diff --git a/pandas/tests/extension/base/ops.py b/pandas/tests/extension/base/ops.py
index bc2048f9c31bb..aafb1900a4236 100644
--- a/pandas/tests/extension/base/ops.py
+++ b/pandas/tests/extension/base/ops.py
@@ -12,6 +12,28 @@
 
 
 class BaseOpsUtil(BaseExtensionTests):
+    series_scalar_exc: type[Exception] | None = TypeError
+    frame_scalar_exc: type[Exception] | None = TypeError
+    series_array_exc: type[Exception] | None = TypeError
+    divmod_exc: type[Exception] | None = TypeError
+
+    def _get_expected_exception(
+        self, op_name: str, obj, other
+    ) -> type[Exception] | None:
+        # Find the Exception, if any we expect to raise calling
+        #  obj.__op_name__(other)
+
+        # The self.obj_bar_exc pattern isn't great in part because it can depend
+        #  on op_name or dtypes, but we use it here for backward-compatibility.
+        if op_name in ["__divmod__", "__rdivmod__"]:
+            return self.divmod_exc
+        if isinstance(obj, pd.Series) and isinstance(other, pd.Series):
+            return self.series_array_exc
+        elif isinstance(obj, pd.Series):
+            return self.series_scalar_exc
+        else:
+            return self.frame_scalar_exc
+
     def _cast_pointwise_result(self, op_name: str, obj, other, pointwise_result):
         # In _check_op we check that the result of a pointwise operation
         #  (found via _combine) matches the result of the vectorized
@@ -24,17 +46,21 @@ def _cast_pointwise_result(self, op_name: str, obj, other, pointwise_result):
     def get_op_from_name(self, op_name: str):
         return tm.get_op_from_name(op_name)
 
-    def check_opname(self, ser: pd.Series, op_name: str, other, exc=Exception):
-        op = self.get_op_from_name(op_name)
-
-        self._check_op(ser, op, other, op_name, exc)
-
-    # Subclasses are not expected to need to override _check_op or _combine.
+    # Subclasses are not expected to need to override check_opname, _check_op,
+    #  _check_divmod_op, or _combine.
     #  Ideally any relevant overriding can be done in _cast_pointwise_result,
     #  get_op_from_name, and the specification of `exc`. If you find a use
     #  case that still requires overriding _check_op or _combine, please let
     #  us know at github.com/pandas-dev/pandas/issues
     @final
+    def check_opname(self, ser: pd.Series, op_name: str, other):
+        exc = self._get_expected_exception(op_name, ser, other)
+        op = self.get_op_from_name(op_name)
+
+        self._check_op(ser, op, other, op_name, exc)
+
+    # see comment on check_opname
+    @final
     def _combine(self, obj, other, op):
         if isinstance(obj, pd.DataFrame):
             if len(obj.columns) != 1:
@@ -44,11 +70,14 @@ def _combine(self, obj, other, op):
             expected = obj.combine(other, op)
         return expected
 
-    # see comment on _combine
+    # see comment on check_opname
     @final
     def _check_op(
         self, ser: pd.Series, op, other, op_name: str, exc=NotImplementedError
     ):
+        # Check that the Series/DataFrame arithmetic/comparison method matches
+        #  the pointwise result from _combine.
+
         if exc is None:
             result = op(ser, other)
             expected = self._combine(ser, other, op)
@@ -59,8 +88,14 @@ def _check_op(
             with pytest.raises(exc):
                 op(ser, other)
 
-    def _check_divmod_op(self, ser: pd.Series, op, other, exc=Exception):
-        # divmod has multiple return values, so check separately
+    # see comment on check_opname
+    @final
+    def _check_divmod_op(self, ser: pd.Series, op, other):
+        # check that divmod behavior matches behavior of floordiv+mod
+        if op is divmod:
+            exc = self._get_expected_exception("__divmod__", ser, other)
+        else:
+            exc = self._get_expected_exception("__rdivmod__", ser, other)
         if exc is None:
             result_div, result_mod = op(ser, other)
             if op is divmod:
@@ -96,26 +131,24 @@ def test_arith_series_with_scalar(self, data, all_arithmetic_operators):
         # series & scalar
         op_name = all_arithmetic_operators
         ser = pd.Series(data)
-        self.check_opname(ser, op_name, ser.iloc[0], exc=self.series_scalar_exc)
+        self.check_opname(ser, op_name, ser.iloc[0])
 
