Question

Помогите решить примеры, а то как-то запутался в дробях :'(
$frac{5}{6} ( frac{1}{2}x-frac{2}{3} )=3x-2frac{1}{4}$
$-4frac{5}{6}+3frac{3}{23}(-11frac{4}{9}-(-3,6)/frac{9}{35})=$

Answer 1

Я решила как смогла!

Answer 2

$frac{5}{6} ( frac{1}{2} x - frac{2}{3} ) = 3x - 2 frac{1}{4} \ \ frac{5}{12} x - frac{10}{18} = 3x - 2 frac{1}{4} \ \ frac{5}{12} x - frac{5}{9} = 3x - 2 frac{1}{4} \ \ frac{5}{12} x - 3x = - 2 frac{1}{4}+ frac{5}{9} \ \ - 2 frac{7}{12} x = frac{-81+20}{36} \ \ - frac{31}{12} x = - frac{61}{36} \ \ x= - frac{61}{36} : (- frac{31}{12}) = frac{61}{36} * frac{12}{31} = frac{61*1}{3*31} \ \ x= frac{61}{93}$

проверим:
$frac{5}{6} ( frac{1}{2} * frac{61}{93} - frac{2}{3} ) = 3* frac{61}{93} - 2 frac{1}{4} \ \ frac{5}{6} ( frac{61}{186} - frac{124}{186} ) = frac{183}{93} - frac{9}{4} \ \ frac{5}{6} * (- frac{63}{186} ) = frac{732-837}{372} \ \ - frac{5*7}{2*62} = frac{732-837}{372} \ \ - frac{35}{124} = - frac{105:3}{372:3} \ \ - frac{35}{124} =- frac{35}{124}$

$- 4 frac{5}{6} +3 frac{3}{23} (-11 frac{4}{9} - (-3,6) : frac{9}{35} ) = \ \ =- 4 frac{5}{6} +3 frac{3}{23} (-11 frac{4}{9} - (- frac{36*35}{10*9} ) = \ \ =- 4 frac{5}{6} +3 frac{3}{23} (-11 frac{4}{9} -(- frac{2*7}{1*1} )) = \ \ =- 4 frac{5}{6} +frac{3*23+3}{23} (-11 frac{4}{9} +14 ) = \ \ =- 4 frac{5}{6} + frac{72}{23} * frac{23}{9} = - 4 frac{5}{6} +8 = 3 frac{1}{6}$


проверим по действиям:
$1) (-3,6) : frac{9}{35}=- frac{36}{10} * frac{35}{9} = - frac{4*7}{2*1} = - (2*7) =-14 \ \ 2) -11 frac{4}{9} -(-14) = 2 frac{5}{9} \ \ 3) 3 frac{3}{23}* 2 frac{5}{9} = frac{72*23}{23*9} = 8 \ \ 4) -4 frac{5}{6} +8 = 3 frac{1}{6}$