Вариант 3. Выполните вычитание: a) $$1-\frac{5}{9}$$ б) $$5-1\frac{4}{5}$$ в) $$5\frac{1}{20}-2\frac{1}{12}$$ г) $$1\frac{3}{26}-3\frac{8}{39}$$ д) $$4\frac{2}{15}-\frac{9}{40}$$ е) $$6\frac{7}{15}-3\frac{9}{10}$$

Решение:

1. \( 1 - \frac{5}{9} = \frac{9}{9} - \frac{5}{9} = \frac{4}{9} \)
2. \( 5 - 1\frac{4}{5} = 4\frac{5}{5} - 1\frac{4}{5} = 3\frac{1}{5} \)
3. \( 5\frac{1}{20} - 2\frac{1}{12} = 5\frac{3}{60} - 2\frac{5}{60} = 4\frac{63}{60} - 2\frac{5}{60} = 2\frac{58}{60} = 2\frac{29}{30} \)
4. \( 1\frac{3}{26} - 3\frac{8}{39} = \frac{29}{26} - \frac{123}{39} = \frac{29}{2 \cdot 13} - \frac{123}{3 \cdot 13} = \frac{29 \cdot 3 - 123 \cdot 2}{78} = \frac{87 - 246}{78} = -\frac{159}{78} = -\frac{53}{26} \)
5. \( 4\frac{2}{15} - \frac{9}{40} = 4\frac{16}{120} - \frac{27}{120} = \frac{496}{120} - \frac{27}{120} = \frac{469}{120} \)
6. \( 6\frac{7}{15} - 3\frac{9}{10} = 6\frac{14}{30} - 3\frac{27}{30} = 5\frac{44}{30} - 3\frac{27}{30} = 2\frac{17}{30} \)