1.33. Вычислите:

Вычисления:

1. \(\text{A)}\ \frac{4}{7} + \frac{2}{7} = \frac{4+2}{7} = \frac{6}{7}\)
2. \(\text{Б)}\ \frac{8}{11} + \frac{7}{11} = \frac{8+7}{11} = \frac{15}{11} = 1\frac{4}{11}\)
3. \(\text{В)}\ \frac{4}{11} + \frac{8}{11} + \frac{9}{11} = \frac{4+8+9}{11} = \frac{21}{11} = 1\frac{10}{11}\)
4. \(\text{Г)}\ \frac{10}{13} - \frac{7}{13} = \frac{10-7}{13} = \frac{3}{13}\)
5. \(\text{Д)}\ \frac{1}{2} + \frac{1}{3} = \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}\)
6. \(\text{Е)}\ \frac{1}{4} + \frac{3}{16} = \frac{1 \times 4}{4 \times 4} + \frac{3}{16} = \frac{4}{16} + \frac{3}{16} = \frac{7}{16}\)
7. \(\text{Ё)}\ \frac{1}{20} + \frac{4}{5} = \frac{1}{20} + \frac{4 \times 4}{5 \times 4} = \frac{1}{20} + \frac{16}{20} = \frac{17}{20}\)
8. \(\text{Ж)}\ \frac{1}{18} + \frac{1}{24}\)

Общий знаменатель 72. \(\frac{1 \times 4}{18 \times 4} + \frac{1 \times 3}{24 \times 3} = \frac{4}{72} + \frac{3}{72} = \frac{7}{72}\)

9. \(\text{3)}\ \frac{9}{13} + \frac{5}{26} + \frac{1}{78}\)

Общий знаменатель 78. \(\frac{9 \times 6}{13 \times 6} + \frac{5 \times 3}{26 \times 3} + \frac{1}{78} = \frac{54}{78} + \frac{15}{78} + \frac{1}{78} = \frac{70}{78} = \frac{35}{39}\)

10. \(\text{И)}\ \frac{1}{9} + \frac{7}{3} = \frac{1}{9} + \frac{7 \times 3}{3 \times 3} = \frac{1}{9} + \frac{21}{9} = \frac{22}{9} = 2\frac{4}{9}\)
11. \(\text{Й)}\ 4\frac{15}{49} - 2\frac{3}{14}\)

Приведём к общему знаменателю 98. \(4\frac{15 \times 2}{49 \times 2} - 2\frac{3 \times 7}{14 \times 7} = 4\frac{30}{98} - 2\frac{21}{98} = (4-2) + (\frac{30}{98} - \frac{21}{98}) = 2\frac{9}{98}\)

12. \(\text{К)}\ 28\frac{3}{4} - 10\frac{7}{10}\)

Приведём к общему знаменателю 20. \(28\frac{3 \times 5}{4 \times 5} - 10\frac{7 \times 2}{10 \times 2} = 28\frac{15}{20} - 10\frac{14}{20} = (28-10) + (\frac{15}{20} - \frac{14}{20}) = 18\frac{1}{20}\)

13. \(\text{Л)}\ \frac{3}{16} \cdot 7 = \frac{3 \times 7}{16} = \frac{21}{16} = 1\frac{5}{16}\)
14. \(\text{М)}\ 1\frac{1}{5} \cdot 3 = \frac{1 \times 5 + 1}{5} \cdot 3 = \frac{6}{5} \cdot 3 = \frac{18}{5} = 3\frac{3}{5}\)
15. \(\text{Н)}\ \frac{5}{12} \cdot \frac{4}{9} = \frac{5 \times 4}{12 \times 9} = \frac{20}{108} = \frac{5}{27}\)
16. \(\text{О)}\ \frac{8}{15} : \frac{25}{28}\)

\(\frac{8}{15} \cdot \frac{28}{25} = \frac{8 \times 28}{15 \times 25} = \frac{224}{375}\)

17. \(\text{П)}\ \frac{1}{6} \cdot 8\frac{2}{5}\)

