Flat slab design entails analysing and designing an orthogonal grid of flexural elements, supported by columns at the intersections of these elements.
The slab forms these flexural elements, with the element width equal to the sum of half the support spacings on each side of the support column. The centre portion of the flexural element (the column strip) takes a greater proportion of the total bending moment, relative to its width. Your design code should give you the proportions of the bending moment split, as well as rules for checking punching shear etc.