diff --git a/unyt/array.py b/unyt/array.py
index 9b2c94e3..281d31be 100644
--- a/unyt/array.py
+++ b/unyt/array.py
@@ -123,6 +123,7 @@
     UnitOperationError,
     UnitConversionError,
     UnitsNotReducible,
+    SymbolNotFoundError,
 )
 from unyt.equivalencies import equivalence_registry
 from unyt._on_demand_imports import _astropy, _pint
@@ -160,7 +161,13 @@ def _sqrt_unit(unit):
 
 @lru_cache(maxsize=128, typed=False)
 def _multiply_units(unit1, unit2):
-    ret = (unit1 * unit2).simplify()
+    try:
+        ret = (unit1 * unit2).simplify()
+    except SymbolNotFoundError:
+        # Some operators are not natively commutative when operands are
+        # defined within different unit registries, and conversion
+        # is defined one way but not the other.
+        ret = (unit2 * unit1).simplify()
     return ret.as_coeff_unit()
 
 
@@ -195,7 +202,10 @@ def _square_unit(unit):
 
 @lru_cache(maxsize=128, typed=False)
 def _divide_units(unit1, unit2):
-    ret = (unit1 / unit2).simplify()
+    try:
+        ret = (unit1 / unit2).simplify()
+    except SymbolNotFoundError:
+        ret = (1 / (unit2 / unit1).simplify()).units
     return ret.as_coeff_unit()
 
 
diff --git a/unyt/tests/test_units.py b/unyt/tests/test_units.py
index 461f2f69..cc509fd6 100644
--- a/unyt/tests/test_units.py
+++ b/unyt/tests/test_units.py
@@ -28,6 +28,7 @@
 import pytest
 from sympy import Symbol
 
+from unyt.array import unyt_quantity
 from unyt.testing import assert_allclose_units
 from unyt.unit_registry import UnitRegistry
 from unyt.dimensions import (
@@ -874,3 +875,17 @@ def test_degF():
 def test_delta_degF():
     a = 1 * Unit("delta_degF")
     assert str(a) == "1 Δ°F"
+
+
+def test_mixed_registry_operations():
+
+    reg = UnitRegistry(unit_system="cgs")
+    reg.add("fake_length", 0.001, length)
+    a = unyt_quantity(1, units="fake_length", registry=reg)
+    b = unyt_quantity(1, "cm")
+
+    assert_almost_equal(a + b, b + a)
+    assert_almost_equal(a - b, -(b - a))
+    assert_almost_equal(a * b, b * a)
+    assert_almost_equal(b / a, b / a.in_units("km"))
+    assert_almost_equal(a / b, a / b.in_units("km"))