Question

Oblicz:

a) (2/3 + 1/4) : 1 5/6 + 1/2
b) [(5 1/2 - 3 1/4) : 2 1/4 + 7 5/8] : 2 7/8
c) 3/4 - 3/2 + (2 1/2 - 1 7/8) : 1/8 - 2 1/4
d) 1/2 + (4/5 - 1 1/2 : 2 1/2) : 2/5
e) 5/8 + 3/2 * (19/4 : 19)
f) 3 3/4 : 5/6 - 1/2
g) (1 1/2 + 2 2/3) : 5/6
h) (3 1/3 - 1 1/4) : 2 1/12

Answer 1

a) (2/3 + 1/4) : 1 5/6 + 1/2 = (8/12 + 3/12) : 11/6 + 1/2 = 11/12 * 6/11 + 1/2 = 1/2 + 1/2 = 1
b) [(5 1/2 - 3 1/4) : 2 1/4 + 7 5/8] : 2 7/8 = [(11/2 - 13/4) : 9/4 + 61/8] : 23/8 = [(22/4 - 13/4) * 4/9 + 61/8] * 8/23 = (9/4 * 4/9 + 61/8) * 8/23 = (1 + 61/8) * 8/23 = 69/8 * 8/23 = 3
c) 3/4 - 3/2 + (2 1/2 - 1 7/8) : 1/8 - 2 1/4 = 3/4 - 6/4 + (5/2 - 15/8) : 1/8 - 9/4 = (-3/4) + (20/8 - 15/8) * 8 - 9/4 = (-3/4) + 5/8 * 8 - 9/4 = (-3/4) + 5 - 9/4 = (-12/4) + 5 = -3 + 5 = 2 
d) 1/2 + (4/5 - 1 1/2 : 2 1/2) : 2/5 = 1/2 +(4/5 - 3/2 : 5/2) : 2/5 = 1/2 + (4/5 - 3/2 * 2/5) * 5/2 = 1/2 + (4/5 - 3/5) * 5/2 = 1/2 + 1/5 * 5/2 = 1/2 + 1/2 = 1
e) 5/8 + 3/2 * (19/4 : 19) = 5/8 + 3/2 * (19/4 * 1/19) = 5/8 +3/2 * 1/4 = 5/8 + 3/8 = 8/8 = 1
f) 3 3/4 : 5/6 - 1/2 = 15/4 * 6/5 - 1/2 = 9/2 - 1/2 = 8/2 = 4
g) (1 1/2 + 2 2/3) : 5/6 = (3/2 + 8/3) * 6/5 = (9/6 + 16/6) * 6/5 = 25/6 * 6/5 = 5
h) (3 1/3 - 1 1/4) : 2 1/12 = (10/3 - 5/4) : 25/12 = (40/12 - 15/12) * 12/25 = 25/12 * 12/25 = 1