3) Вычислить: а) -24+54:6 б) 24-17.5. в) 35/39 - 13/42 - 1/6 г) 5/12 • (1/5 + 3/23) д) (-4,6+1,9) :1,9 е) 9,2-9,6:1,5

Решение:

а) \(-24 + 54 : 6 = -24 + 9 = -15\)

б) \(24 - 17.5 = 6.5\)

в) \(\frac{35}{39} - \frac{13}{42} - \frac{1}{6} = \frac{35 \cdot 14}{39 \cdot 14} - \frac{13 \cdot 13}{42 \cdot 13} - \frac{1 \cdot 91}{6 \cdot 91} = \frac{490}{546} - \frac{169}{546} - \frac{91}{546} = \frac{490 - 169 - 91}{546} = \frac{230}{546} = \frac{115}{273}\)

г) \(\frac{5}{12} \cdot (\frac{1}{5} + \frac{3}{23}) = \frac{5}{12} \cdot (\frac{23}{115} + \frac{15}{115}) = \frac{5}{12} \cdot \frac{38}{115} = \frac{5 \cdot 38}{12 \cdot 115} = \frac{190}{1380} = \frac{19}{138}\)

д) \((-4.6 + 1.9) : 1.9 = -2.7 : 1.9 = -\frac{27}{10} : \frac{19}{10} = -\frac{27}{10} \cdot \frac{10}{19} = -\frac{27}{19} = -1\frac{8}{19}\)

е) \(9.2 - 9.6 : 1.5 = 9.2 - \frac{96}{10} : \frac{15}{10} = 9.2 - \frac{96}{10} \cdot \frac{10}{15} = 9.2 - \frac{96}{15} = 9.2 - 6.4 = 2.8\)

Ответ: а) -15; б) 6.5; в) \(\frac{115}{273}\); г) \(\frac{19}{138}\); д) \(-1\frac{8}{19}\); е) 2.8