diff --git a/docs/changelog.md b/docs/changelog.md
index a81531e9..8be30875 100644
--- a/docs/changelog.md
+++ b/docs/changelog.md
@@ -2,6 +2,7 @@
 
 ## Unreleased
 
+- Fix binary operations involving unions wrapped in `Annotated` (#779)
 - Fix various issues with Python 3.13 and 3.14 support (#773)
 - Improve `ParamSpec` support (#772, #777)
 - Fix handling of stub functions with positional-only parameters with
diff --git a/pyanalyze/name_check_visitor.py b/pyanalyze/name_check_visitor.py
index 1f39d109..855b14ae 100644
--- a/pyanalyze/name_check_visitor.py
+++ b/pyanalyze/name_check_visitor.py
@@ -5078,10 +5078,13 @@ def _check_dunder_call(
         args: Iterable[Composite],
         allow_call: bool = False,
     ) -> Tuple[Value, bool]:
-        if isinstance(callee_composite.value, MultiValuedValue):
+        val = callee_composite.value
+        if isinstance(val, AnnotatedValue):
+            val = val.value
+        if isinstance(val, MultiValuedValue):
             composites = [
-                Composite(val, callee_composite.varname, callee_composite.node)
-                for val in callee_composite.value.vals
+                Composite(subval, callee_composite.varname, callee_composite.node)
+                for subval in val.vals
             ]
             with qcore.override(self, "in_union_decomposition", True):
                 values_and_exists = [
diff --git a/pyanalyze/test_config.py b/pyanalyze/test_config.py
index ad2a3fc6..4d918d86 100644
--- a/pyanalyze/test_config.py
+++ b/pyanalyze/test_config.py
@@ -7,6 +7,8 @@
 from pathlib import Path
 from typing import Dict, Optional, Tuple
 
+from pyanalyze.annotated_types import Gt
+
 from . import tests, value
 from .arg_spec import ArgSpecCache
 from .error_code import ErrorCode, register_error_code
@@ -59,14 +61,25 @@ def get_constructor(cls: type) -> Optional[Signature]:
     return None
 
 
+def _make_union_in_annotated_impl(ctx: CallContext) -> value.Value:
+    return value.AnnotatedValue(
+        value.TypedValue(float) | value.TypedValue(int),
+        [value.CustomCheckExtension(Gt(0))],
+    )
+
+
 @used  # in test.toml
 def get_known_signatures(
     arg_spec_cache: ArgSpecCache,
 ) -> Dict[object, ConcreteSignature]:
     failing_impl_sig = arg_spec_cache.get_argspec(tests.FailingImpl, impl=_failing_impl)
     custom_sig = arg_spec_cache.get_argspec(tests.custom_code, impl=_custom_code_impl)
+    union_in_anno_sig = arg_spec_cache.get_argspec(
+        tests.make_union_in_annotated, impl=_make_union_in_annotated_impl
+    )
     assert isinstance(custom_sig, Signature), custom_sig
     assert isinstance(failing_impl_sig, Signature), failing_impl_sig
+    assert isinstance(union_in_anno_sig, Signature), union_in_anno_sig
     return {
         tests.takes_kwonly_argument: Signature.make(
             [
@@ -81,6 +94,7 @@ def get_known_signatures(
         ),
         tests.FailingImpl: failing_impl_sig,
         tests.custom_code: custom_sig,
+        tests.make_union_in_annotated: union_in_anno_sig,
         tests.overloaded: OverloadedSignature(
             [
                 Signature.make([], value.TypedValue(int), callable=tests.overloaded),
diff --git a/pyanalyze/test_operations.py b/pyanalyze/test_operations.py
index 0df5a0cc..b7cffb69 100644
--- a/pyanalyze/test_operations.py
+++ b/pyanalyze/test_operations.py
@@ -275,3 +275,42 @@ def capybara():
     def test_text_and_bytes(self):
         def capybara():
             return "foo" + b"bar"  # E: unsupported_operation
+
+
+class TestAnnotated(TestNameCheckVisitorBase):
+
+    @assert_passes()
+    def test_union(self):
+        from typing import Union
+
+        from pyanalyze.annotated_types import Gt as OurGt
+        from pyanalyze.tests import make_union_in_annotated
+        from pyanalyze.value import (
+            AnnotatedValue,
+            CustomCheckExtension,
+            TypedValue,
+            assert_is_value,
+        )
+
+        def want_float_or_int(x: Union[float, int]) -> None:
+            pass
+
+        def capybara() -> None:
+            # unite_values() distributes Annotated metadata over the union,
+            # so we have to really careful to get a type that is Annotated[x | y, ...]
+            # rather than Annotated[x, ...] | Annotated[y, ...]
+            assert_is_value(
+                make_union_in_annotated(),
+                AnnotatedValue(
+                    TypedValue(float) | TypedValue(int),
+                    [CustomCheckExtension(OurGt(0))],
+                ),
+            )
+            y = 10000 * make_union_in_annotated()
+            x = make_union_in_annotated()
+            z = x * 1000000
+            assert_is_value(y, TypedValue(float) | TypedValue(int))
+            assert_is_value(z, TypedValue(float) | TypedValue(int))
+
+            want_float_or_int(make_union_in_annotated())
+            want_float_or_int(x)
diff --git a/pyanalyze/tests.py b/pyanalyze/tests.py
index e2f81b4b..aea71abe 100644
--- a/pyanalyze/tests.py
+++ b/pyanalyze/tests.py
@@ -238,3 +238,7 @@ def assert_never(arg: NoReturn) -> NoReturn:
 
 def make_simple_sequence(typ: type, vals: Sequence[Value]) -> SequenceValue:
     return SequenceValue(typ, [(False, val) for val in vals])
+
+
+def make_union_in_annotated() -> object:
+    return 42