Вычислите 16/15:2/5-6 1/3+2 1/12*4/5

Ответ: -2

Пошаговое объяснение:

Hапишем порядок действий :

$\displaystyle \frac{16}{15} ~\stackrel{ { \boldsymbol { \pmb 1}}}{:}~\frac{2}{5} \stackrel{\boldsymbol{\pmb3}}{-}6\frac{1}{3} \stackrel{\boldsymbol{\pmb 4}}{+}2\frac{1}{12}~ \stackrel{ \boldsymbol{\pmb 2}}{\cdot}~\frac{4}{5} = -2$

$1) ~ \cfrac{16}{15}:\cfrac{2}{5} =\cfrac{\diagup \!\! \!\!\!16^{~8}}{_{3~} \diagup \!\!\!\!\!15}\cdot \cfrac{\diagup \!\!\!5}{ \diagup \!\! \!2} =\cfrac{8}{3}$

$2) ~ 2\cfrac{1}{12} \cdot \cfrac{4}{5} =\cfrac{2\cdot 12+1}{12}\cdot\cfrac{4}{5}=\cfrac{25}{12} \cdot \cfrac{4}{5} =\cfrac{\diagup \!\!\!\!\!25^{5}}{ _3~\diagup \!\!\!\!\!12}\cdot \cfrac{\diagup \!\!\!\!4}{ \diagup \!\!\!\!5} =\cfrac{5}{3}$

$3) ~ \cfrac{8}{3}-6\cfrac{1}{3} = 2+\cfrac{2}{3}- 6-\cfrac{1}{3} =-4+\cfrac{1}{3} = -3\cfrac{2}{3}$

$4) ~ -3\cfrac{2}{3}+\cfrac{5}{3} =-3- \bigg\slash\!\!\!\!\! \cfrac{2}{3}+1+\bigg\slash\!\!\!\!\!\cfrac{2}{3} =-3+1=-2$

Примечание :

$1) ~ \cfrac{8}{3} =2\cfrac{2}{3} \\\\\\ 2) \cfrac{5}{3}=1\cfrac{2}{3}$