1. Выполните сложение: a) \(\frac{3}{5}\) и \(\frac{2}{5}\); б) \(\frac{8}{9}\) и \(\frac{2}{3}\); в) \(\frac{5}{18}\) и \(\frac{5}{12}\); г) \(\frac{5}{8}\) и \(\frac{2}{3}\).

Решение:

a) \(\frac{3}{5} + \frac{2}{5} = \frac{3+2}{5} = \frac{5}{5} = 1\)

Ответ: 1

б) \(\frac{8}{9} + \frac{2}{3} = \frac{8}{9} + \frac{2 \cdot 3}{3 \cdot 3} = \frac{8}{9} + \frac{6}{9} = \frac{8+6}{9} = \frac{14}{9} = 1\frac{5}{9}\)

Ответ: \(1\frac{5}{9}\)

в) \(\frac{5}{18} + \frac{5}{12} = \frac{5 \cdot 2}{18 \cdot 2} + \frac{5 \cdot 3}{12 \cdot 3} = \frac{10}{36} + \frac{15}{36} = \frac{10+15}{36} = \frac{25}{36}\)

Ответ: \(\frac{25}{36}\)

г) \(\frac{5}{8} + \frac{2}{3} = \frac{5 \cdot 3}{8 \cdot 3} + \frac{2 \cdot 8}{3 \cdot 8} = \frac{15}{24} + \frac{16}{24} = \frac{15+16}{24} = \frac{31}{24} = 1\frac{7}{24}\)

Ответ: \(1\frac{7}{24}\)