№1. Вычислите: а) 2\(\frac{1}{2}\) + 1\(\frac{1}{3}\), б) 4 - 2\(\frac{4}{7}\), в) 2,5 + 1\(\frac{2}{3}\) - 3\(\frac{1}{6}\), г) 3\(\frac{1}{4}\) - 1\(\frac{5}{6}\), д) \(\frac{3}{8}\) · 2\(\frac{2}{7}\) · \(\frac{2}{3}\), е) 1\(\frac{3}{7}\) : 10, ж) \(\frac{8}{9}\) : \(\frac{16}{27}\), з) 2\(\frac{2}{3}\) : \(\frac{8}{9}\), и) (1\(\frac{17}{25}\) · 2\(\frac{7}{17}\) - 2\(\frac{4}{7}\) · 1\(\frac{1}{5}\)) · 2\(\frac{7}{9}\).

Question

Вопрос:

№1. Вычислите: а) 2\(\frac{1}{2}\) + 1\(\frac{1}{3}\), б) 4 - 2\(\frac{4}{7}\), в) 2,5 + 1\(\frac{2}{3}\) - 3\(\frac{1}{6}\), г) 3\(\frac{1}{4}\) - 1\(\frac{5}{6}\), д) \(\frac{3}{8}\) · 2\(\frac{2}{7}\) · \(\frac{2}{3}\), е) 1\(\frac{3}{7}\) : 10, ж) \(\frac{8}{9}\) : \(\frac{16}{27}\), з) 2\(\frac{2}{3}\) : \(\frac{8}{9}\), и) (1\(\frac{17}{25}\) · 2\(\frac{7}{17}\) - 2\(\frac{4}{7}\) · 1\(\frac{1}{5}\)) · 2\(\frac{7}{9}\).

Ответ:

ФИО:Телефон:Емаил:Полное описание сути нарушения прав (почему распространение данной информации запрещено Правообладателем):

Accepted Answer

Решение:

а) \(2\frac{1}{2} + 1\frac{1}{3}\)
\(2\frac{1}{2} + 1\frac{1}{3} = \frac{5}{2} + \frac{4}{3} = \frac{15}{6} + \frac{8}{6} = \frac{23}{6} = 3\frac{5}{6}\)
б) \(4 - 2\frac{4}{7}\)
\(4 - 2\frac{4}{7} = 4 - \frac{18}{7} = \frac{28}{7} - \frac{18}{7} = \frac{10}{7} = 1\frac{3}{7}\)
в) \(2,5 + 1\frac{2}{3} - 3\frac{1}{6}\)
\(2,5 + 1\frac{2}{3} - 3\frac{1}{6} = \frac{5}{2} + \frac{5}{3} - \frac{19}{6} = \frac{15}{6} + \frac{10}{6} - \frac{19}{6} = \frac{25 - 19}{6} = \frac{6}{6} = 1\)
г) \(3\frac{1}{4} - 1\frac{5}{6}\)
\(3\frac{1}{4} - 1\frac{5}{6} = \frac{13}{4} - \frac{11}{6} = \frac{39}{12} - \frac{22}{12} = \frac{17}{12} = 1\frac{5}{12}\)
д) \(\frac{3}{8}\) · \(2\frac{2}{7}\) · \(\frac{2}{3}\)
\(\frac{3}{8}\) · \(\frac{16}{7}\) · \(\frac{2}{3}\) = \(\frac{3 \cdot 16 \cdot 2}{8 \cdot 7 \cdot 3}\) = \(\frac{1 \cdot 2 \cdot 2}{1 \cdot 7 \cdot 1}\) = \(\frac{4}{7}\)
е) \(1\frac{3}{7}\) : 10
\(\frac{10}{7}\) : 10 = \(\frac{10}{7}\) · \(\frac{1}{10}\) = \(\frac{1}{7}\)
ж) \(\frac{8}{9}\) : \(\frac{16}{27}\)
\(\frac{8}{9}\) · \(\frac{27}{16}\) = \(\frac{8 \cdot 27}{9 \cdot 16}\) = \(\frac{1 \cdot 3}{1 \cdot 2}\) = \(\frac{3}{2}\) = 1,5\)
з) \(2\frac{2}{3}\) : \(\frac{8}{9}\)
\(\frac{8}{3}\) : \(\frac{8}{9}\) = \(\frac{8}{3}\) · \(\frac{9}{8}\) = \(\frac{1 \cdot 3}{1 \cdot 1}\) = 3\)
и) \((1\frac{17}{25} \cdot 2\frac{7}{17} - 2\frac{4}{7} \cdot 1\frac{1}{5}) \cdot 2\frac{7}{9}\)
\((1\frac{17}{25} \cdot 2\frac{7}{17} - 2\frac{4}{7} \cdot 1\frac{1}{5}) \cdot 2\frac{7}{9}\) = \((\frac{42}{25} \cdot \frac{41}{17} - \frac{18}{7} \cdot \frac{6}{5}) \cdot \frac{25}{9}\)

Ответ: а) \(3\frac{5}{6}\); б) \(1\frac{3}{7}\); в) 1; г) \(1\frac{5}{12}\); д) \(\frac{4}{7}\); е) \(\frac{1}{7}\); ж) \(1,5\); з) 3; и) ...