1) (4/15 + 7/12) : (-38/45)
4/15 + 7/12 = (4*4)/(15*4) + (7*5)/(12*5) = 16/60 + 35/60 = 51/60 = 17/20
(17/20) : (-38/45) = (17/20) * (-45/38) = -(17 * 45) / (20 * 38) = -(17 * 9) / (4 * 38) = -153/152 = -1 1/152
2) (11/16 - 17/24) : (-5/12)
11/16 - 17/24 = (11*3)/(16*3) - (17*2)/(24*2) = 33/48 - 34/48 = -1/48
(-1/48) : (-5/12) = (-1/48) * (-12/5) = 12 / (48 * 5) = 1 / (4 * 5) = 1/20
3) (11/18 + 29/45) : (35/54)
11/18 + 29/45 = (11*5)/(18*5) + (29*2)/(45*2) = 55/90 + 58/90 = 113/90
(113/90) : (35/54) = (113/90) * (54/35) = (113 * 54) / (90 * 35) = (113 * 3) / (5 * 35) = 339/175 = 1 164/175
4) -4 1/7 + 2 1/4 * (-11 2/9 - (-5.4)) : 9/35
-4 1/7 = -29/7
2 1/4 = 9/4
-11 2/9 = -101/9
-5.4 = -54/10 = -27/5
(-101/9 - (-27/5)) = (-101/9 + 27/5) = (-101*5)/(9*5) + (27*9)/(5*9) = -505/45 + 243/45 = -262/45
(9/4) * (-262/45) = (9 * -262) / (4 * 45) = (-262) / (4 * 5) = -131 / 10
(-131/10) : (9/35) = (-131/10) * (35/9) = (-131 * 35) / (10 * 9) = (-131 * 7) / (2 * 9) = -917/18
-29/7 + (-917/18) = -29/7 - 917/18 = (-29*18)/(7*18) - (917*7)/(18*7) = -522/126 - 6419/126 = -6941/126