2.276 Выполните действия: a) + 12 18. 31 B) 4-3- 15 5 8'; 1 д) 1-12. 24 5 5 6) (15-20); г) (5-4)·(-- 12 e) (1 11 (353-427) 15 18

a)

$$\frac{4}{9} + \frac{5}{12} = \frac{4 \cdot 4}{9 \cdot 4} + \frac{5 \cdot 3}{12 \cdot 3} = \frac{16}{36} + \frac{15}{36} = \frac{31}{36}$$ $$\frac{31}{36} \cdot \frac{18}{31} = \frac{31 \cdot 18}{36 \cdot 31} = \frac{18}{36} = \frac{1}{2}$$

Ответ:$$\frac{1}{2}$$

б)

$$\frac{6}{25} \cdot \frac{11}{15} - \frac{9}{20} = \frac{6 \cdot 11}{25 \cdot 15} - \frac{9}{20} = \frac{66}{375} - \frac{9}{20} = \frac{66 \cdot 4}{375 \cdot 4} - \frac{9 \cdot 75}{20 \cdot 75} = \frac{264}{1500} - \frac{675}{1500} = \frac{-411}{1500} = -\frac{137}{500}$$

Ответ: $$\frac{-137}{500}$$

в)

$$4 - 3\frac{7}{15} = \frac{4}{1} - \frac{52}{15} = \frac{4 \cdot 15}{1 \cdot 15} - \frac{52}{15} = \frac{60}{15} - \frac{52}{15} = \frac{8}{15}$$ $$\frac{8}{15} \cdot \frac{5}{8} = \frac{8 \cdot 5}{15 \cdot 8} = \frac{5}{15} = \frac{1}{3}$$

Ответ:$$\frac{1}{3}$$

г)

$$5 - 4\frac{4}{7} = \frac{5}{1} - \frac{32}{7} = \frac{5 \cdot 7}{1 \cdot 7} - \frac{32}{7} = \frac{35}{7} - \frac{32}{7} = \frac{3}{7}$$ $$7\frac{1}{6} - 6\frac{5}{12} = \frac{43}{6} - \frac{77}{12} = \frac{43 \cdot 2}{6 \cdot 2} - \frac{77}{12} = \frac{86}{12} - \frac{77}{12} = \frac{9}{12} = \frac{3}{4}$$ $$\frac{3}{7} \cdot \frac{3}{4} = \frac{3 \cdot 3}{7 \cdot 4} = \frac{9}{28}$$

Ответ:$$\frac{9}{28}$$

д)

$$1\frac{1}{24} - \frac{5}{12} = \frac{25}{24} - \frac{5}{12} = \frac{25}{24} - \frac{5 \cdot 2}{12 \cdot 2} = \frac{25}{24} - \frac{10}{24} = \frac{15}{24} = \frac{5}{8}$$ $$4\frac{1}{8} - 3\frac{5}{24} = \frac{33}{8} - \frac{77}{24} = \frac{33 \cdot 3}{8 \cdot 3} - \frac{77}{24} = \frac{99}{24} - \frac{77}{24} = \frac{22}{24} = \frac{11}{12}$$ $$\frac{5}{8} \cdot \frac{11}{12} = \frac{5 \cdot 11}{8 \cdot 12} = \frac{55}{96}$$

Ответ:$$\frac{55}{96}$$

e)

$$1\frac{2}{15} - \frac{11}{15} = \frac{17}{15} - \frac{11}{15} = \frac{6}{15} = \frac{2}{5}$$ $$5\frac{3}{18} - 4\frac{1}{27} = \frac{93}{18} - \frac{109}{27} = \frac{93 \cdot 3}{18 \cdot 3} - \frac{109 \cdot 2}{27 \cdot 2} = \frac{279}{54} - \frac{218}{54} = \frac{61}{54}$$ $$\frac{2}{5} \cdot \frac{61}{54} = \frac{2 \cdot 61}{5 \cdot 54} = \frac{122}{270} = \frac{61}{135}$$

Ответ:$$\frac{61}{135}$$