diff --git a/pandas/tests/arrays/sparse/test_arithmetics.py b/pandas/tests/arrays/sparse/test_arithmetics.py
index 013814681b5f6..86fbcb337b30e 100644
--- a/pandas/tests/arrays/sparse/test_arithmetics.py
+++ b/pandas/tests/arrays/sparse/test_arithmetics.py
@@ -124,8 +124,13 @@ def test_float_scalar(
 
         if not np_version_under1p20:
             if op in [operator.floordiv, ops.rfloordiv]:
-                mark = pytest.mark.xfail(strict=False, reason="GH#38172")
-                request.node.add_marker(mark)
+                if op is operator.floordiv and scalar != 0:
+                    pass
+                elif op is ops.rfloordiv and scalar == 0:
+                    pass
+                else:
+                    mark = pytest.mark.xfail(reason="GH#38172")
+                    request.node.add_marker(mark)
 
         values = self._base([np.nan, 1, 2, 0, np.nan, 0, 1, 2, 1, np.nan])
 
@@ -170,9 +175,10 @@ def test_float_same_index_with_nans(
         op = all_arithmetic_functions
 
         if not np_version_under1p20:
-            if op in [operator.floordiv, ops.rfloordiv]:
-                mark = pytest.mark.xfail(strict=False, reason="GH#38172")
-                request.node.add_marker(mark)
+            if op is ops.rfloordiv:
+                if not (mix and kind == "block"):
+                    mark = pytest.mark.xfail(reason="GH#38172")
+                    request.node.add_marker(mark)
 
         values = self._base([np.nan, 1, 2, 0, np.nan, 0, 1, 2, 1, np.nan])
         rvalues = self._base([np.nan, 2, 3, 4, np.nan, 0, 1, 3, 2, np.nan])