270. Вычислите: 1) \(\frac{1}{4}+\frac{3}{5}\); 2) \(\frac{9}{11}-\frac{2}{5}\); 3) \(\frac{13}{16}-\frac{9}{32}\); 4) \(\frac{3}{28}+\frac{5}{14}\); 5) \(\frac{14}{15}-\frac{7}{10}\); 6) \(\frac{3}{8}+\frac{1}{6}\); 7) \(\frac{9}{25}-\frac{7}{20}\); 8) \(\frac{37}{42}-\frac{17}{24}\); 9) \(\frac{11}{24}-\frac{3}{16}\); 10) \(\frac{9}{16}+\frac{7}{24}-\frac{3}{8}\); 11) \(\frac{1}{3}-\frac{1}{6}+\frac{1}{4}\); 12) \(\frac{2}{5}+\frac{4}{15}-\frac{5}{9}\);

Выполним вычисления:

1. \(\frac{1}{4}+\frac{3}{5}\)=\(\frac{5}{20}+\frac{12}{20}=\frac{17}{20}\)
2. \(\frac{9}{11}-\frac{2}{5}\)=\(\frac{45}{55}-\frac{22}{55}=\frac{23}{55}\)
3. \(\frac{13}{16}-\frac{9}{32}\)=\(\frac{26}{32}-\frac{9}{32}=\frac{17}{32}\)
4. \(\frac{3}{28}+\frac{5}{14}\)=\(\frac{3}{28}+\frac{10}{28}=\frac{13}{28}\)
5. \(\frac{14}{15}-\frac{7}{10}\)=\(\frac{28}{30}-\frac{21}{30}=\frac{7}{30}\)
6. \(\frac{3}{8}+\frac{1}{6}\)=\(\frac{9}{24}+\frac{4}{24}=\frac{13}{24}\)
7. \(\frac{9}{25}-\frac{7}{20}\)=\(\frac{36}{100}-\frac{35}{100}=\frac{1}{100}\)
8. \(\frac{37}{42}-\frac{17}{24}\)=\(\frac{37 \cdot 4}{42 \cdot 4}-\frac{17 \cdot 7}{24 \cdot 7}=\frac{148}{168}-\frac{119}{168}=\frac{29}{168}\)
9. \(\frac{11}{24}-\frac{3}{16}\)=\(\frac{22}{48}-\frac{9}{48}=\frac{13}{48}\)
10. \(\frac{9}{16}+\frac{7}{24}-\frac{3}{8}\)=\(\frac{27}{48}+\frac{14}{48}-\frac{18}{48}=\frac{23}{48}\)
11. \(\frac{1}{3}-\frac{1}{6}+\frac{1}{4}\)=\(\frac{4}{12}-\frac{2}{12}+\frac{3}{12}=\frac{5}{12}\)
12. \(\frac{2}{5}+\frac{4}{15}-\frac{5}{9}\)=\(\frac{18}{45}+\frac{12}{45}-\frac{25}{45}=\frac{5}{45}=\frac{1}{9}\)

Ответ:

1. \(\frac{17}{20}\)
2. \(\frac{23}{55}\)
3. \(\frac{17}{32}\)
4. \(\frac{13}{28}\)
5. \(\frac{7}{30}\)
6. \(\frac{13}{24}\)
7. \(\frac{1}{100}\)
8. \(\frac{29}{168}\)
9. \(\frac{13}{48}\)
10. \(\frac{23}{48}\)
11. \(\frac{5}{12}\)
12. \(\frac{1}{9}\)