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МатематикаРешите уравнение: 1) \(\frac{1}{3}x+\frac{1}{5}x+\frac{1}{6}x=\frac{21}{40};\) 3) \(8\frac{4}{15}-5\frac{2}{5}x=4\frac{2}{3};\) 2) \(5\frac{1}{4}x-2\frac{2}{3}=\frac{1}{12};\) 4) \(\frac{11}{24}x+7\frac{1}{3}=9\frac{5}{8}.\)
Ответ:
1) \(\frac{1}{3}x+\frac{1}{5}x+\frac{1}{6}x=\frac{21}{40}\) \(\frac{1 \cdot 10 + 1 \cdot 6 + 1 \cdot 5}{30}x = \frac{21}{40}\) \(\frac{10 + 6 + 5}{30}x = \frac{21}{40}\) \(\frac{21}{30}x = \frac{21}{40}\) \(x = \frac{21}{40} : \frac{21}{30}\) \(x = \frac{21}{40} \cdot \frac{30}{21}\) \(x = \frac{30}{40} = \frac{3}{4}\)
3) \(8\frac{4}{15}-5\frac{2}{5}x=4\frac{2}{3}\) \(5\frac{2}{5}x = 8\frac{4}{15} - 4\frac{2}{3}\) \(5\frac{2}{5}x = \frac{8 \cdot 15 + 4}{15} - \frac{4 \cdot 3 + 2}{3}\) \(5\frac{2}{5}x = \frac{124}{15} - \frac{14}{3}\) \(5\frac{2}{5}x = \frac{124 - 14 \cdot 5}{15}\) \(5\frac{2}{5}x = \frac{124 - 70}{15}\) \(5\frac{2}{5}x = \frac{54}{15}\) \(\frac{5 \cdot 5 + 2}{5}x = \frac{54}{15}\) \(\frac{27}{5}x = \frac{54}{15}\) \(x = \frac{54}{15} : \frac{27}{5}\) \(x = \frac{54}{15} \cdot \frac{5}{27}\) \(x = \frac{54 \cdot 5}{15 \cdot 27} = \frac{2 \cdot 27 \cdot 5}{3 \cdot 5 \cdot 27} = \frac{2}{3}\)
2) \(5\frac{1}{4}x-2\frac{2}{3}=\frac{1}{12}\) \(5\frac{1}{4}x = \frac{1}{12} + 2\frac{2}{3}\) \(5\frac{1}{4}x = \frac{1}{12} + \frac{2 \cdot 3 + 2}{3}\) \(5\frac{1}{4}x = \frac{1}{12} + \frac{8}{3}\) \(5\frac{1}{4}x = \frac{1 + 8 \cdot 4}{12}\) \(5\frac{1}{4}x = \frac{1 + 32}{12}\) \(5\frac{1}{4}x = \frac{33}{12}\) \(\frac{5 \cdot 4 + 1}{4}x = \frac{33}{12}\) \(\frac{21}{4}x = \frac{33}{12}\) \(x = \frac{33}{12} : \frac{21}{4}\) \(x = \frac{33}{12} \cdot \frac{4}{21}\) \(x = \frac{33 \cdot 4}{12 \cdot 21} = \frac{3 \cdot 11 \cdot 4}{3 \cdot 4 \cdot 21} = \frac{11}{21}\)
4) \(\frac{11}{24}x+7\frac{1}{3}=9\frac{5}{8}\) \(\frac{11}{24}x = 9\frac{5}{8} - 7\frac{1}{3}\) \(\frac{11}{24}x = \frac{9 \cdot 8 + 5}{8} - \frac{7 \cdot 3 + 1}{3}\) \(\frac{11}{24}x = \frac{77}{8} - \frac{22}{3}\) \(\frac{11}{24}x = \frac{77 \cdot 3 - 22 \cdot 8}{24}\) \(\frac{11}{24}x = \frac{231 - 176}{24}\) \(\frac{11}{24}x = \frac{55}{24}\) \(x = \frac{55}{24} : \frac{11}{24}\) \(x = \frac{55}{24} \cdot \frac{24}{11}\) \(x = \frac{55 \cdot 24}{24 \cdot 11} = \frac{5 \cdot 11}{11} = 5\)
Ответ: 1) \(\frac{3}{4}\); 3) \(\frac{2}{3}\); 2) \(\frac{11}{21}\); 4) \(5\)
Похожие
- Выполните деление: 1) \(\frac{5}{7}:\frac{4}{5};\) 2) \(\frac{6}{35}:\frac{18}{49};\) 3) \(\frac{27}{28}:\frac{9}{56};\) 4) \(\frac{28}{45}:\frac{63}{40}.\)
- Найдите частное: 1) \(6:\frac{2}{7};\) 3) \(\frac{7}{25}:28;\) 5) \(2\frac{2}{3}:2\frac{2}{7};\) 2) \(1:\frac{8}{19};\) 4) \(16\frac{1}{3}:5\frac{5}{6};\) 6) \(4\frac{4}{9}:\frac{5}{27}.\)
- Найдите значение выражения: 1) \(5\frac{1}{3}:\frac{8}{9}:1\frac{1}{3};\) 3) \((8\frac{5}{7}-6\frac{5}{6}):1\frac{1}{36}:4\frac{3}{4};\) 2) \(5\frac{1}{3}:(\frac{8}{9}:1\frac{1}{3});\) 4) \((2\frac{5}{6}+2\frac{2}{9}):3\frac{1}{4}-\frac{2}{7}:1\frac{1}{7}.\)
- Вычислите значение выражения: 1) \((2\frac{4}{5}+2\frac{2}{3}):(10\frac{13}{30}-3\frac{3}{5})\cdot 2,5;\) 2) \((2\frac{5}{14}\cdot 4\frac{2}{3}+12:2\frac{1}{4}-15\frac{1}{4}):(4\frac{7}{18}-2\frac{5}{9}).\)
