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МатематикаВопрос:
Окончание МТ № 29 6 11 5 16 16 3-\frac{2}{3}+\frac{1}{3} 1-\frac{7}{9} \frac{1}{25}\cdot15 4-\frac{1}{5}\cdot1\frac{3}{7} 3-\frac{7}{4}\cdot\frac{7}{9} 1-\frac{2}{5}:\frac{2}{5} \frac{3}{5}:8 3:\frac{1}{2} 7-2\frac{3}{7} 2-\frac{2}{9}\frac{5}{9} 3\frac{1}{5}\frac{1}{2} \frac{1}{8}+\frac{3}{4} \frac{7}{10}\frac{2}{15} 1\frac{3}{4}\frac{4}{7} 7 3\frac{9}{20}-1\frac{7}{20} 2\frac{5}{7}+1\frac{3}{7} 3-\frac{4}{15} 4\cdot\frac{7}{12} 2\frac{1}{7}\cdot1\frac{2}{5} 2\frac{3}{5}\frac{3}{8} 4\frac{2}{7}:\frac{2}{7} 1\frac{1}{8}:2 1:\frac{4}{7} 9-4\frac{5}{14} 2-\frac{3}{7}\frac{6}{7} 5\frac{1}{8}-\frac{1}{3} \frac{2}{5}+\frac{1}{15} \frac{5}{18}\frac{1}{12} 5\frac{4}{9}\cdot1\frac{1}{5} 8 2\frac{5}{8}-\frac{3}{8} 4\frac{4}{9}+2\frac{7}{9} 7-\frac{9}{20} \frac{8}{15}\cdot3 4\frac{1}{2}\cdot2\frac{2}{3} 4\frac{2}{9}:\frac{2}{5} 2\frac{4}{7}:\frac{4}{7} \frac{1}{6}:3 1:\frac{5}{9} 6-3\frac{4}{9} 3-\frac{1}{6}\frac{5}{6} 6\frac{1}{7}\frac{1}{5} \frac{1}{3}+\frac{2}{9} \frac{5}{6}\frac{3}{8} 3-\frac{1}{3}\frac{3}{10}
Ответ:
Ответ: Решения ниже
Краткое пояснение: Выполним действия с дробями по порядку в каждом столбце.
| 6 | 7 | 8 |
|---|---|---|
| \[\frac{11}{16} - \frac{5}{16} = \frac{11-5}{16} = \frac{6}{16} = \frac{3}{8}\] | \[3\frac{9}{20} - 1\frac{7}{20} = (3 - 1) + (\frac{9}{20} - \frac{7}{20}) = 2 + \frac{2}{20} = 2 + \frac{1}{10} = 2\frac{1}{10}\] | \[2\frac{5}{8} - \frac{3}{8} = 2 + \frac{5}{8} - \frac{3}{8} = 2 + \frac{5-3}{8} = 2 + \frac{2}{8} = 2 + \frac{1}{4} = 2\frac{1}{4}\] |
| \[3\frac{2}{3} + \frac{1}{3} = 3 + \frac{2}{3} + \frac{1}{3} = 3 + \frac{2+1}{3} = 3 + \frac{3}{3} = 3 + 1 = 4\] | \[2\frac{5}{7} + 1\frac{3}{7} = (2 + 1) + (\frac{5}{7} + \frac{3}{7}) = 3 + \frac{5+3}{7} = 3 + \frac{8}{7} = 3 + 1\frac{1}{7} = 4\frac{1}{7}\] | \[4\frac{4}{9} + 2\frac{7}{9} = (4 + 2) + (\frac{4}{9} + \frac{7}{9}) = 6 + \frac{4+7}{9} = 6 + \frac{11}{9} = 6 + 1\frac{2}{9} = 7\frac{2}{9}\] |
| \[1 - \frac{7}{9} = \frac{9}{9} - \frac{7}{9} = \frac{9-7}{9} = \frac{2}{9}\] | \[3 - \frac{4}{15} = \frac{45}{15} - \frac{4}{15} = \frac{45-4}{15} = \frac{41}{15} = 2\frac{11}{15}\] | \[7 - \frac{9}{20} = \frac{140}{20} - \frac{9}{20} = \frac{140-9}{20} = \frac{131}{20} = 6\frac{11}{20}\] |
| \[\frac{1}{25} \cdot 15 = \frac{1 \cdot 15}{25} = \frac{15}{25} = \frac{3}{5}\] | \[4 \cdot \frac{7}{12} = \frac{4 \cdot 7}{12} = \frac{28}{12} = \frac{7}{3} = 2\frac{1}{3}\] | \[\frac{8}{15} \cdot 3 = \frac{8 \cdot 3}{15} = \frac{24}{15} = \frac{8}{5} = 1\frac{3}{5}\] |