\(\frac{1}{6} \cdot \frac{8 \times 5 + 2}{5} = \frac{1}{6} \cdot \frac{42}{5} = \frac{1 \times 42}{6 \times 5} = \frac{42}{30} = \frac{7}{5} = 1\frac{2}{5}\)

18. \(\text{Р)}\ 4\frac{7}{9} \cdot \frac{4}{8}\)

\(\frac{4 \times 9 + 7}{9} \cdot \frac{4}{8} = \frac{43}{9} \cdot \frac{4}{8} = \frac{43 \times 4}{9 \times 8} = \frac{172}{72} = \frac{43}{18} = 2\frac{7}{18}\)

19. \(\text{С)}\ 10\frac{2}{7} : 1\frac{2}{9}\)

\(\frac{10 \times 7 + 2}{7} : \frac{1 \times 9 + 2}{9} = \frac{72}{7} : \frac{11}{9} = \frac{72}{7} \cdot \frac{9}{11} = \frac{72 \times 9}{7 \times 11} = \frac{648}{77}\)

20. \(\text{Т)}\ \frac{5}{9} \cdot 4\frac{7}{8}\)

\(\frac{5}{9} \cdot \frac{4 \times 8 + 7}{8} = \frac{5}{9} \cdot \frac{39}{8} = \frac{5 \times 39}{9 \times 8} = \frac{195}{72} = \frac{65}{24} = 2\frac{17}{24}\)

21. \(\text{У)}\ (1\frac{1}{2})^3\)

\((\frac{1 \times 2 + 1}{2})^3 = (\frac{3}{2})^3 = \frac{3^3}{2^3} = \frac{27}{8} = 3\frac{3}{8}\)

22. \(\text{Ф)}\ \frac{1}{2} : \frac{1}{4}\)

\(\frac{1}{2} \cdot \frac{4}{1} = \frac{4}{2} = 2\)

23. \(\text{X)}\ 150 : 225\)

\(\frac{150}{225} = \frac{150 \div 75}{225 \div 75} = \frac{2}{3}\)

24. \(\text{Ц)}\ 3\frac{1}{4}\)

\(3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4}\)

25. \(\text{Ч)}\ \frac{5}{7}\)

\(\frac{5}{7}\)

26. \(\text{Ш)}\ \frac{7}{48} : \frac{6}{7}\)

\(\frac{7}{48} \cdot \frac{7}{6} = \frac{7 \times 7}{48 \times 6} = \frac{49}{288}\)

27. \(\text{Щ)}\ 15\frac{7}{24} : 3\frac{7}{120}\)

\(\frac{15 \times 24 + 7}{24} : \frac{3 \times 120 + 7}{120} = \frac{367}{24} : \frac{367}{120} = \frac{367}{24} \cdot \frac{120}{367} = \frac{120}{24} = 5\)

28. \(\text{Ъ)}\ 2\frac{3}{23} : \frac{21}{46}\)

\(\frac{2 \times 23 + 3}{23} : \frac{21}{46} = \frac{49}{23} : \frac{21}{46} = \frac{49}{23} \cdot \frac{46}{21} = \frac{49 \times 46}{23 \times 21} = \frac{49 \times 2}{21} = \frac{7 \times 2}{3} = \frac{14}{3} = 4\frac{2}{3}\)

29. \(\text{Ы)}\ \frac{11}{12} \cdot \frac{7}{24} \cdot \frac{21}{22}\)

\(\frac{11 \times 7 \times 21}{12 \times 24 \times 22} = \frac{7 \times 21}{12 \times 24 \times 2} = \frac{7 \times 7}{4 \times 24 \times 2} = \frac{49}{192}\)

30. \(\text{Ь)}\ \frac{5}{7}\)

\(\frac{5}{7}\)

31. \(\text{Ь)}\ \frac{11}{7}\)

\(\frac{11}{7}\)

32. \(\text{Ь)}\ \frac{21}{22}\)

\(\frac{21}{22}\)