Question

Как решить? 11 1/3:((1 11/14-4 5/7)*4 2/3-(-1 5/6+3 2/9)*9/25

Answer 1

$11 frac{1}{3}:((1 frac{11}{14}-4 frac{5}{7})*4 frac{2}{3}-(-1 frac{5}{6}+3 frac{2}{9})* frac{9}{25})=$$frac{34}{3}:((frac{25}{14}-frac{33}{7})*frac{14}{3}-(frac{29}{9}-frac{11}{6})* frac{9}{25})=$$frac{34}{3}:(frac{25-33*2}{14}*frac{14}{3}-frac{29*2-11*3}{18}* frac{9}{25})=$$frac{34}{3}:(-frac{41}{14}*frac{14}{3}-frac{25}{18}* frac{9}{25})=$$frac{34}{3}:(-frac{41}{3}-frac{1}{2})=frac{34}{3}:(-frac{85}{6})=frac{34}{3}*(-frac{6}{85})=frac{17*2}{3}*(-frac{3*2}{17*5})=-frac{2*2}{5}=$$- frac{4}{5}$ 

1) $1 frac{11}{14}-4 frac{5}{7}=frac{25}{14}-frac{33}{7}=frac{25-33*2}{14}=-frac{41}{14}$
2) $-1 frac{5}{6}+3 frac{2}{9}=frac{29}{9}-frac{11}{6}=frac{29*2-11*3}{18}=frac{25}{18}$
3) $-frac{41}{14}*4 frac{2}{3}=-frac{41}{14}*frac{14}{3}=-frac{41}{3}$
4) $frac{25}{18}*frac{9}{25}= frac{9}{18}= frac{1}{2}$
5) $-frac{41}{3}-frac{1}{2} = -frac{41*2+1*3}{6}=- frac{85}{6}$
6) $11 frac{1}{3}:(- frac{85}{6} )=frac{34}{3}*(-frac{6}{85})=frac{17*2}{3}*(-frac{3*2}{17*5})=-frac{2*2}{5}=- frac{4}{5}$