-25/18 + 14/27 * 1 17/28 + 4 : 6 2/3

Convert mixed numbers to improper fractions: 1 17/28 = 45/28 and 6 2/3 = 20/3. The expression becomes -25/18 + 14/27 * 45/28 + 4 : 20/3.

Perform multiplication and division: 14/27 * 45/28 = (14*45)/(27*28) = 630/756 = 5/6. 4 : 20/3 = 4 * 3/20 = 12/20 = 3/5.

The expression is now -25/18 + 5/6 + 3/5. Find a common denominator (90): (-25*5)/90 + (5*15)/90 + (3*18)/90 = -125/90 + 75/90 + 54/90 = (-125 + 75 + 54)/90 = 4/90 = 2/45.