7.45 Вычислите: a) (1 3/4 : 3/5) : 6; б) 1 8/3 : 4/3 - 5/9; в) 7 7/5 : (9/10 - 2/5) : 8/9

Решение:

a) \( \left( 1 \frac{3}{4} : \frac{3}{5} \right) : 6 = \left( \frac{7}{4} : \frac{3}{5} \right) : 6 = \left( \frac{7}{4} \times \frac{5}{3} \right) : 6 = \frac{35}{12} : 6 = \frac{35}{12} \times \frac{1}{6} = \frac{35}{72} \)

б) \( 1 \frac{8}{3} : \frac{4}{3} - \frac{5}{9} = \frac{11}{3} : \frac{4}{3} - \frac{5}{9} = \frac{11}{3} \times \frac{3}{4} - \frac{5}{9} = \frac{11}{4} - \frac{5}{9} = \frac{11 \times 9 - 5 \times 4}{36} = \frac{99 - 20}{36} = \frac{79}{36} = 2 \frac{7}{36} \)

в) \( 7 \frac{7}{5} : \left( \frac{9}{10} - \frac{2}{5} \right) : \frac{8}{9} = 7 \frac{7}{5} : \left( \frac{9}{10} - \frac{4}{10} \right) : \frac{8}{9} = 7 \frac{7}{5} : \frac{5}{10} : \frac{8}{9} = \frac{42}{5} : \frac{1}{2} : \frac{8}{9} = \frac{42}{5} \times 2 \times \frac{9}{8} = \frac{84}{5} \times \frac{9}{8} = \frac{21 \times 9}{5 \times 2} = \frac{189}{10} = 18.9 \)

Ответ: а) 35/72; б) 79/36; в) 18,9.