Вопрос:

199. Найдите значение выражения: 1) (5/12 + 11/16) : (-13/72); 2) (9/14 - 5/21) : (-2 9/14); 3) (7/16 - 31/40) : (17/24 + 27/40); 4) -3 3/4 - (-8 2/9 - (-4,5)) : 2 1/4.

Ответ:

1) (5/12 + 11/16) : (-13/72) 5/12 + 11/16 = (5*4)/(12*4) + (11*3)/(16*3) = 20/48 + 33/48 = 53/48 (53/48) : (-13/72) = (53/48) * (-72/13) = -(53 * 72) / (48 * 13) = -(53 * 3) / (2 * 13) = -159/26 = -6 3/26 2) (9/14 - 5/21) : (-2 9/14) 9/14 - 5/21 = (9*3)/(14*3) - (5*2)/(21*2) = 27/42 - 10/42 = 17/42 -2 9/14 = -37/14 (17/42) : (-37/14) = (17/42) * (-14/37) = -(17 * 14) / (42 * 37) = -(17 * 1) / (3 * 37) = -17/111 3) (7/16 - 31/40) : (17/24 + 27/40) 7/16 - 31/40 = (7*5)/(16*5) - (31*2)/(40*2) = 35/80 - 62/80 = -27/80 17/24 + 27/40 = (17*5)/(24*5) + (27*3)/(40*3) = 85/120 + 81/120 = 166/120 = 83/60 (-27/80) : (83/60) = (-27/80) * (60/83) = -(27 * 60) / (80 * 83) = -(27 * 3) / (4 * 83) = -81/332 4) -3 3/4 - (-8 2/9 - (-4,5)) : 2 1/4 -3 3/4 = -15/4 -8 2/9 = -74/9 -4,5 = -9/2 2 1/4 = 9/4 -74/9 - (-9/2) = -74/9 + 9/2 = (-74*2)/(9*2) + (9*9)/(2*9) = -148/18 + 81/18 = -67/18 (-67/18) : (9/4) = (-67/18) * (4/9) = -(67 * 4) / (18 * 9) = -(67 * 2) / (9 * 9) = -134/81 -15/4 - (-134/81) = -15/4 + 134/81 = (-15*81)/(4*81) + (134*4)/(81*4) = -1215/324 + 536/324 = -679/324
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