  It is standard in chemistry to represent a sequence of reactions by a single
overall reaction, often called a complex reaction in contrast to an elementary
reaction. Photosynthesis $6 \text{CO}_2+6 \text{H}_2\text{O} \to \
\text{C}_6\text{H}_{12}\text{O}_6$ $+\ 6 \text{O}_2$ is an example of such
complex reaction. We introduce a mathematical operation that corresponds to
summing two chemical reactions. Specifically, we define an associative and
non-communicative operation on the product space $\mathbb{N}_0^n\times
\mathbb{N}_0^n$ (representing the reactant and the product of a chemical
reaction, respectively). The operation models the overall effect of two
reactions happening in succession, one after the other. We study the algebraic
properties of the operation and apply the results to stochastic reaction
networks, in particular to reachability of states, and to reduction of reaction
networks.
