Задание 2. Найдите значение выражения 1) (\frac{9}{16}+2\frac{3}{8})\cdot 4; 5) (1\frac{3}{4}+2\frac{4}{5})\cdot 30; 2) (\frac{4}{9}-3\frac{1}{15})\cdot 9; 6) (13\frac{1}{4}-2\frac{3}{4})\cdot 26; 9) 4\frac{7}{8}:(2\frac{3}{4}+1\frac{10}{19}); 10) 1\frac{1}{12}:(\frac{11}{18}-2\frac{5}{9});

Решение:

1. $$\left(\frac{9}{16}+2\frac{3}{8}\right)\cdot 4 = \left(\frac{9}{16}+\frac{19}{8}\right)\cdot 4 = \left(\frac{9}{16}+\frac{19\cdot 2}{8\cdot 2}\right)\cdot 4 = \left(\frac{9}{16}+\frac{38}{16}\right)\cdot 4 = \frac{47}{16} \cdot 4 = \frac{47}{16} \cdot \frac{4}{1} = \frac{47}{4} = 11\frac{3}{4}$$
2. $$\left(\frac{4}{9}-3\frac{1}{15}\right)\cdot 9 = \left(\frac{4}{9}-\frac{46}{15}\right)\cdot 9 = \left(\frac{4 \cdot 5}{9 \cdot 5}-\frac{46 \cdot 3}{15 \cdot 3}\right)\cdot 9 = \left(\frac{20}{45}-\frac{138}{45}\right)\cdot 9 = \frac{-118}{45} \cdot 9 = \frac{-118}{45} \cdot \frac{9}{1} = \frac{-118}{5} = -23\frac{3}{5}$$
3. $$(1\frac{3}{4}+2\frac{4}{5})\cdot 30 = (\frac{7}{4}+\frac{14}{5}) \cdot 30 = (\frac{7 \cdot 5}{4 \cdot 5}+\frac{14 \cdot 4}{5 \cdot 4}) \cdot 30 = (\frac{35}{20}+\frac{56}{20}) \cdot 30 = \frac{91}{20} \cdot 30 = \frac{91}{2} \cdot 3 = \frac{273}{2} = 136\frac{1}{2}$$
4. $$(13\frac{1}{4}-2\frac{3}{4})\cdot 26 = (\frac{53}{4}-\frac{11}{4})\cdot 26 = \frac{42}{4}\cdot 26 = \frac{21}{2}\cdot 26 = 21 \cdot 13 = 273$$
5. $$4\frac{7}{8}:(2\frac{3}{4}+1\frac{10}{19}) = \frac{39}{8}:(\frac{11}{4}+\frac{29}{19}) = \frac{39}{8}:(\frac{11 \cdot 19}{4 \cdot 19}+\frac{29 \cdot 4}{19 \cdot 4}) = \frac{39}{8}:(\frac{209}{76}+\frac{116}{76}) = \frac{39}{8}:\frac{325}{76} = \frac{39}{8} \cdot \frac{76}{325} = \frac{39}{2} \cdot \frac{19}{325} = \frac{3 \cdot 19}{25} = \frac{57}{25} = 2\frac{7}{25}$$
6. $$1\frac{1}{12}:(\frac{11}{18}-2\frac{5}{9}) = \frac{13}{12}:(\frac{11}{18}-\frac{23}{9}) = \frac{13}{12}:(\frac{11}{18}-\frac{23 \cdot 2}{9 \cdot 2}) = \frac{13}{12}:(\frac{11}{18}-\frac{46}{18}) = \frac{13}{12}:(\frac{-35}{18}) = \frac{13}{12} \cdot \frac{18}{-35} = \frac{13}{2} \cdot \frac{3}{-35} = \frac{39}{-70} = -\frac{39}{70}$$

Ответ: 1) $$11\frac{3}{4}$$, 2) $$-23\frac{3}{5}$$, 3) $$136\frac{1}{2}$$, 4) $$273$$, 5) $$2\frac{7}{25}$$, 6) $$\frac{-39}{70}$$