  Hindman's finite sums theorem states that in any finite coloring of the
naturals, there is an infinite sequence all of whose finite subset sums are the
same color. In 1979, Hindman showed that there is a finite coloring of the
naturals so that no infinite sequence has all of its pairwise sums and pairwise
products the same color. Hindman conjectured that for any $n$, a finite
coloring of the naturals contains $n$ numbers all of whose subset sums and
subset products are the same color. In this paper we prove the version of this
statement where we color the rationals instead of the integers. In other words,
we show that the pattern $\{ \sum_{i \in S}x_i, \prod_{i \in S}x_i \}$, where
$S$ ranges over all nonempty subsets of $[n]$, is partition regular over the
rationals.
