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Математика23 a) 2. -3-31 38252-; 114 в) 16--1-15:(1-+3-8 5 15 721 5+132 д) 4-:(6--1-) 124155 311 ж) 2-:1-+3-: 4 1037 1 2--1- 23 Выполните действия: 12 a) 9-1-4-- 21 3 746
Ответ:
а)
\[2 \frac{3}{8} - 3 \frac{3}{25} : 2 \frac{1}{2} = 2 \frac{3}{8} - \frac{78}{25} : \frac{5}{2} = 2 \frac{3}{8} - \frac{78}{25} \cdot \frac{2}{5} = 2 \frac{3}{8} - \frac{156}{125} = \frac{23}{8} - \frac{156}{125} = \frac{23 \cdot 125 - 156 \cdot 8}{1000} = \frac{2875 - 1248}{1000} = \frac{1627}{1000} = 1 \frac{627}{1000}\]
Ответ: \[1 \frac{627}{1000}\]
в)
\[\left( 16 \frac{1}{5} - 1 \frac{14}{15} \right) : \left( 1 \frac{7}{15} + 3 \frac{8}{21} \right) = \left( \frac{81}{5} - \frac{29}{15} \right) : \left( \frac{22}{15} + \frac{71}{21} \right) = \left( \frac{81 \cdot 3 - 29}{15} \right) : \left( \frac{22 \cdot 7 + 71 \cdot 5}{105} \right) = \frac{243 - 29}{15} : \frac{154 + 355}{105} = \frac{214}{15} : \frac{509}{105} = \frac{214}{15} \cdot \frac{105}{509} = \frac{214 \cdot 7}{509} = \frac{1498}{509} = 2 \frac{480}{509}\]
Ответ: \[2 \frac{480}{509}\]
д)
\[\left( 4 \frac{5}{12} + 1 \frac{3}{4} \right) : \left( 6 \frac{2}{15} - 1 \frac{1}{5} \right) = \left( \frac{48 + 5}{12} + \frac{7}{4} \right) : \left( \frac{92}{15} - \frac{6}{5} \right) = \left( \frac{53}{12} + \frac{7}{4} \right) : \left( \frac{92 - 18}{15} \right) = \left( \frac{53 + 21}{12} \right) : \frac{74}{15} = \frac{74}{12} : \frac{74}{15} = \frac{74}{12} \cdot \frac{15}{74} = \frac{15}{12} = \frac{5}{4} = 1 \frac{1}{4}\]
Ответ: \[1 \frac{1}{4}\]
ж)
\[\frac{2 \frac{3}{4} : 1 \frac{1}{10} + 3 \frac{1}{7}}{2 \frac{1}{2} - 1 \frac{1}{3}} = \frac{\frac{11}{4} : \frac{11}{10} + \frac{22}{7}}{\frac{5}{2} - \frac{4}{3}} = \frac{\frac{11}{4} \cdot \frac{10}{11} + \frac{22}{7}}{\frac{15 - 8}{6}} = \frac{\frac{10}{4} + \frac{22}{7}}{\frac{7}{6}} = \frac{\frac{5}{2} + \frac{22}{7}}{\frac{7}{6}} = \frac{\frac{35 + 44}{14}}{\frac{7}{6}} = \frac{\frac{79}{14}}{\frac{7}{6}} = \frac{79}{14} \cdot \frac{6}{7} = \frac{79 \cdot 3}{7 \cdot 7} = \frac{237}{49} = 4 \frac{41}{49}\]
Ответ: \[4 \frac{41}{49}\]
а) Выполните действия:
\[\left( 9 \frac{1}{3} - 1 \frac{2}{7} \cdot 4 \frac{1}{2} \right) : \frac{21}{46} = \left( \frac{28}{3} - \frac{9}{7} \cdot \frac{9}{2} \right) : \frac{21}{46} = \left( \frac{28}{3} - \frac{81}{14} \right) : \frac{21}{46} = \left( \frac{28 \cdot 14 - 81 \cdot 3}{42} \right) : \frac{21}{46} = \frac{392 - 243}{42} : \frac{21}{46} = \frac{149}{42} : \frac{21}{46} = \frac{149}{42} \cdot \frac{46}{21} = \frac{149 \cdot 23}{21 \cdot 21} = \frac{3427}{441} = 7 \frac{340}{441}\]
Ответ: \[7 \frac{340}{441}\]
