1. Вычислите: а) $$1\frac{4}{9}+2\frac{5}{18}$$; б) $$3\frac{5}{24}-1\frac{7}{36}$$; в) $$2\frac{7}{30}+3\frac{9}{20}-4\frac{59}{60}$$.

Решение:

1. а) $$1\frac{4}{9}+2\frac{5}{18}$$

   • Приведем дроби к общему знаменателю 18:
   • $$1\frac{4}{9} = 1\frac{4\times2}{9\times2} = 1\frac{8}{18}$$
   • $$1\frac{8}{18} + 2\frac{5}{18} = (1+2) + (\frac{8}{18} + \frac{5}{18}) = 3 + \frac{13}{18} = 3\frac{13}{18}$$

2. б) $$3\frac{5}{24}-1\frac{7}{36}$$

   • Приведем дроби к общему знаменателю 72:
   • $$3\frac{5}{24} = 3\frac{5\times3}{24\times3} = 3\frac{15}{72}$$
   • $$1\frac{7}{36} = 1\frac{7\times2}{36\times2} = 1\frac{14}{72}$$
   • $$3\frac{15}{72} - 1\frac{14}{72} = (3-1) + (\frac{15}{72} - \frac{14}{72}) = 2 + \frac{1}{72} = 2\frac{1}{72}$$

3. в) $$2\frac{7}{30}+3\frac{9}{20}-4\frac{59}{60}$$

   • Приведем дроби к общему знаменателю 60:
   • $$2\frac{7}{30} = 2\frac{7\times2}{30\times2} = 2\frac{14}{60}$$
   • $$3\frac{9}{20} = 3\frac{9\times3}{20\times3} = 3\frac{27}{60}$$
   • $$2\frac{14}{60} + 3\frac{27}{60} - 4\frac{59}{60} = (2+3-4) + (\frac{14}{60} + \frac{27}{60} - \frac{59}{60}) = 1 + \frac{41-59}{60} = 1 + \frac{-18}{60} = 1 - \frac{18}{60}$$
   • Сократим дробь $$\frac{18}{60} = \frac{18\div6}{60\div6} = \frac{3}{10}$$
   • $$1 - \frac{3}{10} = \frac{10}{10} - \frac{3}{10} = \frac{7}{10}$$

Ответ: а) $$3\frac{13}{18}$$; б) $$2\frac{1}{72}$$; в) $$\frac{7}{10}$$.