle \frac{7}{4}}\mathrm{\ne }{\displaystyle \frac{1+1}{2}}=1\backslash dfrac\{1+6\}\{2+2\}=\; \backslash dfrac\{7\}\{4\}\backslash neq\; \backslash dfrac\{1+1\}\{2\}=1$ Falsch!

Betrachte ${\displaystyle \frac{3}{7}}:\backslash dfrac\{3\}\{7\}:$ ${\displaystyle \frac{3+6}{7+2}}={\displaystyle \frac{9}{9}}=1\mathrm{\ne }{\displaystyle \frac{3+3}{2}}={\displaystyle \frac{6}{2}}=3\backslash dfrac\{3+6\}\{7+2\}=\; \backslash dfrac\{9\}\{9\}=1\backslash neq\; \backslash dfrac\{3+3\}\{2\}=\; \backslash dfrac\{6\}\{2\}=3$ Falsch!

Betrachte ${\displaystyle \frac{3}{4}}\backslash dfrac\{3\}\{4\}$: ${\displaystyle \frac{3+6}{4+2}}={\displaystyle \frac{9}{6}}={\displaystyle \frac{3}{2}}={\displaystyle \frac{3+3}{4}}={\displaystyle \frac{6}{4}}={\displaystyle \frac{3}{2}}\backslash dfrac\{3+6\}\{4+2\}=\; \backslash dfrac\{9\}\{6\}=\; \backslash dfrac\{3\}\{2\}=\; \backslash dfrac\{3+3\}\{4\}=\; \backslash dfrac\{6\}\{4\}=\backslash dfrac\{3\}\{2\}$ Richtig!

Betrachte: ${\displaystyle \frac{7}{8}}\backslash dfrac\{7\}\{8\}$: ${\displaystyle \frac{7+6}{8+2}}={\displaystyle \frac{13}{10}}\mathrm{\ne }{\displaystyle \frac{7+7}{8}}={\displaystyle \frac{14}{8}}\backslash dfrac\{7+6\}\{8+2\}=\; \backslash dfrac\{13\}\{10\}\backslash neq\; \backslash dfrac\{7+7\}\{8\}=\; \backslash dfrac\{14\}\{8\}$ Falsch!