1. Найдите значение выражени 1) a) 1/2 + 3/4 - 5/8 б) 2/3 + 1/6 - 1/2 в) 5/8 - (2/3 - 5/12) г) 1/2 + (3/5 - 1/3) 3) a) (1/9 + 1/3) : 2/3 б) 2 - 2/3 : 7/9 в) 3/4 : 12 - 1/32 г) 1 1/5 : 2/3 + 1/3 2. Запишите числовое выраже а) произведения суммы дробей 1 1/2 б) разности выражений 1 + (1/2)^2

1) a)

\[\frac{1}{2} + \frac{3}{4} - \frac{5}{8} = \frac{4}{8} + \frac{6}{8} - \frac{5}{8} = \frac{4+6-5}{8} = \frac{5}{8}\]

б)

\[\frac{2}{3} + \frac{1}{6} - \frac{1}{2} = \frac{4}{6} + \frac{1}{6} - \frac{3}{6} = \frac{4+1-3}{6} = \frac{2}{6} = \frac{1}{3}\]

в)

\[\frac{5}{8} - (\frac{2}{3} - \frac{5}{12}) = \frac{5}{8} - (\frac{8}{12} - \frac{5}{12}) = \frac{5}{8} - \frac{3}{12} = \frac{5}{8} - \frac{1}{4} = \frac{5}{8} - \frac{2}{8} = \frac{3}{8}\]

г)

\[\frac{1}{2} + (\frac{3}{5} - \frac{1}{3}) = \frac{1}{2} + (\frac{9}{15} - \frac{5}{15}) = \frac{1}{2} + \frac{4}{15} = \frac{15}{30} + \frac{8}{30} = \frac{23}{30}\]

3) a)

\[(\frac{1}{9} + \frac{1}{3}) : \frac{2}{3} = (\frac{1}{9} + \frac{3}{9}) : \frac{2}{3} = \frac{4}{9} : \frac{2}{3} = \frac{4}{9} \cdot \frac{3}{2} = \frac{2}{3}\]

б)

\[2 - \frac{2}{3} : \frac{7}{9} = 2 - \frac{2}{3} \cdot \frac{9}{7} = 2 - \frac{6}{7} = \frac{14}{7} - \frac{6}{7} = \frac{8}{7} = 1\frac{1}{7}\]

в)

\[\frac{3}{4} : 12 - \frac{1}{32} = \frac{3}{4} \cdot \frac{1}{12} - \frac{1}{32} = \frac{1}{16} - \frac{1}{32} = \frac{2}{32} - \frac{1}{32} = \frac{1}{32}\]

г)

\[1 \frac{1}{5} : \frac{2}{3} + \frac{1}{3} = \frac{6}{5} : \frac{2}{3} + \frac{1}{3} = \frac{6}{5} \cdot \frac{3}{2} + \frac{1}{3} = \frac{9}{5} + \frac{1}{3} = \frac{27}{15} + \frac{5}{15} = \frac{32}{15} = 2 \frac{2}{15}\]