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Математика1117. Выполните действия: a) 5 + 20; ж) 3음+5; M) 4-2음 6) 10 - 7; 4 3)9-7 12' H) 4-; в) 4 + 10; 6 0) 8-12 15 г) 120-12; к) 80+712; 13 13' Ⅱ) 5-30; д) 4+3; л) 50 - 1; p) 4-30.
Ответ:
Ответ: a) 7\(\frac{5}{8}\); б) 3\(\frac{1}{3}\); в) 14\(\frac{1}{6}\); г) 0\(\frac{7}{8}\); д) 7\(\frac{7}{9}\); e) 3\(\frac{1}{15}\); ж) 8\(\frac{7}{11}\); з) 2\(\frac{1}{4}\); и) 7\(\frac{5}{12}\); к) 16\(\frac{5}{13}\); л) 3\(\frac{11}{15}\); м) 1\(\frac{3}{8}\)
Решение:
a) \(5 + 2\frac{5}{8} = 5 + \frac{2 \cdot 8 + 5}{8} = 5 + \frac{16 + 5}{8} = 5 + \frac{21}{8} = \frac{5 \cdot 8 + 21}{8} = \frac{40 + 21}{8} = \frac{61}{8} = 7\frac{5}{8}\)
б) \(10\frac{1}{3} - 7\frac{4}{5} = \frac{10 \cdot 3 + 1}{3} - \frac{7 \cdot 5 + 4}{5} = \frac{31}{3} - \frac{39}{5} = \frac{31 \cdot 5 - 39 \cdot 3}{15} = \frac{155 - 117}{15} = \frac{38}{15} = 2\frac{8}{15}\)
в) \(4\frac{1}{6} + 10 = 10 + 4\frac{1}{6} = 14\frac{1}{6}\)
г) \(12\frac{8}{15} - 12 = \frac{12 \cdot 15 + 8}{15} - 12 = \frac{180 + 8}{15} - 12 = \frac{188}{15} - 12 = \frac{188 - 12 \cdot 15}{15} = \frac{188 - 180}{15} = \frac{8}{15}\)
д) \(4\frac{1}{9} + 3\frac{4}{5} = \frac{4 \cdot 9 + 1}{9} + \frac{3 \cdot 5 + 4}{5} = \frac{37}{9} + \frac{19}{5} = \frac{37 \cdot 5 + 19 \cdot 9}{45} = \frac{185 + 171}{45} = \frac{356}{45} = 7\frac{41}{45}\)
e) \(7\frac{5}{7} - 4\frac{3}{4} = \frac{7 \cdot 7 + 5}{7} - \frac{4 \cdot 4 + 3}{4} = \frac{54}{7} - \frac{19}{4} = \frac{54 \cdot 4 - 19 \cdot 7}{28} = \frac{216 - 133}{28} = \frac{83}{28} = 2\frac{27}{28}\)
ж) \(3\frac{8}{11} + 5\frac{2}{5} = \frac{3 \cdot 11 + 8}{11} + \frac{5 \cdot 5 + 2}{5} = \frac{41}{11} + \frac{27}{5} = \frac{41 \cdot 5 + 27 \cdot 11}{55} = \frac{205 + 297}{55} = \frac{502}{55} = 9\frac{7}{55}\)
з) \(9\frac{6}{12} - 7\frac{5}{12} = \frac{9 \cdot 12 + 6}{12} - \frac{7 \cdot 12 + 5}{12} = \frac{108 + 6}{12} - \frac{84 + 5}{12} = \frac{114}{12} - \frac{89}{12} = \frac{114 - 89}{12} = \frac{25}{12} = 2\frac{1}{12}\)
и) \(4\frac{1}{3} + 2\frac{4}{5} = \frac{4 \cdot 3 + 1}{3} + \frac{2 \cdot 5 + 4}{5} = \frac{13}{3} + \frac{14}{5} = \frac{13 \cdot 5 + 14 \cdot 3}{15} = \frac{65 + 42}{15} = \frac{107}{15} = 7\frac{2}{15}\)
к) \(8\frac{9}{13} + 7\frac{12}{13} = \frac{8 \cdot 13 + 9}{13} + \frac{7 \cdot 13 + 12}{13} = \frac{104 + 9}{13} + \frac{91 + 12}{13} = \frac{113}{13} + \frac{103}{13} = \frac{113 + 103}{13} = \frac{216}{13} = 16\frac{8}{13}\)
л) \(5\frac{5}{8} - 1\frac{3}{5} = \frac{5 \cdot 8 + 5}{8} - \frac{1 \cdot 5 + 3}{5} = \frac{45}{8} - \frac{8}{5} = \frac{45 \cdot 5 - 8 \cdot 8}{40} = \frac{225 - 64}{40} = \frac{161}{40} = 4\frac{1}{40}\)
м) \(4\frac{5}{11} - 2\frac{2}{8} = 4\frac{5}{11} - 2\frac{1}{4} = \frac{4 \cdot 11 + 5}{11} - \frac{2 \cdot 4 + 1}{4} = \frac{49}{11} - \frac{9}{4} = \frac{49 \cdot 4 - 9 \cdot 11}{44} = \frac{196 - 99}{44} = \frac{97}{44} = 2\frac{9}{44}\)
Ответ: a) 7\(\frac{5}{8}\); б) 3\(\frac{1}{3}\); в) 14\(\frac{1}{6}\); г) 0\(\frac{7}{8}\); д) 7\(\frac{7}{9}\); e) 3\(\frac{1}{15}\); ж) 8\(\frac{7}{11}\); з) 2\(\frac{1}{4}\); и) 7\(\frac{5}{12}\); к) 16\(\frac{5}{13}\); л) 3\(\frac{11}{15}\); м) 1\(\frac{3}{8}\)
