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In the present work we introduce a novel approach to study $f({\sf R},{\sfT})$ gravity theory from a different perspective. Here, ${\sf T}$ denotes thetrace of energy-momentum tensor ({\sf EMT}) of matter fluids. The usual method(as discussed in the literature) is to choose an $h({\sf T})$ function and thensolve for the resulted Friedman equations. Nevertheless, our aim here is,without loss of generality, to reformulate a particular class of $f({\sfR},{\sf T})$ gravity models in which the Einstein-Hilbert action is promoted byan arbitrary function of the trace of {\sf EMT}. The strategy is theredefinition of the equation of motion in terms of the components of aneffective fluid. We show that in this case the {\sf EMT} is automaticallyconserved. As we shall see, adopting such a point of view (at least) in $f({\sfR},{\sf T})$ gravity is accompanied by two significant points. On one hand,$h({\sf T})$ function is chosen based upon a physical concept and on the other,we clearly understand the overall or effective behavior of matter in terms of aconserved effective fluid. To illustrate the idea, we study some models inwhich different physical properties for the effective fluid is attributed toeach model. Particularly, we discuss models with constant effective density,constant effective pressure and constant effective equation of state ({\sfEoS}) parameter. Moreover, two models with a relation between the effectivedensity and the effective pressure will be considered. An elegant result isthat in $f({\sf R},{\sf T})$ gravity, there is a possibility that a perfectfluid could effectively behave as a modified Chaplygin gas with four freeparameters.

Interpretation of $f({\sf R},{\sf T})$ gravity in terms of a conserved effective fluid