4. Найдите значение выражения: 1) $9\frac{1}{4}\cdot 8-3\frac{2}{3}\cdot4\frac{1}{2}-10\frac{4}{5}\cdot4\frac{7}{12}$; 2) $1\frac{1}{22}\cdot3\frac{2}{3}-\left(2\frac{5}{6}+3\frac{5}{6}\cdot\frac{7}{23}\right)\cdot\frac{3}{5}$; 3) $\left(3\frac{1}{4}+2\frac{1}{6}\right):2\frac{3}{5}-\frac{2}{3}:\frac{4}{9}$; 4) $\left(5{,}07:\frac{1}{20}-23{,}4:13\right)\cdot\frac{1}{4}+0{,}074:\frac{1}{2}$; 5) $(-1{,}2+4{,}32:(-1{,}8)):(-0{,}001)\cdot(-0{,}3)$; 6) $\left(\frac{10}{21}-\frac{25}{28}\right):\left(-\frac{11}{14}+\frac{24}{35}\right)$.

Question

Вопрос: $Фото задания: 4. Найдите значение выражения: 1) $9\frac{1}{4}\cdot 8-3\frac{2}{3}\cdot4\frac{1}{2}-10\frac{4}{5}\cdot4\frac{7}{12}$; 2)…$ Фото задания

4. Найдите значение выражения: 1) $9\frac{1}{4}\cdot 8-3\frac{2}{3}\cdot4\frac{1}{2}-10\frac{4}{5}\cdot4\frac{7}{12}$; 2) $1\frac{1}{22}\cdot3\frac{2}{3}-\left(2\frac{5}{6}+3\frac{5}{6}\cdot\frac{7}{23}\right)\cdot\frac{3}{5}$; 3) $\left(3\frac{1}{4}+2\frac{1}{6}\right):2\frac{3}{5}-\frac{2}{3}:\frac{4}{9}$; 4) $\left(5{,}07:\frac{1}{20}-23{,}4:13\right)\cdot\frac{1}{4}+0{,}074:\frac{1}{2}$; 5) $(-1{,}2+4{,}32:(-1{,}8)):(-0{,}001)\cdot(-0{,}3)$; 6) $\left(\frac{10}{21}-\frac{25}{28}\right):\left(-\frac{11}{14}+\frac{24}{35}\right)$.

Accepted Answer

Сначала выполняем умножение:
$9\frac{1}{4}\cdot8=\frac{37}{4}\cdot8=74$; $3\frac{2}{3}\cdot4\frac{1}{2}=\frac{11}{3}\cdot\frac{9}{2}=\frac{33}{2}$; $10\frac{4}{5}\cdot4\frac{7}{12}=\frac{54}{5}\cdot\frac{55}{12}=\frac{99}{2}$.
$74-\frac{33}{2}-\frac{99}{2}=74-66=8$.
$1\frac{1}{22}\cdot3\frac{2}{3}=\frac{23}{22}\cdot\frac{11}{3}=\frac{23}{6}$.
В скобках: $2\frac{5}{6}+3\frac{5}{6}\cdot\frac{7}{23}=\frac{17}{6}+\frac{23}{6}\cdot\frac{7}{23}=\frac{17}{6}+\frac{7}{6}=4$.
Итак, $\frac{23}{6}-4\cdot\frac{3}{5}=\frac{23}{6}-\frac{12}{5}=\frac{115-72}{30}=\frac{43}{30}=1\frac{13}{30}$.
$3\frac{1}{4}+2\frac{1}{6}=\frac{13}{4}+\frac{13}{6}=\frac{65}{12}$, а $2\frac{3}{5}=\frac{13}{5}$.
$\frac{65}{12}:\frac{13}{5}=\frac{65}{12}\cdot\frac{5}{13}=\frac{25}{12}$; $\frac{2}{3}:\frac{4}{9}=\frac{2}{3}\cdot\frac{9}{4}=\frac{3}{2}$.
$\frac{25}{12}-\frac{3}{2}=\frac{25}{12}-\frac{18}{12}=\frac{7}{12}$.
$5{,}07:\frac{1}{20}=5{,}07\cdot20=101{,}4$; $23{,}4:13=1{,}8$; $0{,}074:\frac{1}{2}=0{,}148$.
$(101{,}4-1{,}8)\cdot\frac{1}{4}+0{,}148=99{,}6\cdot0{,}25+0{,}148=24{,}9+0{,}148=25{,}048$.
$4{,}32:(-1{,}8)=-2{,}4$, поэтому $(-1{,}2-2{,}4):(-0{,}001)\cdot(-0{,}3)=(-3{,}6):(-0{,}001)\cdot(-0{,}3)=3600\cdot(-0{,}3)=-1080$.
$\frac{10}{21}-\frac{25}{28}=\frac{40}{84}-\frac{75}{84}=-\frac{35}{84}=-\frac{5}{12}$.
$-\frac{11}{14}+\frac{24}{35}=-\frac{55}{70}+\frac{48}{70}=-\frac{7}{70}=-\frac{1}{10}$.
$-\frac{5}{12}:-\frac{1}{10}=-\frac{5}{12}\cdot(-10)=\frac{25}{6}=4\frac{1}{6}$.

Ответ: 1) 8; 2) $1\frac{13}{30}$; 3) $\frac{7}{12}$; 4) 25,048; 5) −1080; 6) $4\frac{1}{6}$.