Вопрос:

199. Найдите значение выражения: 1) (5/9 + 14/15) : (17/30); 2) (5/18 - 11/27) : (-25/16); 3) (11/17 - 5/24) : (5/18 + 4/15); 4) -4 5/6 + 3 1/23 * (-11 4/9 - (-3,6)) : 9/35.

Ответ:

1) (5/9 + 14/15) : (17/30) 5/9 + 14/15 = (5*5)/(9*5) + (14*3)/(15*3) = 25/45 + 42/45 = 67/45 (67/45) : (17/30) = (67/45) * (30/17) = (67 * 30) / (45 * 17) = (67 * 2) / (3 * 17) = 134/51 = 2 32/51 2) (5/18 - 11/27) : (-25/16) 5/18 - 11/27 = (5*3)/(18*3) - (11*2)/(27*2) = 15/54 - 22/54 = -7/54 (-7/54) : (-25/16) = (-7/54) * (-16/25) = (7 * 16) / (54 * 25) = (7 * 8) / (27 * 25) = 56/675 3) (11/17 - 5/24) : (5/18 + 4/15) 11/17 - 5/24 = (11*24)/(17*24) - (5*17)/(24*17) = 264/408 - 85/408 = 179/408 5/18 + 4/15 = (5*5)/(18*5) + (4*6)/(15*6) = 25/90 + 24/90 = 49/90 (179/408) : (49/90) = (179/408) * (90/49) = (179 * 90) / (408 * 49) = (179 * 15) / (68 * 49) = 2685/3332 4) -4 5/6 + 3 1/23 * (-11 4/9 - (-3,6)) : 9/35 -4 5/6 = -29/6 3 1/23 = 70/23 -11 4/9 = -103/9 -3.6 = -36/10 = -18/5 (-103/9 - (-18/5)) = (-103/9 + 18/5) = (-103*5)/(9*5) + (18*9)/(5*9) = -515/45 + 162/45 = -353/45 (70/23) * (-353/45) = (70 * -353) / (23 * 45) = (-4942) / (23 * 45) = -24710/1035 = -9884/414 (-9884/414) : (9/35) = (-9884/414) * (35/9) = -(9884*35) / (414*9) = -345940/3726 -29/6 + (-345940/3726) = (-29 * 621) / (6 * 621) + (-345940/3726) = -18009/3726 - 345940/3726 = -363949/3726
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