31. Сократите дробь: 12 68 4 20 6 10 90 150 33 45 520 65 4 16 123 123 4 6 20 50 40 118 124 24 20 18 540 20 32. Выполните действия над дробями, предварительно сократив их: 12 18 + 12 21 10 - 28 40 12 30 - 16 120 10 9 14 + - 50 20 35 6 4 18 - + 18 12 27 9 18 20 +- 12 24 16

31. Сократите дробь:

Давай сократим дроби по порядку:

1. \[\frac{12}{68} = \frac{12:4}{68:4} = \frac{3}{17}\]
2. \[\frac{4}{20} = \frac{4:4}{20:4} = \frac{1}{5}\]
3. \[\frac{6}{10} = \frac{6:2}{10:2} = \frac{3}{5}\]
4. \[\frac{90}{150} = \frac{90:30}{150:30} = \frac{3}{5}\]
5. \[\frac{33}{45} = \frac{33:3}{45:3} = \frac{11}{15}\]
6. \[\frac{520}{65} = \frac{520:5}{65:5} = \frac{104}{13} = \frac{104:13}{13:13} = \frac{8}{1} = 8\]
7. \[\frac{4}{6} = \frac{4:2}{6:2} = \frac{2}{3}\]
8. \[\frac{20}{50} = \frac{20:10}{50:10} = \frac{2}{5}\]
9. \[\frac{40}{118} = \frac{40:2}{118:2} = \frac{20}{59}\]
10. \[\frac{124}{24} = \frac{124:4}{24:4} = \frac{31}{6}\]
11. \[\frac{4}{16} = \frac{4:4}{16:4} = \frac{1}{4}\]
12. \[\frac{123}{123} = \frac{123:123}{123:123} = \frac{1}{1} = 1\]
13. \[\frac{9}{120} = \frac{9:3}{120:3} = \frac{3}{40}\]
14. \[\frac{20}{18} = \frac{20:2}{18:2} = \frac{10}{9}\]
15. \[\frac{48}{102} = \frac{48:6}{102:6} = \frac{8}{17}\]
16. \[\frac{540}{20} = \frac{540:20}{20:20} = \frac{27}{1}\]

32. Выполните действия над дробями, предварительно сократив их:

1. \[\frac{12}{18} + \frac{4}{12} = \frac{12:6}{18:6} + \frac{4:4}{12:4} = \frac{2}{3} + \frac{1}{3} = \frac{2+1}{3} = \frac{3}{3} = 1\]
2. \[\frac{21}{28} - \frac{10}{40} = \frac{21:7}{28:7} - \frac{10:10}{40:10} = \frac{3}{4} - \frac{1}{4} = \frac{3-1}{4} = \frac{2}{4} = \frac{2:2}{4:2} = \frac{1}{2}\]
3. \[\frac{12}{16} - \frac{30}{120} = \frac{12:4}{16:4} - \frac{30:30}{120:30} = \frac{3}{4} - \frac{1}{4} = \frac{3-1}{4} = \frac{2}{4} = \frac{2:2}{4:2} = \frac{1}{2}\]
4. \[\frac{10}{50} + \frac{9}{20} - \frac{14}{35} = \frac{10:10}{50:10} + \frac{9}{20} - \frac{14:7}{35:7} = \frac{1}{5} + \frac{9}{20} - \frac{2}{5} = \frac{4}{20} + \frac{9}{20} - \frac{8}{20} = \frac{4+9-8}{20} = \frac{5}{20} = \frac{5:5}{20:5} = \frac{1}{4}\]
5. \[\frac{6}{18} - \frac{4}{12} + \frac{18}{27} = \frac{6:6}{18:6} - \frac{4:4}{12:4} + \frac{18:9}{27:9} = \frac{1}{3} - \frac{1}{3} + \frac{2}{3} = \frac{1-1+2}{3} = \frac{2}{3}\]
6. \[\frac{9}{12} + \frac{18}{24} - \frac{20}{16} = \frac{9:3}{12:3} + \frac{18:6}{24:6} - \frac{20:4}{16:4} = \frac{3}{4} + \frac{3}{4} - \frac{5}{4} = \frac{3+3-5}{4} = \frac{1}{4}\]

Ответ: Задания выполнены.

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