3. Вычислите: 1) 1\(\frac{7}{18} - \frac{4}{15}\) 2) 4\(\frac{4}{5}\) : 4\(\frac{1}{6}\) 3) 3\(\frac{1}{9}\) : 4\(\frac{2}{3}\) 4) \(\(30:27 - \frac{1}{3}\) \(\cdot\) 2\(\frac{1}{5}\) + \(\frac{2}{5}\)\)

Решение:

1. \( 1\frac{7}{18} - \frac{4}{15} = \frac{18 \times 1 + 7}{18} - \frac{4}{15} = \frac{25}{18} - \frac{4}{15} \). Общий знаменатель для 18 и 15 — 90. \( \frac{25 \times 5}{18 \times 5} - \frac{4 \times 6}{15 \times 6} = \frac{125}{90} - \frac{24}{90} = \frac{101}{90} = 1\frac{11}{90} \)
2. \( 4\frac{4}{5} : 4\frac{1}{6} = \frac{24}{5} : \frac{25}{6} = \frac{24}{5} \times \frac{6}{25} = \frac{144}{125} = 1\frac{19}{125} \)
3. \( 3\frac{1}{9} : 4\frac{2}{3} = \frac{28}{9} : \frac{14}{3} = \frac{28}{9} \times \frac{3}{14} = \frac{28 \times 3}{9 \times 14} = \frac{2 \times 1}{3 \times 1} = \frac{2}{3} \)
4. \(\(30:27 - \frac{1}{3}\) \(\cdot\) 2\(\frac{1}{5}\) + \(\frac{2}{5}\)\) = \(\( \frac{30}{27} - \frac{1}{3}\) \(\cdot\) \(\frac{11}{5}\) + \(\frac{2}{5}\)\) = \(\( \frac{10}{9} - \frac{3}{9}\) \(\cdot\) \(\frac{11}{5}\) + \(\frac{2}{5}\)\) = \(\( \frac{7}{9}\) \(\cdot\) \(\frac{11}{5}\) + \(\frac{2}{5}\)\) = \( \frac{77}{45} + \frac{2 \times 9}{5 \times 9}\) = \( \frac{77}{45} + \frac{18}{45}\) = \( \frac{95}{45}\) = \( \frac{19}{9}\) = 2\(\frac{1}{9}\)

Ответ: 1) \(1\frac{11}{90}\) 2) \(1\frac{19}{125}\) 3) \(\frac{2}{3}\) 4) \(2\frac{1}{9}\)