An attempt is made to clarify two frequently used applied mathematical techniques. Section 1 begins with a description of the basic simplification procedure in which a term is neglected under the assumption that it is small, and the consistency of this assumption is later checked. Successful uses of the basic simplification procedure are illustrated. Wretched consistent approximations are presented, showing that the procedure can be misused. The situation is clarified by a discussion of the relation between the size of the residual and the goodness of the approximation in three simple problem classes. Section 2 discusses scaling : how to choose dimensionless variables in such a way that the relative size of the various terms in an equation is explicitly indicated by the magnitudes of the dimensionless parameters which precede them. Scaling is illustrated on a simple physical problem and on several known functions. It is pointed out that more than one scale may be necessary, and the connection with singula...