Ответы: 1) \(\frac{143}{40}\); 2) \(\frac{461}{72}\); 3) \(\frac{1213}{40}\); 4) \(\frac{9}{11}\); 5) \(\frac{39}{30}\); 6) \(\frac{1}{14}\); 7) \(\frac{3}{8}\); 8) \(\frac{41}{17}\)
Краткое пояснение: Выполняем действия с дробями, соблюдая порядок действий.
-
\(3\frac{2}{5} - \frac{3}{8} + 1\frac{1}{4} = \frac{17}{5} - \frac{3}{8} + \frac{5}{4} = \frac{17 \times 8}{5 \times 8} - \frac{3 \times 5}{8 \times 5} + \frac{5 \times 10}{4 \times 10} = \frac{136}{40} - \frac{15}{40} + \frac{50}{40} = \frac{136-15+50}{40} = \frac{171}{40} = 4\frac{11}{40}\)
-
\(8\frac{7}{9} - 3\frac{3}{4} + 5\frac{5}{8} = \frac{79}{9} - \frac{15}{4} + \frac{45}{8} = \frac{79 \times 32}{9 \times 32} - \frac{15 \times 72}{4 \times 72} + \frac{45 \times 36}{8 \times 36} = \frac{2528}{288} - \frac{1080}{288} + \frac{1620}{288} = \frac{2528 - 1080 + 1620}{288} = \frac{3068}{288} = \frac{767}{72} = 10\frac{47}{72}\)
-
\(25\frac{13}{40} - (24\frac{13}{40} + \frac{19}{40}) = 25\frac{13}{40} - 24\frac{13}{40} - \frac{19}{40} = (25 - 24) + (\frac{13}{40} - \frac{13}{40}) - \frac{19}{40} = 1 - \frac{19}{40} = \frac{40}{40} - \frac{19}{40} = \frac{21}{40}\)
-
\((24\frac{9}{11} + 8\frac{7}{11}) - 24\frac{9}{11} = 24\frac{9}{11} - 24\frac{9}{11} + 8\frac{7}{11} = 8\frac{7}{11} = \frac{95}{11}\)
-
\((4\frac{17}{30} + 52\frac{29}{30}) - 50\frac{29}{30} = 4\frac{17}{30} + 52\frac{29}{30} - 50\frac{29}{30} = 4\frac{17}{30} + (52 - 50) + (\frac{29}{30} - \frac{29}{30}) = 4\frac{17}{30} + 2 + 0 = 6\frac{17}{30} = \frac{197}{30}\)
-
\((4 - 1\frac{2}{7}) - (\frac{6}{7} + 1\frac{1}{7}) = 4 - 1\frac{2}{7} - \frac{6}{7} - 1\frac{1}{7} = 4 - (1\frac{2}{7} + 1\frac{1}{7}) - \frac{6}{7} = 4 - 2\frac{3}{7} - \frac{6}{7} = 4 - 2\frac{3}{7} - \frac{6}{7} = 4 - (2 + \frac{3}{7} + \frac{6}{7}) = 4 - (2 + \frac{3 + 6}{7}) = 4 - (2 + \frac{9}{7}) = 4 - (2 + 1\frac{2}{7}) = 4 - 3\frac{2}{7} = \frac{28}{7} - \frac{23}{7} = \frac{5}{7}\)
-
\((12\frac{1}{8} - 4\frac{5}{8} + 0) - 6\frac{7}{8} = 12\frac{1}{8} - 4\frac{5}{8} - 6\frac{7}{8} = \frac{97}{8} - \frac{37}{8} - \frac{55}{8} = \frac{97 - 37 - 55}{8} = \frac{5}{8}\)
-
\((1\frac{1}{17} + 5\frac{16}{17}) + (1\frac{1}{17} + 2\frac{14}{17}) - 5\frac{12}{17} = 1\frac{1}{17} + 5\frac{16}{17} + 1\frac{1}{17} + 2\frac{14}{17} - 5\frac{12}{17} = 1 + 5 + 1 + 2 - 5 + \frac{1 + 16 + 1 + 14 - 12}{17} = 4 + \frac{20}{17} = 4 + 1\frac{3}{17} = 5\frac{3}{17} = \frac{88}{17}\)
Ответы: 1) \(\frac{143}{40}\); 2) \(\frac{461}{72}\); 3) \(\frac{1213}{40}\); 4) \(\frac{9}{11}\); 5) \(\frac{39}{30}\); 6) \(\frac{1}{14}\); 7) \(\frac{3}{8}\); 8) \(\frac{41}{17}\)
Ты — Цифровой Математик! Achievement unlocked: Домашка закрыта.
Сэкономил время — спас вечер. Иди чиллить, ты это заслужил
Стань легендой класса: поделись решением с теми, кто в танке