| \[4\frac{1}{5} \cdot 1\frac{3}{7} = \frac{4 \cdot 5 + 1}{5} \cdot \frac{1 \cdot 7 + 3}{7} = \frac{21}{5} \cdot \frac{10}{7} = \frac{21 \cdot 10}{5 \cdot 7} = \frac{3 \cdot 2}{1 \cdot 1} = 6\] | \[2\frac{1}{7} \cdot 1\frac{2}{5} = \frac{2 \cdot 7 + 1}{7} \cdot \frac{1 \cdot 5 + 2}{5} = \frac{15}{7} \cdot \frac{7}{5} = \frac{15 \cdot 7}{7 \cdot 5} = \frac{3 \cdot 1}{1 \cdot 1} = 3\] | \[4\frac{1}{2} \cdot 2\frac{2}{3} = \frac{4 \cdot 2 + 1}{2} \cdot \frac{2 \cdot 3 + 2}{3} = \frac{9}{2} \cdot \frac{8}{3} = \frac{9 \cdot 8}{2 \cdot 3} = \frac{3 \cdot 4}{1 \cdot 1} = 12\] |
| \[3\frac{7}{4} \cdot \frac{7}{9} = \frac{3 \cdot 4 + 7}{4} \cdot \frac{7}{9} = \frac{19}{4} \cdot \frac{7}{9} = \frac{19 \cdot 7}{4 \cdot 9} = \frac{133}{36} = 3\frac{25}{36}\] | \[2\frac{3}{5} \cdot \frac{3}{8} = \frac{2 \cdot 5 + 3}{5} \cdot \frac{3}{8} = \frac{13}{5} \cdot \frac{3}{8} = \frac{13 \cdot 3}{5 \cdot 8} = \frac{39}{40}\] | \[4\frac{2}{9} : \frac{2}{5} = \frac{4 \cdot 9 + 2}{9} : \frac{2}{5} = \frac{38}{9} : \frac{2}{5} = \frac{38}{9} \cdot \frac{5}{2} = \frac{38 \cdot 5}{9 \cdot 2} = \frac{19 \cdot 5}{9 \cdot 1} = \frac{95}{9} = 10\frac{5}{9}\] |
| \[1\frac{2}{5} : \frac{2}{5} = \frac{1 \cdot 5 + 2}{5} : \frac{2}{5} = \frac{7}{5} : \frac{2}{5} = \frac{7}{5} \cdot \frac{5}{2} = \frac{7 \cdot 5}{5 \cdot 2} = \frac{7}{2} = 3\frac{1}{2}\] | \[4\frac{2}{7} : \frac{2}{7} = \frac{4 \cdot 7 + 2}{7} : \frac{2}{7} = \frac{30}{7} : \frac{2}{7} = \frac{30}{7} \cdot \frac{7}{2} = \frac{30 \cdot 7}{7 \cdot 2} = \frac{15 \cdot 1}{1 \cdot 1} = 15\] | \[2\frac{4}{7} : \frac{4}{7} = \frac{2 \cdot 7 + 4}{7} : \frac{4}{7} = \frac{18}{7} : \frac{4}{7} = \frac{18}{7} \cdot \frac{7}{4} = \frac{18 \cdot 7}{7 \cdot 4} = \frac{9 \cdot 1}{1 \cdot 2} = \frac{9}{2} = 4\frac{1}{2}\] |
| \[\frac{3}{5} : 8 = \frac{3}{5} : \frac{8}{1} = \frac{3}{5} \cdot \frac{1}{8} = \frac{3 \cdot 1}{5 \cdot 8} = \frac{3}{40}\] | \[1\frac{1}{8} : 2 = \frac{1 \cdot 8 + 1}{8} : \frac{2}{1} = \frac{9}{8} : \frac{2}{1} = \frac{9}{8} \cdot \frac{1}{2} = \frac{9 \cdot 1}{8 \cdot 2} = \frac{9}{16}\] | \[\frac{1}{6} : 3 = \frac{1}{6} : \frac{3}{1} = \frac{1}{6} \cdot \frac{1}{3} = \frac{1 \cdot 1}{6 \cdot 3} = \frac{1}{18}\] |
| \[3 : \frac{1}{2} = \frac{3}{1} : \frac{1}{2} = \frac{3}{1} \cdot \frac{2}{1} = \frac{3 \cdot 2}{1 \cdot 1} = 6\] | \[1 : \frac{4}{7} = \frac{1}{1} : \frac{4}{7} = \frac{1}{1} \cdot \frac{7}{4} = \frac{1 \cdot 7}{1 \cdot 4} = \frac{7}{4} = 1\frac{3}{4}\] | \[1 : \frac{5}{9} = \frac{1}{1} : \frac{5}{9} = \frac{1}{1} \cdot \frac{9}{5} = \frac{1 \cdot 9}{1 \cdot 5} = \frac{9}{5} = 1\frac{4}{5}\] |
