1) $-\frac{2}{3}\cdot\left(1\frac{1}{2}-\frac{2}{5}\right)$; 2) $\frac{5}{6}:\left(-1\frac{2}{3}+\frac{1}{4}\right)$; 3) $-5\frac{1}{3}-1\frac{1}{3}\cdot0.5$; 4) $-2\frac{3}{4}+1\frac{1}{4}\cdot0.4$; 5) $\frac{16-2\frac{1}{3}}{-4}$; 6) $\frac{5}{4\frac{1}{7}-15}$; 7) $-3\frac{1}{6}-2\frac{5}{8}:2\frac{1}{4}$; 8) $-2\frac{2}{5}+3\frac{1}{15}:2\frac{1}{11}$. Найти значения числовых выражений.

Question

1) $-\frac{2}{3}\cdot\left(1\frac{1}{2}-\frac{2}{5}\right)$; 2) $\frac{5}{6}:\left(-1\frac{2}{3}+\frac{1}{4}\right)$; 3) $-5\frac{1}{3}-1\frac{1}{3}\cdot0.5$; 4) $-2\frac{3}{4}+1\frac{1}{4}\cdot0.4$; 5) $\frac{16-2\frac{1}{3}}{-4}$; 6) $\frac{5}{4\frac{1}{7}-15}$; 7) $-3\frac{1}{6}-2\frac{5}{8}:2\frac{1}{4}$; 8) $-2\frac{2}{5}+3\frac{1}{15}:2\frac{1}{11}$. Найти значения числовых выражений.

$Фото задания: 1) $-\frac{2}{3}\cdot\left(1\frac{1}{2}-\frac{2}{5}\right)$; 2) $\frac{5}{6}:\left(-1\frac{2}{3}+\frac{1}{4}\right)$;…$ Фото задания

Accepted Answer

Преобразуем смешанные числа: $1\frac{1}{2}=\frac{3}{2}$. Тогда $\frac{3}{2}-\frac{2}{5}=\frac{15-4}{10}=\frac{11}{10}$.
$-\frac{2}{3}\cdot\frac{11}{10}=-\frac{11}{15}$.
$-1\frac{2}{3}=-\frac{5}{3}$, поэтому $-\frac{5}{3}+\frac{1}{4}=\frac{-20+3}{12}=-\frac{17}{12}$.
$\frac{5}{6}:\left(-\frac{17}{12}\right)=\frac{5}{6}\cdot\left(-\frac{12}{17}\right)=-\frac{10}{17}$.
$-5\frac{1}{3}=-\frac{16}{3}$, $1\frac{1}{3}=\frac{4}{3}$, $0.5=\frac{1}{2}$.
$-\frac{16}{3}-\frac{4}{3}\cdot\frac{1}{2}=-\frac{16}{3}-\frac{2}{3}=-6$.
$-2\frac{3}{4}=-\frac{11}{4}$, $1\frac{1}{4}=\frac{5}{4}$, $0.4=\frac{2}{5}$.
$-\frac{11}{4}+\frac{5}{4}\cdot\frac{2}{5}=-\frac{11}{4}+\frac{1}{2}=-\frac{9}{4}=-2\frac{1}{4}$.
Числитель: $16-2\frac{1}{3}=16-\frac{7}{3}=\frac{41}{3}$.
$\frac{\frac{41}{3}}{-4}=\frac{41}{3}\cdot\left(-\frac{1}{4}\right)=-\frac{41}{12}=-3\frac{5}{12}$.
Знаменатель: $4\frac{1}{7}-15=\frac{29}{7}-\frac{105}{7}=-\frac{76}{7}$.
$\frac{5}{-\frac{76}{7}}=5\cdot\left(-\frac{7}{76}\right)=-\frac{35}{76}$.
$-3\frac{1}{6}=-\frac{19}{6}$, $2\frac{5}{8}=\frac{21}{8}$, $2\frac{1}{4}=\frac{9}{4}$.
$\frac{21}{8}:\frac{9}{4}=\frac{21}{8}\cdot\frac{4}{9}=\frac{7}{6}$.
$-\frac{19}{6}-\frac{7}{6}=-\frac{26}{6}=-\frac{13}{3}=-4\frac{1}{3}$.
$-2\frac{2}{5}=-\frac{12}{5}$, $3\frac{1}{15}=\frac{46}{15}$, $2\frac{1}{11}=\frac{23}{11}$.
$\frac{46}{15}:\frac{23}{11}=\frac{46}{15}\cdot\frac{11}{23}=\frac{22}{15}$.
$-\frac{12}{5}+\frac{22}{15}=-\frac{36}{15}+\frac{22}{15}=-\frac{14}{15}$.

Ответ: 1) $-\frac{11}{15}$; 2) $-\frac{10}{17}$; 3) $-6$; 4) $-2\frac{1}{4}$; 5) $-3\frac{5}{12}$; 6) $-\frac{35}{76}$; 7) $-4\frac{1}{3}$; 8) $-\frac{14}{15}$.