Question

(-3 1\3*1.9+19.5: 4 1/3): (0.16-62/72)

Answer 1

(-3 1/3 * 1,9 + 19,5 : 4 1/3) : (0,16 - 62/72)= 2  388/631

$\displaystyle 1)\ -3\frac{1}{3} *1,9=-\frac{10}{3} *\frac{19}{10} =-\frac{10*19}{10*3}=-\frac{19}{3}$

$\displaystyle 2)\ 19,5:4\frac{1}{3}=\frac{195:5}{10:5} :\frac{13}{3} =\frac{39}{2} *\frac{3}{13} =\frac{13*3*3}{13*2} =\frac{9}{2}$

$\displaystyle 3)\ -\frac{19}{3}+\frac{9}{2}=-\frac{19*2}{3*2}+\frac{9*3}{2*3}=-\frac{38}{6}+\frac{27}{6}=\frac{-38+27}{6}=-\frac{11}{6}$

$\displaystyle 4)\ 0,16-\frac{62}{72}=\frac{16:4}{100:4}-\frac{62:2}{72:2}=\frac{4}{25}-\frac{31}{36}=\frac{4*36}{25*36}-\frac{31*25}{36*25}=\\\\=\frac{144}{900}-\frac{775}{900}=\frac{144-775}{900}=-\frac{631}{900}$

$\displaystyle 5)\ -\frac{11}{6}:(-\frac{631}{900})=\frac{11}{6}*\frac{900}{631}=\frac{11*6*150}{6*631}=\frac{11*150}{631}=\frac{1650}{631}=2\frac{388}{631}$

В оригинале (см. рисунок) последняя дробь равна 62/75:

(-3 1/3 * 1,9 + 19,5 : 4 1/3) : (0,16 - 62/75)= 2,75

и поэтому выполним 4) и 5) действия:

$\displaystyle 4)\ 0,16-\frac{62}{75}=\frac{16:4}{100:4}-\frac{62}{75}=\frac{4}{25}-\frac{62}{75}=\frac{4*3}{25*3}-\frac{62}{75}=\\\\=\frac{12}{75}-\frac{62}{75}=\frac{12-62}{75}=-\frac{50}{75}=-\frac{50:25}{75:25}=-\frac{2}{3}$

$\displaystyle 5)\ -\frac{11}{6}:(-\frac{2}{3})=\frac{11}{6}*\frac{3}{2}=\frac{11*3}{2*3*2}=\frac{11}{4}=2\frac{3}{4}=2,75$