A) 10\(\cdot\)(3\(\frac{2}{15}\)-\(\frac{5}{18}\))+12\(\cdot\)(1\(\frac{5}{6}\)+\(\frac{3}{4}\)) Б) \(\frac{2}{3}+\frac{5}{8}+\frac{11}{12}\)\(\cdot\)\(\frac{1}{3}\) B) \(\(\frac{1}{2}\)-\(\frac{3}{8}\)\)\(\(\frac{1}{2}\)-\(\frac{5}{6}\)\)\(\cdot\)\(\frac{1}{3}\) Г) \(\(\frac{1}{2}\)-\(\frac{3}{8}\)\)\(\cdot\)\(\frac{2}{3}\)\(\cdot\)\(\frac{4}{5}\)-\(\(\frac{1}{3}\)-\(\frac{7}{9}\)\) Д) \(\(\frac{7}{12}\)-\(\frac{17}{36}\)\)\(\cdot\)\(\frac{1}{2}\)+\(\frac{1}{3}\)\(\cdot\)\(\frac{3}{26}\)+\(\frac{1}{2}\) E) \(\(\(\frac{3}{5}\)+\(\frac{7}{10}\)\)\(\cdot\)\(\frac{3}{17}\)-\(\(\frac{7}{23}\)-\(\frac{1}{46}\)\)\(\cdot\)\(\frac{45}{80}\)\)\(\cdot\)\(\frac{1}{3}\) Ë) 8\(\frac{2}{11}\)\(\(\frac{3}{4}\)\(\cdot\)\(\frac{4}{57}\)+\(\frac{7}{3}\)\(\cdot\)\(\frac{2}{9}\)\)+15\(\(\frac{5}{8}\)\(\cdot\)\(\frac{7}{47}\)-\(\frac{3}{2}\)\(\cdot\)\(\frac{2}{3}\)\(\cdot\)\(\frac{31}{55}\)) Ж) \(\frac{3}{8}\)\(\cdot\)\(\frac{5}{4}\)+\(\frac{1}{6}\)\(\cdot\)\(\frac{2}{10}\)-\(\frac{1}{9}\)\(\cdot\)\(\frac{9}{20}\)\(\cdot\)\(\6\) 3) \(\(\frac{7}{15}\)+\(\frac{7}{30}\)+\(\frac{4}{5}\)\):\(\(\2\)-\(\frac{1}{3}\)-\(\frac{1}{2}\)\) И) \(\(\frac{1}{6}\)+\(\frac{1}{10}\)+\(\frac{1}{15}\)\):\(\(\frac{3}{5}\)-\(\frac{1}{3}\)-\(\frac{1}{4}\)\)

Решение:

A)

1. \(\(\frac{2}{15}\)-\(\frac{5}{18}\) = \(\frac{12}{90}\)-\(\frac{25}{90}\) = \(-\frac{13}{90}\)\)
2. \(\(\frac{5}{6}\)+\(\frac{3}{4}\) = \(\frac{10}{12}\)+\(\frac{9}{12}\) = \(\frac{19}{12}\)\)
3. \(10\(\cdot\)\(\frac{-13}{90}\) = \(-\frac{13}{9}\)\)
4. \(12\(\cdot\)\(\frac{19}{12}\) = 19\)
5. \(-\frac{13}{9}\) + 19 = \(-\frac{13}{9}\) + \(\frac{171}{9}\) = \(\frac{158}{9}\)

Б)

1. \(\(\frac{2}{3}\)+\(\frac{5}{8}\)+\(\frac{11}{12}\) = \(\frac{16}{24}\)+\(\frac{15}{24}\)+\(\frac{22}{24}\) = \(\frac{53}{24}\)\)
2. \(\(\frac{53}{24}\)\(\cdot\)\(\frac{1}{3}\) = \(\frac{53}{72}\)\)

B)

