2026/01/14 18:39 TECNO * * * * * * * 17 414 87 912 1 4 5-6 + 5 2-3 54 11 3 + 3216 1 1 14+2 11 2+3 53 32 71 17 9 7 11 + 812 4 615 15 3 25 2114 37 11 5 18 6

В данном задании необходимо решить примеры на сложение дробей.

Рассмотрим каждый пример:

1. $$4 \frac{1}{14} = \frac{4 \cdot 14 + 1}{14} = \frac{56 + 1}{14} = \frac{57}{14}$$
2. $$ \frac{8}{9} + \frac{7}{12} = \frac{8 \cdot 4}{9 \cdot 4} + \frac{7 \cdot 3}{12 \cdot 3} = \frac{32}{36} + \frac{21}{36} = \frac{32 + 21}{36} = \frac{53}{36} = 1 \frac{17}{36}$$
3. $$1 \frac{4}{3} + \frac{1}{45} = \frac{7}{64} + \frac{1}{45} = \frac{3 \cdot 45}{3 \cdot 45} + \frac{1 \cdot 4}{45 \cdot 4} = \frac{135}{180} + \frac{4}{180} = \frac{139}{180}$$
4. $$11 \frac{3}{32} + \frac{3}{16} = \frac{11 \cdot 32 + 3}{32} + \frac{3}{16} = \frac{352 + 3}{32} + \frac{3}{16} = \frac{355}{32} + \frac{3 \cdot 2}{16 \cdot 2} = \frac{355}{32} + \frac{6}{32} = \frac{355 + 6}{32} = \frac{361}{32} = 11 \frac{9}{32}$$
5. $$14 \frac{1}{14} + \frac{1}{2} = \frac{14 \cdot 14 + 1}{14} + \frac{1}{2} = \frac{196 + 1}{14} + \frac{1}{2} = \frac{197}{14} + \frac{1 \cdot 7}{2 \cdot 7} = \frac{197}{14} + \frac{7}{14} = \frac{197 + 7}{14} = \frac{204}{14} = \frac{102}{7} = 14 \frac{4}{7}$$
6. $$1 \frac{1}{2} + \frac{1}{3} = \frac{3}{2} + \frac{1}{3} = \frac{3 \cdot 3}{2 \cdot 3} + \frac{1 \cdot 2}{3 \cdot 2} = \frac{9}{6} + \frac{2}{6} = \frac{9+2}{6} = \frac{11}{6} = 1 \frac{5}{6}$$
7. $$5 \frac{3}{8} + \frac{3}{4} = \frac{5 \cdot 8 + 3}{8} + \frac{3}{4} = \frac{40 + 3}{8} + \frac{3}{4} = \frac{43}{8} + \frac{3 \cdot 2}{4 \cdot 2} = \frac{43}{8} + \frac{6}{8} = \frac{43 + 6}{8} = \frac{49}{8} = 6 \frac{1}{8}$$
8. $$3 \frac{2}{4} + \frac{2}{5} = \frac{3 \cdot 4 + 2}{4} + \frac{2}{5} = \frac{12 + 2}{4} + \frac{2}{5} = \frac{14}{4} + \frac{2}{5} = \frac{7}{2} + \frac{2}{5} = \frac{7 \cdot 5}{2 \cdot 5} + \frac{2 \cdot 2}{5 \cdot 2} = \frac{35}{10} + \frac{4}{10} = \frac{39}{10} = 3 \frac{9}{10}$$
9. $$7 \frac{1}{9} + \frac{1}{18} = \frac{7 \cdot 9 + 1}{9} + \frac{1}{18} = \frac{63 + 1}{9} + \frac{1}{18} = \frac{64}{9} + \frac{1}{18} = \frac{64 \cdot 2}{9 \cdot 2} + \frac{1}{18} = \frac{128}{18} + \frac{1}{18} = \frac{128 + 1}{18} = \frac{129}{18} = 7 \frac{3}{18} = 7 \frac{1}{6}$$
10. $$1 \frac{5}{2} + \frac{5}{7} = \frac{1 \cdot 2 + 5}{2} + \frac{5}{7} = \frac{2 + 5}{2} + \frac{5}{7} = \frac{7}{2} + \frac{5}{7} = \frac{7 \cdot 7}{2 \cdot 7} + \frac{5 \cdot 2}{7 \cdot 2} = \frac{49}{14} + \frac{10}{14} = \frac{49 + 10}{14} = \frac{59}{14} = 4 \frac{3}{14}$$
11. $$3 \frac{1}{5} + \frac{1}{4} = \frac{3 \cdot 5 + 1}{5} + \frac{1}{4} = \frac{15 + 1}{5} + \frac{1}{4} = \frac{16}{5} + \frac{1}{4} = \frac{16 \cdot 4}{5 \cdot 4} + \frac{1 \cdot 5}{4 \cdot 5} = \frac{64}{20} + \frac{5}{20} = \frac{64 + 5}{20} = \frac{69}{20} = 3 \frac{9}{20}$$
12. $$2 \frac{5}{21} + \frac{5}{14} = \frac{2 \cdot 21 + 5}{21} + \frac{5}{14} = \frac{42 + 5}{21} + \frac{5}{14} = \frac{47}{21} + \frac{5}{14} = \frac{47 \cdot 2}{21 \cdot 2} + \frac{5 \cdot 3}{14 \cdot 3} = \frac{94}{42} + \frac{15}{42} = \frac{94 + 15}{42} = \frac{109}{42} = 2 \frac{25}{42}$$
13. $$4 \frac{6}{5} + \frac{6}{7} = \frac{4 \cdot 5 + 6}{5} + \frac{6}{7} = \frac{20 + 6}{5} + \frac{6}{7} = \frac{26}{5} + \frac{6}{7} = \frac{26 \cdot 7}{5 \cdot 7} + \frac{6 \cdot 5}{7 \cdot 5} = \frac{182}{35} + \frac{30}{35} = \frac{182 + 30}{35} = \frac{212}{35} = 6 \frac{2}{35}$$
14. $$3 \frac{7}{4} + \frac{2}{20} = \frac{3 \cdot 4 + 7}{4} + \frac{2}{20} = \frac{12 + 7}{4} + \frac{2}{20} = \frac{19}{4} + \frac{2}{20} = \frac{19 \cdot 5}{4 \cdot 5} + \frac{2}{20} = \frac{95}{20} + \frac{2}{20} = \frac{97}{20} = 4 \frac{17}{20}$$
15. $$11 \frac{5}{18} + \frac{5}{6} = \frac{11 \cdot 18 + 5}{18} + \frac{5}{6} = \frac{198 + 5}{18} + \frac{5}{6} = \frac{203}{18} + \frac{5 \cdot 3}{6 \cdot 3} = \frac{203}{18} + \frac{15}{18} = \frac{203 + 15}{18} = \frac{218}{18} = \frac{109}{9} = 12 \frac{1}{9}$$

Ответ: Решения примеров выше.