Арифметические действия с дробями. №1. Вычислите: a) \(\frac{4}{15} \cdot 2 + \frac{2}{3} : 5;\) б) \(\frac{7}{8} : 3 - \frac{1}{24} \cdot 5;\) в) \(\frac{3}{16} \cdot 5 - \frac{3}{4} : 4;\) г) \(\frac{9}{13} : 4 + \frac{5}{52} \cdot 3.\)

Решение:

1. a) \(\frac{4}{15} \cdot 2 + \frac{2}{3} : 5 = \frac{4 \cdot 2}{15} + \frac{2}{3 \cdot 5} = \frac{8}{15} + \frac{2}{15} = \frac{8+2}{15} = \frac{10}{15} = \frac{2}{3}\)
2. б) \(\frac{7}{8} : 3 - \frac{1}{24} \cdot 5 = \frac{7}{8 \cdot 3} - \frac{1 \cdot 5}{24} = \frac{7}{24} - \frac{5}{24} = \frac{7-5}{24} = \frac{2}{24} = \frac{1}{12}\)
3. в) \(\frac{3}{16} \cdot 5 - \frac{3}{4} : 4 = \frac{3 \cdot 5}{16} - \frac{3}{4 \cdot 4} = \frac{15}{16} - \frac{3}{16} = \frac{15-3}{16} = \frac{12}{16} = \frac{3}{4}\)
4. г) \(\frac{9}{13} : 4 + \frac{5}{52} \cdot 3 = \frac{9}{13 \cdot 4} + \frac{5 \cdot 3}{52} = \frac{9}{52} + \frac{15}{52} = \frac{9+15}{52} = \frac{24}{52} = \frac{6}{13}\)

Ответ: a) \(\frac{2}{3}\); б) \(\frac{1}{12}\); в) \(\frac{3}{4}\); г) \(\frac{6}{13}\).