     def test_arith_frame_with_scalar(self, data, all_arithmetic_operators):
         # frame & scalar
         op_name = all_arithmetic_operators
         df = pd.DataFrame({"A": data})
-        self.check_opname(df, op_name, data[0], exc=self.frame_scalar_exc)
+        self.check_opname(df, op_name, data[0])
 
     def test_arith_series_with_array(self, data, all_arithmetic_operators):
         # ndarray & other series
         op_name = all_arithmetic_operators
         ser = pd.Series(data)
-        self.check_opname(
-            ser, op_name, pd.Series([ser.iloc[0]] * len(ser)), exc=self.series_array_exc
-        )
+        self.check_opname(ser, op_name, pd.Series([ser.iloc[0]] * len(ser)))
 
     def test_divmod(self, data):
         ser = pd.Series(data)
-        self._check_divmod_op(ser, divmod, 1, exc=self.divmod_exc)
-        self._check_divmod_op(1, ops.rdivmod, ser, exc=self.divmod_exc)
+        self._check_divmod_op(ser, divmod, 1)
+        self._check_divmod_op(1, ops.rdivmod, ser)
 
     def test_divmod_series_array(self, data, data_for_twos):
         ser = pd.Series(data)
diff --git a/pandas/tests/extension/decimal/test_decimal.py b/pandas/tests/extension/decimal/test_decimal.py
index 944ed0dbff66e..5ee41387e1809 100644
--- a/pandas/tests/extension/decimal/test_decimal.py
+++ b/pandas/tests/extension/decimal/test_decimal.py
@@ -1,3 +1,5 @@
+from __future__ import annotations
+
 import decimal
 import operator
 
@@ -311,8 +313,14 @@ def test_astype_dispatches(frame):
 
 
 class TestArithmeticOps(base.BaseArithmeticOpsTests):
-    def check_opname(self, s, op_name, other, exc=None):
-        super().check_opname(s, op_name, other, exc=None)
+    series_scalar_exc = None
+    frame_scalar_exc = None
+    series_array_exc = None
+
+    def _get_expected_exception(
+        self, op_name: str, obj, other
+    ) -> type[Exception] | None:
+        return None
 
     def test_arith_series_with_array(self, data, all_arithmetic_operators):
         op_name = all_arithmetic_operators
@@ -336,10 +344,6 @@ def test_arith_series_with_array(self, data, all_arithmetic_operators):
         context.traps[decimal.DivisionByZero] = divbyzerotrap
         context.traps[decimal.InvalidOperation] = invalidoptrap
 
-    def _check_divmod_op(self, s, op, other, exc=NotImplementedError):
-        # We implement divmod
-        super()._check_divmod_op(s, op, other, exc=None)
-
 
 class TestComparisonOps(base.BaseComparisonOpsTests):
     def test_compare_scalar(self, data, comparison_op):
diff --git a/pandas/tests/extension/json/test_json.py b/pandas/tests/extension/json/test_json.py
index 8a571d9295e1f..0c9abd45a51a5 100644
--- a/pandas/tests/extension/json/test_json.py
+++ b/pandas/tests/extension/json/test_json.py
@@ -323,9 +323,6 @@ def test_divmod_series_array(self):
         # skipping because it is not implemented
         super().test_divmod_series_array()
 
-    def _check_divmod_op(self, s, op, other, exc=NotImplementedError):
-        return super()._check_divmod_op(s, op, other, exc=TypeError)
-
 
 class TestComparisonOps(BaseJSON, base.BaseComparisonOpsTests):
     pass
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 655ca9cc39c58..2438626cf0347 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -10,6 +10,8 @@
 classes (if they are relevant for the extension interface for all dtypes), or
 be added to the array-specific tests in `pandas/tests/arrays/`.
 """
+from __future__ import annotations
+
 from datetime import (
     date,
     datetime,
@@ -964,16 +966,26 @@ def _is_temporal_supported(self, opname, pa_dtype):
             and pa.types.is_temporal(pa_dtype)
         )
 
