Let $R$ be a unital ring. Let $P'$, $P$, and $P''$ be finitely generated projective left $R$-modules, and let $i:P'\to P$ and $q:P\to P''$ be $R$-linear maps such that $i$ is injective, $q$ is surjective, and $\operatorname{im} i=\ker q$. Let $V(R)$ be the commutative monoid of isomorphism classes of finitely generated projective left $R$-modules under direct sum, let $K_0(R)$ be the group completion of $V(R)$, and let $\iota:V(R)\to K_0(R)$ be the canonical monoid homomorphism. For a finitely generated projective left $R$-module $M$, write $[M]=\iota([M]_{V(R)})\in K_0(R)$, where $[M]_{V(R)}$ is the isomorphism class of $M$ in $V(R)$. Then $[P]=[P']+[P'']$ in $K_0(R)$.