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Математика5 д) α) 1-6) 5-2000) 210-12 3 5 б) 8--7- 4 6 5 9 3 г) 2--1- 8 10 1. Вычислите: 2.12 1 13 14 21 e) 819-37 20 30 3 a).1; 6) 3.2; B) 1층.10; 3
Ответ:
а) \( 1 - \frac{5}{6} = \frac{6}{6} - \frac{5}{6} = \frac{6-5}{6} = \frac{1}{6} \)
б) \( 5 - 2\frac{5}{9} = 5 - \frac{23}{9} = \frac{45}{9} - \frac{23}{9} = \frac{45-23}{9} = \frac{22}{9} = 2\frac{4}{9} \)
в) \( 2\frac{13}{14} - 1\frac{20}{21} = \frac{41}{14} - \frac{41}{21} = \frac{41 \cdot 3}{14 \cdot 3} - \frac{41 \cdot 2}{21 \cdot 2} = \frac{123}{42} - \frac{82}{42} = \frac{123-82}{42} = \frac{41}{42} \)
г) \( 8\frac{3}{4} - 7\frac{5}{6} = \frac{35}{4} - \frac{47}{6} = \frac{35 \cdot 3}{4 \cdot 3} - \frac{47 \cdot 2}{6 \cdot 2} = \frac{105}{12} - \frac{94}{12} = \frac{105-94}{12} = \frac{11}{12} \)
д) \( 2\frac{5}{8} - 1\frac{3}{10} = \frac{21}{8} - \frac{13}{10} = \frac{21 \cdot 5}{8 \cdot 5} - \frac{13 \cdot 4}{10 \cdot 4} = \frac{105}{40} - \frac{52}{40} = \frac{105-52}{40} = \frac{53}{40} = 1\frac{13}{40} \)
e) \( 8\frac{19}{20} - 3\frac{7}{30} = \frac{179}{20} - \frac{97}{30} = \frac{179 \cdot 3}{20 \cdot 3} - \frac{97 \cdot 2}{30 \cdot 2} = \frac{537}{60} - \frac{194}{60} = \frac{537-194}{60} = \frac{343}{60} = 5\frac{43}{60} \)
1. Вычислите:
а) \( \frac{2}{3} \cdot 1\frac{2}{7} = \frac{2}{3} \cdot \frac{9}{7} = \frac{2 \cdot 9}{3 \cdot 7} = \frac{2 \cdot 3}{1 \cdot 7} = \frac{6}{7} \)
б) \( 3\frac{1}{8} \cdot 2 = \frac{25}{8} \cdot 2 = \frac{25 \cdot 2}{8} = \frac{25 \cdot 1}{4} = \frac{25}{4} = 6\frac{1}{4} \)
в) \( 1\frac{1}{7} \cdot 1\frac{3}{7} = \frac{8}{7} \cdot \frac{10}{7} = \frac{8 \cdot 10}{7 \cdot 7} = \frac{80}{49} = 1\frac{31}{49} \)
Ответ: а) \(\frac{1}{6}\); б) \(2\frac{4}{9}\); в) \(\frac{41}{42}\); г) \(\frac{11}{12}\); д) \(1\frac{13}{40}\); e) \(5\frac{43}{60}\); 1. а) \(\frac{6}{7}\); б) \(6\frac{1}{4}\); в) \(1\frac{31}{49}\)
