Question

Помогите решить а )и б) удобными способами

Answer 1

Ответ:

$a)\ \ \displaystyle -3\frac{5}{6}+\Big(-2\frac{4}{9}\Big)+8\frac{13}{24}+\Big(-2\frac{11}{12}\Big)+\Big(-3\frac{2}{9}\Big)+\Big(-4\frac{5}{24}\Big)=\\\\\\=-\frac{23}{6}-\frac{22}{9}+\frac{205}{24}-\frac{35}{12}-\frac{29}{9}-\frac{101}{24}=\\\\\\=\frac{-23\cdot 36-22\cdot 24+205\cdot 9-24\cdot 18-29\cdot 24-101\cdot 9}{24\cdot 9}=\\\\\\=\frac{-23\cdot 36-24\cdot (22+18+29)+9\cdot (205-101)}{24\cdot 9}=$

$\displaystyle =\frac{-23\cdot 12\cdot 3-24\cdot 69-9\cdot 104}{24\cdot 9}=\frac{12\cdot 3\cdot (23-2\cdot 23-26)}{24\cdot 9}=\\\\\\=\frac{-49}{2\cdot 3}=-\frac{49}{6}=-8\frac{1}{6}$

$b)\ \ \displaystyle -3\frac{1}{3}\cdot \Big(-1\frac{2}{7}\Big)\cdot (-3)\cdot (-7)=+\frac{10}{3}\cdot \frac{9}{7}\cdot 3\cdot 7=10\cdot 9=90$