Реши примеры

Привет! Давай решим эти примеры по порядку.

a) $\left(\frac{1}{6} + \frac{2}{3}\right) \cdot 3$ $$ \frac{1}{6} + \frac{2}{3} = \frac{1}{6} + \frac{4}{6} = \frac{5}{6} $$ $$ \frac{5}{6} \cdot 3 = \frac{5 \cdot 3}{6} = \frac{15}{6} = \frac{5}{2} = 2\frac{1}{2} $$

б) $\left(\frac{1}{8} + \frac{3}{4}\right) : 5$ $$ \frac{1}{8} + \frac{3}{4} = \frac{1}{8} + \frac{6}{8} = \frac{7}{8} $$ $$ \frac{7}{8} : 5 = \frac{7}{8} \cdot \frac{1}{5} = \frac{7}{40} $$

в) $\left(\frac{1}{2} + \frac{1}{3}\right) \cdot 2$ $$ \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} $$ $$ \frac{5}{6} \cdot 2 = \frac{5 \cdot 2}{6} = \frac{10}{6} = \frac{5}{3} = 1\frac{2}{3} $$

г) $\left(\frac{17}{30} - \frac{2}{15}\right) : 13$ $$ \frac{17}{30} - \frac{2}{15} = \frac{17}{30} - \frac{4}{30} = \frac{13}{30} $$ $$ \frac{13}{30} : 13 = \frac{13}{30} \cdot \frac{1}{13} = \frac{1}{30} $$

д) $\left(\frac{4}{3} + \frac{1}{9}\right) \cdot 4$ $$ \frac{4}{3} + \frac{1}{9} = \frac{12}{9} + \frac{1}{9} = \frac{13}{9} $$ $$ \frac{13}{9} \cdot 4 = \frac{13 \cdot 4}{9} = \frac{52}{9} = 5\frac{7}{9} $$

e) $\left(\frac{1}{2} - \frac{1}{3}\right) \cdot 3$ $$ \frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6} $$ $$ \frac{1}{6} \cdot 3 = \frac{1 \cdot 3}{6} = \frac{3}{6} = \frac{1}{2} $$

Ответы: a) $2\frac{1}{2}$ б) $\frac{7}{40}$ в) $1\frac{2}{3}$ г) $\frac{1}{30}$ д) $5\frac{7}{9}$ e) $\frac{1}{2}$