| \[7 - 2\frac{3}{7} = 7 - \frac{2 \cdot 7 + 3}{7} = 7 - \frac{17}{7} = \frac{49}{7} - \frac{17}{7} = \frac{49 - 17}{7} = \frac{32}{7} = 4\frac{4}{7}\] | \[9 - 4\frac{5}{14} = 9 - \frac{4 \cdot 14 + 5}{14} = 9 - \frac{61}{14} = \frac{126}{14} - \frac{61}{14} = \frac{126 - 61}{14} = \frac{65}{14} = 4\frac{9}{14}\] | \[6 - 3\frac{4}{9} = 6 - \frac{3 \cdot 9 + 4}{9} = 6 - \frac{31}{9} = \frac{54}{9} - \frac{31}{9} = \frac{54 - 31}{9} = \frac{23}{9} = 2\frac{5}{9}\] |
| \[2\frac{2}{9} - \frac{5}{9} = \frac{2 \cdot 9 + 2}{9} - \frac{5}{9} = \frac{20}{9} - \frac{5}{9} = \frac{20 - 5}{9} = \frac{15}{9} = \frac{5}{3} = 1\frac{2}{3}\] | \[2\frac{3}{7} - \frac{6}{7} = \frac{2 \cdot 7 + 3}{7} - \frac{6}{7} = \frac{17}{7} - \frac{6}{7} = \frac{17 - 6}{7} = \frac{11}{7} = 1\frac{4}{7}\] | \[3\frac{1}{6} - \frac{5}{6} = \frac{3 \cdot 6 + 1}{6} - \frac{5}{6} = \frac{19}{6} - \frac{5}{6} = \frac{19 - 5}{6} = \frac{14}{6} = \frac{7}{3} = 2\frac{1}{3}\] |
| \[3\frac{1}{5} - \frac{1}{2} = \frac{3 \cdot 5 + 1}{5} - \frac{1}{2} = \frac{16}{5} - \frac{1}{2} = \frac{32}{10} - \frac{5}{10} = \frac{32 - 5}{10} = \frac{27}{10} = 2\frac{7}{10}\] | \[5\frac{1}{8} - \frac{1}{3} = \frac{5 \cdot 8 + 1}{8} - \frac{1}{3} = \frac{41}{8} - \frac{1}{3} = \frac{123}{24} - \frac{8}{24} = \frac{123 - 8}{24} = \frac{115}{24} = 4\frac{19}{24}\] | \[6\frac{1}{7} - \frac{1}{5} = \frac{6 \cdot 7 + 1}{7} - \frac{1}{5} = \frac{43}{7} - \frac{1}{5} = \frac{215}{35} - \frac{7}{35} = \frac{215 - 7}{35} = \frac{208}{35} = 5\frac{33}{35}\] |
| \[\frac{1}{8} + \frac{3}{4} = \frac{1}{8} + \frac{6}{8} = \frac{1 + 6}{8} = \frac{7}{8}\] | \[\frac{2}{5} + \frac{1}{15} = \frac{6}{15} + \frac{1}{15} = \frac{6 + 1}{15} = \frac{7}{15}\] | \[\frac{1}{3} + \frac{2}{9} = \frac{3}{9} + \frac{2}{9} = \frac{3 + 2}{9} = \frac{5}{9}\] |
| \[\frac{7}{10} - \frac{2}{15} = \frac{21}{30} - \frac{4}{30} = \frac{21 - 4}{30} = \frac{17}{30}\] | \[\frac{5}{18} - \frac{1}{12} = \frac{10}{36} - \frac{3}{36} = \frac{10 - 3}{36} = \frac{7}{36}\] | \[\frac{5}{6} - \frac{3}{8} = \frac{20}{24} - \frac{9}{24} = \frac{20 - 9}{24} = \frac{11}{24}\] |
| \[1\frac{3}{4} \cdot \frac{4}{7} = \frac{1 \cdot 4 + 3}{4} \cdot \frac{4}{7} = \frac{7}{4} \cdot \frac{4}{7} = \frac{7 \cdot 4}{4 \cdot 7} = 1\] | \[5\frac{4}{9} \cdot 1\frac{1}{5} = \frac{5 \cdot 9 + 4}{9} \cdot \frac{1 \cdot 5 + 1}{5} = \frac{49}{9} \cdot \frac{6}{5} = \frac{49 \cdot 6}{9 \cdot 5} = \frac{49 \cdot 2}{3 \cdot 5} = \frac{98}{15} = 6\frac{8}{15}\] | \[3\frac{1}{3} \cdot \frac{3}{10} = \frac{3 \cdot 3 + 1}{3} \cdot \frac{3}{10} = \frac{10}{3} \cdot \frac{3}{10} = \frac{10 \cdot 3}{3 \cdot 10} = 1\] |
Ответ: Решения выше
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