Задание № 6. Дроби. Вычислите: 1) 3/4 · 6/5; 2) 21/5 · 3/7; 3) 12/5 : 15/2; 4) 6/5 : 4/11; 5) (17/10 − 1/20) · 2/15; 6) (5/22 − 8/11) · 11/5; 7) (3/4 − 1/6) · 3; 8) (2/5 + 13/15) · 6; 9) (9/16 + 2 3/8) · 4; 10) (4/9 − 3 1/15) · 9; 11) (1 3/4 + 2 4/5) · 30; 12) (1/13 − 2 3/4) · 26; 13) 4 7/8 : (2 3/4 + 1 10/19); 14) 1 1/12 : (1 13/18 − 2 5/9); 15) 1/(1/30 + 1/42); 16) 1/(1/36 − 1/44); 17) 1/(1/35 − 1/60); 18) 1/(1/21 + 1/28); 19) 10 · (1/5)² − 12 · 1/5; 20) 8 · (1/4)² − 14 · 1/4; 21) 6 · (1/3)² − 17 · 1/3; 22) 18 · (1/9)² − 20 · 1/9; 23) 9,3 + 7,8; 24) 8,7 + 4,6; 25) 5,2 · 3,1; 26) 2,1 · 9,6; 27) 2,1/(6,6 − 2,4); 28) 7,2/(8,3 − 8,6); 29) (9,5 + 8,9)/2,3; 30) (6,8 − 4,7)/1,4; 31) 27/(3,4 · 4,5); 32) 16/(3,2 · 2); 33) (8,4 · 1,3)/0,7; 34) (4,4 · 0,3)/6,6; 35) 1/4 − 3/25; 36) 1/5 − 27/50; 37) 14/25 + 3/2; 38) 9/4 + 8/5; 39) 0,9/(1 + 1/5); 40) 2,6/(1 − 1/14); 41) 1,3/(1 + 1/12); 42) 1,2/(1 − 1/3); 43) 0,6/(1 + 1/2); 44) 0,8/(1 − 1/9).

При умножении дробей перемножаем числители и знаменатели; при делении умножаем на обратную дробь. Сначала выполняем действия в скобках.

1. \(\frac{3}{4}\cdot\frac{6}{5}=\frac{9}{10}\).
2. \(\frac{21}{5}\cdot\frac{3}{7}=\frac{9}{5}\).
3. \(\frac{12}{5}:\frac{15}{2}=\frac{12}{5}\cdot\frac{2}{15}=\frac{8}{25}\).
4. \(\frac{6}{5}:\frac{4}{11}=\frac{6}{5}\cdot\frac{11}{4}=\frac{33}{10}\).
5. \((\frac{17}{10}-\frac{1}{20})\cdot\frac{2}{15}=\frac{33}{20}\cdot\frac{2}{15}=\frac{11}{50}\).
6. \((\frac{5}{22}-\frac{8}{11})\cdot\frac{11}{5}=-\frac{1}{2}\cdot\frac{11}{5}=-\frac{11}{10}\).
7. \((\frac{3}{4}-\frac{1}{6})\cdot3=\frac{7}{12}\cdot3=\frac{7}{4}\).
8. \((\frac{2}{5}+\frac{13}{15})\cdot6=\frac{19}{15}\cdot6=\frac{38}{5}\).
9. \((\frac{9}{16}+2\frac{3}{8})\cdot4=\frac{47}{16}\cdot4=\frac{47}{4}\).
10. \((\frac{4}{9}-3\frac{1}{15})\cdot9=-\frac{118}{45}\cdot9=-\frac{118}{5}\).
11. \((1\frac{3}{4}+2\frac{4}{5})\cdot30=\frac{91}{20}\cdot30=\frac{273}{2}\).
12. \((\frac{1}{13}-2\frac{3}{4})\cdot26=-\frac{139}{52}\cdot26=-\frac{139}{2}\).
13. \(4\frac{7}{8}:(2\frac{3}{4}+1\frac{10}{19})=\frac{39}{8}:\frac{325}{76}=\frac{741}{650}\).
14. \(1\frac{1}{12}:(1\frac{13}{18}-2\frac{5}{9})=\frac{13}{12}:(-\frac{5}{6})=-\frac{13}{10}\).
15. \(1:(\frac{1}{30}+\frac{1}{42})=1:\frac{2}{35}=\frac{35}{2}\).
16. \(1:(\frac{1}{36}-\frac{1}{44})=1:\frac{1}{198}=198\).
17. \(1:(\frac{1}{35}-\frac{1}{60})=1:\frac{1}{84}=84\).
18. \(1:(\frac{1}{21}+\frac{1}{28})=1:\frac{1}{12}=12\).
19. \(10\cdot(\frac{1}{5})^2-12\cdot\frac{1}{5}=\frac{2}{5}-\frac{12}{5}=-2\).
20. \(8\cdot(\frac{1}{4})^2-14\cdot\frac{1}{4}=\frac{1}{2}-\frac{7}{2}=-3\).
21. \(6\cdot(\frac{1}{3})^2-17\cdot\frac{1}{3}=\frac{2}{3}-\frac{17}{3}=-5\).
22. \(18\cdot(\frac{1}{9})^2-20\cdot\frac{1}{9}=\frac{2}{9}-\frac{20}{9}=-2\).
23. \(9,3+7,8=17,1\).
24. \(8,7+4,6=13,3\).
25. \(5,2\cdot3,1=16,12\).
26. \(2,1\cdot9,6=20,16\).
27. \(2,1:(6,6-2,4)=2,1:4,2=0,5\).
28. \(7,2:(8,3-8,6)=7,2:(-0,3)=-24\).
29. \((9,5+8,9):2,3=18,4:2,3=8\).
30. \((6,8-4,7):1,4=2,1:1,4=1,5\).
31. \(27:(3,4\cdot4,5)=27:15,3=\frac{30}{17}\).
32. \(16:(3,2\cdot2)=16:6,4=2,5\).
33. \((8,4\cdot1,3):0,7=10,92:0,7=15,6\).
34. \((4,4\cdot0,3):6,6=1,32:6,6=0,2\).
35. \(\frac{1}{4}-\frac{3}{25}=\frac{13}{100}\).
36. \(\frac{1}{5}-\frac{27}{50}=-\frac{17}{50}\).
37. \(\frac{14}{25}+\frac{3}{2}=\frac{103}{50}\).
38. \(\frac{9}{4}+\frac{8}{5}=\frac{77}{20}\).
39. \(0,9:(1+\frac{1}{5})=0,9:1,2=0,75\).
40. \(2,6:(1-\frac{1}{14})=2,6:\frac{13}{14}=2,8\).
41. \(1,3:(1+\frac{1}{12})=1,3:\frac{13}{12}=1,2\).
42. \(1,2:(1-\frac{1}{3})=1,2:\frac{2}{3}=1,8\).
43. \(0,6:(1+\frac{1}{2})=0,6:1,5=0,4\).
44. \(0,8:(1-\frac{1}{9})=0,8:\frac{8}{9}=0,9\).