-    def _get_scalar_exception(self, opname, pa_dtype):
-        arrow_temporal_supported = self._is_temporal_supported(opname, pa_dtype)
-        if opname in {
+    def _get_expected_exception(
+        self, op_name: str, obj, other
+    ) -> type[Exception] | None:
+        if op_name in ("__divmod__", "__rdivmod__"):
+            return self.divmod_exc
+
+        dtype = tm.get_dtype(obj)
+        # error: Item "dtype[Any]" of "dtype[Any] | ExtensionDtype" has no
+        # attribute "pyarrow_dtype"
+        pa_dtype = dtype.pyarrow_dtype  # type: ignore[union-attr]
+
+        arrow_temporal_supported = self._is_temporal_supported(op_name, pa_dtype)
+        if op_name in {
             "__mod__",
             "__rmod__",
         }:
             exc = NotImplementedError
         elif arrow_temporal_supported:
             exc = None
-        elif opname in ["__add__", "__radd__"] and (
+        elif op_name in ["__add__", "__radd__"] and (
             pa.types.is_string(pa_dtype) or pa.types.is_binary(pa_dtype)
         ):
             exc = None
@@ -1060,10 +1072,6 @@ def test_arith_series_with_scalar(self, data, all_arithmetic_operators, request)
         ):
             pytest.skip("Skip testing Python string formatting")
 
-        self.series_scalar_exc = self._get_scalar_exception(
-            all_arithmetic_operators, pa_dtype
-        )
-
         mark = self._get_arith_xfail_marker(all_arithmetic_operators, pa_dtype)
         if mark is not None:
             request.node.add_marker(mark)
@@ -1078,10 +1086,6 @@ def test_arith_frame_with_scalar(self, data, all_arithmetic_operators, request):
         ):
             pytest.skip("Skip testing Python string formatting")
 
-        self.frame_scalar_exc = self._get_scalar_exception(
-            all_arithmetic_operators, pa_dtype
-        )
-
         mark = self._get_arith_xfail_marker(all_arithmetic_operators, pa_dtype)
         if mark is not None:
             request.node.add_marker(mark)
@@ -1091,10 +1095,6 @@ def test_arith_frame_with_scalar(self, data, all_arithmetic_operators, request):
     def test_arith_series_with_array(self, data, all_arithmetic_operators, request):
         pa_dtype = data.dtype.pyarrow_dtype
 
-        self.series_array_exc = self._get_scalar_exception(
-            all_arithmetic_operators, pa_dtype
-        )
-
         if (
             all_arithmetic_operators
             in (
@@ -1124,7 +1124,7 @@ def test_arith_series_with_array(self, data, all_arithmetic_operators, request):
         # since ser.iloc[0] is a python scalar
         other = pd.Series(pd.array([ser.iloc[0]] * len(ser), dtype=data.dtype))
 
-        self.check_opname(ser, op_name, other, exc=self.series_array_exc)
+        self.check_opname(ser, op_name, other)
 
     def test_add_series_with_extension_array(self, data, request):
         pa_dtype = data.dtype.pyarrow_dtype
diff --git a/pandas/tests/extension/test_boolean.py b/pandas/tests/extension/test_boolean.py
index e5f6da5371742..508e2da214336 100644
--- a/pandas/tests/extension/test_boolean.py
+++ b/pandas/tests/extension/test_boolean.py
@@ -122,17 +122,14 @@ class TestMissing(base.BaseMissingTests):
 class TestArithmeticOps(base.BaseArithmeticOpsTests):
     implements = {"__sub__", "__rsub__"}
 
-    def check_opname(self, s, op_name, other, exc=None):
-        # overwriting to indicate ops don't raise an error
-        exc = None
+    def _get_expected_exception(self, op_name, obj, other):
         if op_name.strip("_").lstrip("r") in ["pow", "truediv", "floordiv"]:
             # match behavior with non-masked bool dtype
-            exc = NotImplementedError
+            return NotImplementedError
         elif op_name in self.implements:
             # exception message would include "numpy boolean subtract""
-            exc = TypeError
-
-        super().check_opname(s, op_name, other, exc=exc)
+            return TypeError
+        return None
 
     def _cast_pointwise_result(self, op_name: str, obj, other, pointwise_result):
         if op_name in (
@@ -170,18 +167,9 @@ def _cast_pointwise_result(self, op_name: str, obj, other, pointwise_result):
     def test_divmod_series_array(self, data, data_for_twos):
         super().test_divmod_series_array(data, data_for_twos)
 