1. \(\(\frac{1}{2}\)-\(\frac{3}{8}\) = \(\frac{4}{8}\)-\(\frac{3}{8}\) = \(\frac{1}{8}\)\)
2. \(\(\frac{1}{2}\)-\(\frac{5}{6}\) = \(\frac{3}{6}\)-\(\frac{5}{6}\) = \(-\frac{2}{6}\) = \(-\frac{1}{3}\)\)
3. \(\(\frac{1}{8}\)\(\cdot\)\(\frac{-1}{3}\)\(\cdot\)\(\frac{1}{3}\) = \(-\frac{1}{72}\)\)

Г)

1. \(\(\frac{1}{2}\)-\(\frac{3}{8}\) = \(\frac{4}{8}\)-\(\frac{3}{8}\) = \(\frac{1}{8}\)\)
2. \(\(\frac{1}{3}\)-\(\frac{7}{9}\) = \(\frac{3}{9}\)-\(\frac{7}{9}\) = \(-\frac{4}{9}\)\)
3. \(\(\frac{1}{8}\)\(\cdot\)\(\frac{2}{3}\)\(\cdot\)\(\frac{4}{5}\) = \(\frac{8}{120}\) = \(\frac{1}{15}\)\)
4. \(\frac{1}{15}\)-\(\frac{-4}{9}\) = \(\frac{1}{15}\)+\(\frac{4}{9}\) = \(\frac{3}{45}\)+\(\frac{20}{45}\) = \(\frac{23}{45}\)\)

Д)

1. \(\(\frac{7}{12}\)-\(\frac{17}{36}\) = \(\frac{21}{36}\)-\(\frac{17}{36}\) = \(\frac{4}{36}\) = \(\frac{1}{9}\)\)
2. \(\frac{1}{9}\)\(\cdot\)\(\frac{1}{2}\) = \(\frac{1}{18}\)\)
3. \(\frac{1}{3}\)\(\cdot\)\(\frac{3}{26}\) = \(\frac{1}{26}\)\)
4. \(\frac{1}{18}\)+\(\frac{1}{26}\)+\(\frac{1}{2}\) = \(\frac{1}{18}\)+\(\frac{1}{26}\)+\(\frac{13}{26}\) = \(\frac{1}{18}\)+\(\frac{14}{26}\) = \(\frac{1}{18}\)+\(\frac{7}{13}\) = \(\frac{13}{234}\)+\(\frac{126}{234}\) = \(\frac{139}{234}\)\)

E)

1. \(\(\frac{3}{5}\)+\(\frac{7}{10}\) = \(\frac{6}{10}\)+\(\frac{7}{10}\) = \(\frac{13}{10}\)\)
2. \(\(\frac{13}{10}\)\(\cdot\)\(\frac{3}{17}\) = \(\frac{39}{170}\)\)
3. \(\(\frac{7}{23}\)-\(\frac{1}{46}\) = \(\frac{14}{46}\)-\(\frac{1}{46}\) = \(\frac{13}{46}\)\)
4. \(\(\frac{13}{46}\)\(\cdot\)\(\frac{45}{80}\) = \(\frac{13\(\cdot\)9}{46\(\cdot\)16}\) = \(\frac{117}{736}\)\)
5. \(\(\frac{39}{170}\)-\(\frac{117}{736}\)\)\(\cdot\)\(\frac{1}{3}\) = \(\(\frac{39\(\cdot\)736-117\(\cdot\)170}{170\(\cdot\)736}\)\)\(\cdot\)\(\frac{1}{3}\) = \(\(\frac{28604-19890}{125120}\)\)\(\cdot\)\(\frac{1}{3}\) = \(\(\frac{8714}{125120}\)\)\(\cdot\)\(\frac{1}{3}\) = \(\frac{8714}{375360}\) = \(\frac{4357}{187680}\)\)

Ë)

