This paper deals with the question: Under what restrictions is the division operator \((fg,g)\mapsto (fg)/g=f\), where f and g run over the smooth real-valued functions on a manifold M, jointly continuous in the numerator fg and denominator g, using Fréchet \(C^{\infty}\) function space topologies? There are classical results, reviewed in the paper, for the related problem in which g is fixed, but the joint continuity problem seems to be new. The main result says that the quotient \(f=(f\cdot p(G))/p(G)\), whee p is a fixed analytic function on a manifold N and G runs over the smooth maps from M to N, is jointly continuous in the numerator (f\(\cdot p(G))\) and in G (not, in general, in the denominator p(G)) if one restricts to maps G which are transversal to a Whitney stratification of the zero set of p for which p vanishes to constant order on each stratum. As a corollary, the division operator \((fg,g)\mapsto (fg)/g=f\) is jointly continuous if one restricts to denominators g whose differential is nowhere zero on the zero set of g. Another corollary says that the operator (AX,A)\(\mapsto X\), where X is a smooth n-vector-valued function and A is a smooth \(n\times n\) matrix- valued function, is continuous if one restricts to maps A which are transversal to a suitable Whitney stratification of the zero set of the determinant function, regarded as a polynomial on the Euclidean space of \(n\times n\) matrices.