Вычислите 29 4 : 5 4 - 3 4 · (3 - 19 30 )

Решение:

1. \[ 3 - \frac{19}{30} = \frac{90}{30} - \frac{19}{30} = \frac{71}{30} \]
2. \[ \frac{3}{4} \cdot \frac{71}{30} = \frac{3 \cdot 71}{4 \cdot 30} = \frac{71}{4 \cdot 10} = \frac{71}{40} \]
3. \[ \frac{29}{4} : \frac{5}{4} = \frac{29}{4} \cdot \frac{4}{5} = \frac{29}{5} \]
4. \[ \frac{29}{5} - \frac{71}{40} = \frac{29 \cdot 8}{5 \cdot 8} - \frac{71}{40} = \frac{232}{40} - \frac{71}{40} = \frac{161}{40} \]

Ответ: 161/40