A new set of simple equations for analyzing the Fresnel diffraction field distribution of an one-dimensional rectangular grating with the opening ratio 1/M (where M is a positive integer) is derived. In the equations the connection of the structure of a grating with the fractional Talbot distance is considered. They are more convenient to describe the fractional Talbot effect than that of the distance-oriented equations and the step-by-step equation. A new way to study the fractional Talbot effect of a grating is presented.