2 вариант: вычислите выражения: 1 − 14/45; 2 − 15/23; 11 − 1 11/38; 9 − 3 4/15; 2 3/5 + 3 2/3; 5 1/4 + 3 8/11; 6 8/9 + 3 1/12; 5 7/9 + 5 4/15; 7/9 − 0,(6); 0,3(4) + 8/11.

1. \(1-\frac{14}{45}=\frac{45-14}{45}=\frac{31}{45}\).

2. \(2-\frac{15}{23}=\frac{46-15}{23}=\frac{31}{23}=1\frac{8}{23}\).

3. \(11-1\frac{11}{38}=10-\frac{11}{38}=9\frac{38-11}{38}=9\frac{27}{38}\).

4. \(9-3\frac{4}{15}=6-\frac{4}{15}=5\frac{15-4}{15}=5\frac{11}{15}\).

5. Приведём дроби к знаменателю 15: \(2\frac{3}{5}+3\frac{2}{3}=5+\frac{9}{15}+\frac{10}{15}=6\frac{4}{15}\).

6. \(5\frac{1}{4}+3\frac{8}{11}=8+\frac{11}{44}+\frac{32}{44}=8\frac{43}{44}\).

7. \(6\frac{8}{9}+3\frac{1}{12}=9+\frac{32}{36}+\frac{3}{36}=9\frac{35}{36}\).

8. \(5\frac{7}{9}+5\frac{4}{15}=10+\frac{35}{45}+\frac{12}{45}=11\frac{2}{45}\).

9. Так как \(0,(6)=\frac{2}{3}\), то \(\frac{7}{9}-0,(6)=\frac{7}{9}-\frac{6}{9}=\frac{1}{9}\).

10. Преобразуем периодическую дробь: \(0,3(4)=\frac{31}{90}\). Тогда \(0,3(4)+\frac{8}{11}=\frac{341}{990}+\frac{720}{990}=\frac{1061}{990}=1\frac{71}{990}\).

Ответ: \(\frac{31}{45};\ 1\frac{8}{23};\ 9\frac{27}{38};\ 5\frac{11}{15};\ 6\frac{4}{15};\ 8\frac{43}{44};\ 9\frac{35}{36};\ 11\frac{2}{45};\ \frac{1}{9};\ 1\frac{71}{990}\).