Вычислите:(3 1/2-2 2/3+5 5/6+4 3/5)*24(дам 50 баллов)

$(3 \frac{1}{2} - 2 \frac{2}{3} + 5 \frac{5}{6} +4 \frac{3}{5} ) * 24 = (3 \frac{15}{30} - 2 \frac{20}{30} +5 \frac{25}{30} +4 \frac{18}{30} ) *24 = \\ \\ =11 \frac{8}{30} *24= 11 \frac{4}{15} * 24 = \frac{11*15+4}{15} * \frac{24}{1} = \\ \\ = \frac{169*24}{15*1} = \frac{169*8}{5*1} = \frac{1352}{5} =270 \frac{2}{5}$

Посмотрим по действиям:

$(3 \frac{1}{2} - 2 \frac{2}{3} + 5 \frac{5}{6} +4 \frac{3}{5} ) * 24 =\\ \\ 1) 3 \frac{1}{2} - 2 \frac{2}{3}= \frac{3*2+1}{2} - \frac{2*3+2}{3} = \frac{7*3- 8*2}{2*3} = \frac{21-16}{6} = \frac{5}{6} \\ \\ 2) \frac{5}{6} +5 \frac{5}{6} =5+ \frac{10}{6} =6 \frac{4}{6} =6 \frac{2}{3} \\ \\ 3) 6 \frac{2}{3} + 4 \frac{3}{5} = 6 \frac{10}{15} +4 \frac{9}{15} = 11 \frac{4}{15} \\ \\$
$4) 11 \frac{4}{15} * 24 = \frac{169*24}{15*1} = \frac{169*8}{5*1} = \frac{1352}{5} = 270 \frac{2}{5}$