-    @pytest.mark.xfail(
-        reason="Inconsistency between floordiv and divmod; we raise for floordiv "
-        "but not for divmod. This matches what we do for non-masked bool dtype."
-    )
-    def test_divmod(self, data):
-        super().test_divmod(data)
-
 
 class TestComparisonOps(base.BaseComparisonOpsTests):
-    def check_opname(self, s, op_name, other, exc=None):
-        # overwriting to indicate ops don't raise an error
-        super().check_opname(s, op_name, other, exc=None)
+    pass
 
 
 class TestReshaping(base.BaseReshapingTests):
diff --git a/pandas/tests/extension/test_categorical.py b/pandas/tests/extension/test_categorical.py
index fc4dfe3af3bca..5de1debb21d93 100644
--- a/pandas/tests/extension/test_categorical.py
+++ b/pandas/tests/extension/test_categorical.py
@@ -268,9 +268,6 @@ def test_divmod_series_array(self):
         # skipping because it is not implemented
         pass
 
-    def _check_divmod_op(self, s, op, other, exc=NotImplementedError):
-        return super()._check_divmod_op(s, op, other, exc=TypeError)
-
 
 class TestComparisonOps(base.BaseComparisonOpsTests):
     def _compare_other(self, s, data, op, other):
diff --git a/pandas/tests/extension/test_datetime.py b/pandas/tests/extension/test_datetime.py
index d8adc4c8c91a5..ab21f768e6521 100644
--- a/pandas/tests/extension/test_datetime.py
+++ b/pandas/tests/extension/test_datetime.py
@@ -130,22 +130,10 @@ class TestInterface(BaseDatetimeTests, base.BaseInterfaceTests):
 class TestArithmeticOps(BaseDatetimeTests, base.BaseArithmeticOpsTests):
     implements = {"__sub__", "__rsub__"}
 
-    def test_arith_frame_with_scalar(self, data, all_arithmetic_operators):
-        # frame & scalar
-        if all_arithmetic_operators in self.implements:
-            df = pd.DataFrame({"A": data})
-            self.check_opname(df, all_arithmetic_operators, data[0], exc=None)
-        else:
-            # ... but not the rest.
-            super().test_arith_frame_with_scalar(data, all_arithmetic_operators)
-
-    def test_arith_series_with_scalar(self, data, all_arithmetic_operators):
-        if all_arithmetic_operators in self.implements:
-            ser = pd.Series(data)
-            self.check_opname(ser, all_arithmetic_operators, ser.iloc[0], exc=None)
-        else:
-            # ... but not the rest.
-            super().test_arith_series_with_scalar(data, all_arithmetic_operators)
+    def _get_expected_exception(self, op_name, obj, other):
+        if op_name in self.implements:
+            return None
+        return super()._get_expected_exception(op_name, obj, other)
 
     def test_add_series_with_extension_array(self, data):
         # Datetime + Datetime not implemented
@@ -154,14 +142,6 @@ def test_add_series_with_extension_array(self, data):
         with pytest.raises(TypeError, match=msg):
             ser + data
 
-    def test_arith_series_with_array(self, data, all_arithmetic_operators):
-        if all_arithmetic_operators in self.implements:
-            ser = pd.Series(data)
-            self.check_opname(ser, all_arithmetic_operators, ser.iloc[0], exc=None)
-        else:
-            # ... but not the rest.
-            super().test_arith_series_with_scalar(data, all_arithmetic_operators)
-
     def test_divmod_series_array(self):
         # GH 23287
         # skipping because it is not implemented
diff --git a/pandas/tests/extension/test_masked_numeric.py b/pandas/tests/extension/test_masked_numeric.py
index b171797dd6359..ce41c08cafbd6 100644
--- a/pandas/tests/extension/test_masked_numeric.py
+++ b/pandas/tests/extension/test_masked_numeric.py
@@ -163,21 +163,20 @@ def _cast_pointwise_result(self, op_name: str, obj, other, pointwise_result):
             expected = expected.astype(sdtype)
         return expected
 
-    def check_opname(self, ser: pd.Series, op_name: str, other, exc=None):
-        # overwriting to indicate ops don't raise an error
-        super().check_opname(ser, op_name, other, exc=None)
-
-    def _check_divmod_op(self, ser: pd.Series, op, other, exc=None):
-        super()._check_divmod_op(ser, op, other, None)
+    series_scalar_exc = None
+    series_array_exc = None
+    frame_scalar_exc = None
+    divmod_exc = None
 
 
 class TestComparisonOps(base.BaseComparisonOpsTests):
+    series_scalar_exc = None
+    series_array_exc = None
+    frame_scalar_exc = None
+
     def _cast_pointwise_result(self, op_name: str, obj, other, pointwise_result):
         return pointwise_result.astype("boolean")
 