1. \(\(\frac{3}{4}\)\(\cdot\)\(\frac{4}{57}\) = \(\frac{3}{57}\) = \(\frac{1}{19}\)\)
2. \(\(\frac{7}{3}\)\(\cdot\)\(\frac{2}{9}\) = \(\frac{14}{27}\)\)
3. \(\frac{1}{19}\)+\(\frac{14}{27}\) = \(\frac{27+14\(\cdot\)19}{19\(\cdot\)27}\) = \(\frac{27+266}{513}\) = \(\frac{293}{513}\)\)
4. \(8\(\frac{2}{11}\) = \(\frac{90}{11}\)\)
5. \(\frac{90}{11}\)\(\cdot\)\(\frac{293}{513}\) = \(\frac{30\(\cdot\)293}{11\(\cdot\)171}\) = \(\frac{8790}{1881}\)\)
6. \(\(\frac{5}{8}\)\(\cdot\)\(\frac{7}{47}\) = \(\frac{35}{376}\)\)
7. \(\(\frac{3}{2}\)\(\cdot\)\(\frac{2}{3}\)\(\cdot\)\(\frac{31}{55}\) = \(\frac{31}{55}\)\)
8. \(\frac{35}{376}\)-\(\frac{31}{55}\) = \(\frac{35\(\cdot\)55-31\(\cdot\)376}{376\(\cdot\)55}\) = \(\frac{1925-11656}{20680}\) = \(-\frac{9731}{20680}\)\)
9. 15\(\cdot\)\(\frac{-9731}{20680}\) = \(-\frac{29193}{4136}\)\)
10. \(\frac{8790}{1881}\) + \(-\frac{29193}{4136}\) = \(\frac{8790\(\cdot\)4136-29193\(\cdot\)1881}{1881\(\cdot\)4136}\) = \(\frac{36330240-54901773}{7771856}\) = \(-\frac{18571533}{7771856}\)\)

Ж)

1. \(\frac{3}{8}\)\(\cdot\)\(\frac{5}{4}\) = \(\frac{15}{32}\)\)
2. \(\frac{1}{6}\)\(\cdot\)\(\frac{2}{10}\) = \(\frac{2}{60}\) = \(\frac{1}{30}\)\)
3. \(\frac{1}{9}\)\(\cdot\)\(\frac{9}{20}\)\(\cdot\)\(\6\) = \(\frac{1}{20}\)\(\cdot\)\(\6\) = \(\frac{6}{20}\) = \(\frac{3}{10}\)\)
4. \(\frac{15}{32}\)+\(\frac{1}{30}\)-\(\frac{3}{10}\) = \(\frac{15\(\cdot\)15+1\(\cdot\)16-3\(\cdot\)48}{480}\) = \(\frac{225+16-144}{480}\) = \(\frac{97}{480}\)\)

3)

1. \(\(\frac{7}{15}\)+\(\frac{7}{30}\)+\(\frac{4}{5}\) = \(\frac{14}{30}\)+\(\frac{7}{30}\)+\(\frac{24}{30}\) = \(\frac{45}{30}\) = \(\frac{3}{2}\)\)
2. \(\(\2\)-\(\frac{1}{3}\)-\(\frac{1}{2}\) = \(\frac{12}{6}\)-\(\frac{2}{6}\)-\(\frac{3}{6}\) = \(\frac{7}{6}\)\)
3. \(\frac{3}{2}\):\(\frac{7}{6}\) = \(\frac{3}{2}\)\(\cdot\)\(\frac{6}{7}\) = \(\frac{18}{14}\) = \(\frac{9}{7}\)\)

И)

1. \(\(\frac{1}{6}\)+\(\frac{1}{10}\)+\(\frac{1}{15}\) = \(\frac{5}{30}\)+\(\frac{3}{30}\)+\(\frac{2}{30}\) = \(\frac{10}{30}\) = \(\frac{1}{3}\)\)
2. \(\(\frac{3}{5}\)-\(\frac{1}{3}\)-\(\frac{1}{4}\) = \(\frac{36}{60}\)-\(\frac{20}{60}\)-\(\frac{15}{60}\) = \(\frac{1}{60}\)\)
3. \(\frac{1}{3}\):\(\frac{1}{60}\) = \(\frac{1}{3}\)\(\cdot\)\(\60\) = 20\)

Ответ: A) \(\frac{158}{9}\); Б) \(\frac{53}{72}\); B) \(-\frac{1}{72}\); Г) \(\frac{23}{45}\); Д) \(\frac{139}{234}\); E) \(\frac{4357}{187680}\); Ë) \(-\frac{18571533}{7771856}\); Ж) \(\frac{97}{480}\); 3) \(\frac{9}{7}\); И) 20.