№4 Выполните сложение: а) \(\frac{4}{7}\) + \(\frac{5}{6}\); б) \(\frac{5}{18}\) + \(\frac{7}{30}\); в) \(\frac{5}{12}\) + \(\frac{2}{15}\)

Чтобы сложить дроби, нужно привести их к общему знаменателю и сложить числители.

а) \(\frac{4}{7}\) + \(\frac{5}{6}\)
НОК(7, 6) = 42
\(\frac{4}{7}\) = \(\frac{4 \cdot 6}{7 \cdot 6}\) = \(\frac{24}{42}\)
\(\frac{5}{6}\) = \(\frac{5 \cdot 7}{6 \cdot 7}\) = \(\frac{35}{42}\)
\(\frac{24}{42}\) + \(\frac{35}{42}\) = \(\frac{24 + 35}{42}\) = \(\frac{59}{42}\) = 1\(\frac{17}{42}\)

б) \(\frac{5}{18}\) + \(\frac{7}{30}\)
НОК(18, 30) = 90
\(\frac{5}{18}\) = \(\frac{5 \cdot 5}{18 \cdot 5}\) = \(\frac{25}{90}\)
\(\frac{7}{30}\) = \(\frac{7 \cdot 3}{30 \cdot 3}\) = \(\frac{21}{90}\)
\(\frac{25}{90}\) + \(\frac{21}{90}\) = \(\frac{25 + 21}{90}\) = \(\frac{46}{90}\) = \(\frac{23}{45}\)

в) \(\frac{5}{12}\) + \(\frac{2}{15}\)
НОК(12, 15) = 60
\(\frac{5}{12}\) = \(\frac{5 \cdot 5}{12 \cdot 5}\) = \(\frac{25}{60}\)
\(\frac{2}{15}\) = \(\frac{2 \cdot 4}{15 \cdot 4}\) = \(\frac{8}{60}\)
\(\frac{25}{60}\) + \(\frac{8}{60}\) = \(\frac{25 + 8}{60}\) = \(\frac{33}{60}\) = \(\frac{11}{20}\)

Ответ:
а) 1\(\frac{17}{42}\); б) \(\frac{23}{45}\); в) \(\frac{11}{20}\)