-    def check_opname(self, ser: pd.Series, op_name: str, other, exc=None):
-        super().check_opname(ser, op_name, other, exc=None)
-
     def _compare_other(self, ser: pd.Series, data, op, other):
         op_name = f"__{op.__name__}__"
         self.check_opname(ser, op_name, other)
diff --git a/pandas/tests/extension/test_numpy.py b/pandas/tests/extension/test_numpy.py
index db191954c8d59..13645065bce14 100644
--- a/pandas/tests/extension/test_numpy.py
+++ b/pandas/tests/extension/test_numpy.py
@@ -281,7 +281,7 @@ def test_divmod(self, data):
     @skip_nested
     def test_divmod_series_array(self, data):
         ser = pd.Series(data)
-        self._check_divmod_op(ser, divmod, data, exc=None)
+        self._check_divmod_op(ser, divmod, data)
 
     @skip_nested
     def test_arith_series_with_scalar(self, data, all_arithmetic_operators):
diff --git a/pandas/tests/extension/test_period.py b/pandas/tests/extension/test_period.py
index bc0872d359d47..7b6bc98ee8c05 100644
--- a/pandas/tests/extension/test_period.py
+++ b/pandas/tests/extension/test_period.py
@@ -116,36 +116,10 @@ class TestInterface(BasePeriodTests, base.BaseInterfaceTests):
 
 
 class TestArithmeticOps(BasePeriodTests, base.BaseArithmeticOpsTests):
-    implements = {"__sub__", "__rsub__"}
-
-    def test_arith_frame_with_scalar(self, data, all_arithmetic_operators):
-        # frame & scalar
-        if all_arithmetic_operators in self.implements:
-            df = pd.DataFrame({"A": data})
-            self.check_opname(df, all_arithmetic_operators, data[0], exc=None)
-        else:
-            # ... but not the rest.
-            super().test_arith_frame_with_scalar(data, all_arithmetic_operators)
-
-    def test_arith_series_with_scalar(self, data, all_arithmetic_operators):
-        # we implement substitution...
-        if all_arithmetic_operators in self.implements:
-            s = pd.Series(data)
-            self.check_opname(s, all_arithmetic_operators, s.iloc[0], exc=None)
-        else:
-            # ... but not the rest.
-            super().test_arith_series_with_scalar(data, all_arithmetic_operators)
-
-    def test_arith_series_with_array(self, data, all_arithmetic_operators):
-        if all_arithmetic_operators in self.implements:
-            s = pd.Series(data)
-            self.check_opname(s, all_arithmetic_operators, s.iloc[0], exc=None)
-        else:
-            # ... but not the rest.
-            super().test_arith_series_with_scalar(data, all_arithmetic_operators)
-
-    def _check_divmod_op(self, s, op, other, exc=NotImplementedError):
-        super()._check_divmod_op(s, op, other, exc=TypeError)
+    def _get_expected_exception(self, op_name, obj, other):
+        if op_name in ("__sub__", "__rsub__"):
+            return None
+        return super()._get_expected_exception(op_name, obj, other)
 
     def test_add_series_with_extension_array(self, data):
         # we don't implement + for Period
diff --git a/pandas/tests/extension/test_sparse.py b/pandas/tests/extension/test_sparse.py
index 77898abb70f4f..a39133c784380 100644
--- a/pandas/tests/extension/test_sparse.py
+++ b/pandas/tests/extension/test_sparse.py
@@ -415,10 +415,6 @@ def test_arith_frame_with_scalar(self, data, all_arithmetic_operators, request):
             request.node.add_marker(mark)
         super().test_arith_frame_with_scalar(data, all_arithmetic_operators)
 
-    def _check_divmod_op(self, ser, op, other, exc=NotImplementedError):
-        # We implement divmod
-        super()._check_divmod_op(ser, op, other, exc=None)
-
 
 class TestComparisonOps(BaseSparseTests):
     def _compare_other(self, data_for_compare: SparseArray, comparison_op, other):