Question

Вычислите:
1) 5/9 + 1 5/7 (4 2/3 - 2 5/8) : 1 3/4 =
2) 2 - 3 1/7 * ( 2 - 1 9/11) : 8/21 =
3) 2 1/3 + 4 1/10 : ( 2 7/15 - 5/12) * 5/6 =
4) 4 5/12 - 1 1/2 : ( 2 1/6 + 8/15 ) * 1 4/5 =

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Answer 1

Переводим смешанные дроби в неправильные:

1. $\frac{5}{9} + \frac{12}{7} (\frac{14}{3} - \frac{21}{8}) : \frac{7}{4} = 2\frac{5}{9}$

1) $\frac{14}{3} - \frac{21}{8} = \frac{112}{24} - \frac{63}{24} = \frac{49}{24}$

2) $\frac{49}{24} * \frac{4}{7} = \frac{7}{6}$

3) $\frac{12}{7} * \frac{7}{6} = \frac{2}{1}$

4) $\frac{5}{9} + \frac{2}{1} = \frac{5}{9} + \frac{18}{9} = \frac{23}{9} = 2\frac{5}{9}$

2. $2 - \frac{22}{7} * (2 - \frac{20}{11}) : \frac{8}{21} = -1$

1) $\frac{2}{1} - \frac{20}{11} = \frac{22}{11} - \frac{20}{11} = \frac{2}{11}$

2) $\frac{2}{11} * \frac{21}{8} = \frac{21}{44}$

3) $\frac{22}{7} * \frac{21}{44} = \frac{6}{2} = 3$

4) 2 - 3 = -1

3. $\frac{7}{3} + \frac{41}{10} : (\frac{37}{15} - \frac{5}{12}) * \frac{5}{6} = 4\frac{11}{15}$

1) $\frac{37}{15} - \frac{5}{12} = \frac{148}{60} - \frac{25}{60} = \frac{123}{60}$

2) $\frac{123}{60} * \frac{5}{6} = \frac{41}{24}$

3) $\frac{41}{10} * \frac{24}{41} = \frac{12}{5}$

4) $\frac{7}{3} + \frac{12}{5} = \frac{35}{15} + \frac{36}{15} = \frac{71}{15} = 4\frac{11}{15}$  

4. $\frac{53}{12} - \frac{3}{2} : (\frac{13}{6} + \frac{8}{15}) * \frac{9}{5} = 4\frac{55}{852}$

1) $\frac{13}{6} + \frac{8}{15} = \frac{65}{30} + \frac{16}{30} = \frac{81}{30}$

2) $\frac{81}{30} * \frac{9}{5} = \frac{243}{50}$

3) $\frac{3}{2} * \frac{50}{243} = \frac{25}{71}$

4) $\frac{53}{12} - \frac{25}{71} = \frac{3763}{852} - \frac{300}{852} = \frac{3463}{852} = 4\frac{55}{852}$