diff --git a/django/db/models/expressions.py b/django/db/models/expressions.py
index 6e4722d4f31..c48204f4201 100644
--- a/django/db/models/expressions.py
+++ b/django/db/models/expressions.py
@@ -238,7 +238,16 @@ class BaseExpression(object):
         """
         Attempts to infer the output type of the expression. If the output
         fields of all source fields match then we can simply infer the same
-        type here.
+        type here. This isn't always correct, but it makes sense most of the
+        time.
+
+        Consider the difference between `2 + 2` and `2 / 3`. Inferring
+        the type here is a convenience for the common case. The user should
+        supply their own output_field with more complex computations.
+
+        If a source does not have an `_output_field` then we exclude it from
+        this check. If all sources are `None`, then an error will be thrown
+        higher up the stack in the `output_field` property.
         """
         if self._output_field is None:
             sources = self.get_source_fields()
@@ -246,8 +255,9 @@ class BaseExpression(object):
             if num_sources == 0:
                 self._output_field = None
             else:
-                self._output_field = sources[0]
                 for source in sources:
+                    if self._output_field is None:
+                        self._output_field = source
                     if source is not None and not isinstance(self._output_field, source.__class__):
                         raise FieldError(
                             "Expression contains mixed types. You must set output_field")
diff --git a/tests/annotations/tests.py b/tests/annotations/tests.py
index 3f50463b48b..55ef30b575b 100644
--- a/tests/annotations/tests.py
+++ b/tests/annotations/tests.py
@@ -99,6 +99,14 @@ class NonAggregateAnnotationTestCase(TestCase):
                 sum_rating=Sum('rating')
             ).filter(sum_rating=F('nope')))
 
+    def test_combined_annotation_commutative(self):
+        book1 = Book.objects.annotate(adjusted_rating=F('rating') + 2).get(pk=self.b1.pk)
+        book2 = Book.objects.annotate(adjusted_rating=2 + F('rating')).get(pk=self.b1.pk)
+        self.assertEqual(book1.adjusted_rating, book2.adjusted_rating)
+        book1 = Book.objects.annotate(adjusted_rating=F('rating') + None).get(pk=self.b1.pk)
+        book2 = Book.objects.annotate(adjusted_rating=None + F('rating')).get(pk=self.b1.pk)
+        self.assertEqual(book1.adjusted_rating, book2.adjusted_rating)
+
     def test_update_with_annotation(self):
         book_preupdate = Book.objects.get(pk=2)
         Book.objects.annotate(other_rating=F('rating') - 1).update(rating=F('other_rating'))