diff --git a/pandas/tests/arrays/integer/test_arithmetic.py b/pandas/tests/arrays/integer/test_arithmetic.py
index cf382dd5e37e0..ae5538a2a85a2 100644
--- a/pandas/tests/arrays/integer/test_arithmetic.py
+++ b/pandas/tests/arrays/integer/test_arithmetic.py
@@ -3,6 +3,8 @@
 import numpy as np
 import pytest
 
+from pandas.compat.numpy import _np_version_under1p20
+
 import pandas as pd
 import pandas._testing as tm
 from pandas.core.arrays import integer_array
@@ -197,7 +199,9 @@ def test_arith_coerce_scalar(data, all_arithmetic_operators):
     result = op(s, other)
     expected = op(s.astype(float), other)
     # rfloordiv results in nan instead of inf
-    if all_arithmetic_operators == "__rfloordiv__":
+    if all_arithmetic_operators == "__rfloordiv__" and _np_version_under1p20:
+        # for numpy 1.20 https://github.com/numpy/numpy/pull/16161
+        #  updated floordiv, now matches our behavior defined in core.ops
         expected[(expected == np.inf) | (expected == -np.inf)] = np.nan
 
     tm.assert_series_equal(result, expected)
diff --git a/pandas/tests/arrays/sparse/test_arithmetics.py b/pandas/tests/arrays/sparse/test_arithmetics.py
index c9f1dd7f589fc..61f4e3e50d09d 100644
--- a/pandas/tests/arrays/sparse/test_arithmetics.py
+++ b/pandas/tests/arrays/sparse/test_arithmetics.py
@@ -3,6 +3,8 @@
 import numpy as np
 import pytest
 
+from pandas.compat.numpy import _np_version_under1p20
+
 import pandas as pd
 import pandas._testing as tm
 from pandas.core import ops
@@ -116,9 +118,15 @@ def _check_logical_ops(self, a, b, a_dense, b_dense):
     @pytest.mark.parametrize("scalar", [0, 1, 3])
     @pytest.mark.parametrize("fill_value", [None, 0, 2])
     def test_float_scalar(
-        self, kind, mix, all_arithmetic_functions, fill_value, scalar
+        self, kind, mix, all_arithmetic_functions, fill_value, scalar, request
     ):
         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)
+
         values = self._base([np.nan, 1, 2, 0, np.nan, 0, 1, 2, 1, np.nan])
 
         a = self._klass(values, kind=kind, fill_value=fill_value)
@@ -142,15 +150,11 @@ def test_float_scalar_comparison(self, kind):
         self._check_comparison_ops(a, 0, values, 0)
         self._check_comparison_ops(a, 3, values, 3)
 
-    def test_float_same_index(self, kind, mix, all_arithmetic_functions):
+    def test_float_same_index_without_nans(
+        self, kind, mix, all_arithmetic_functions, request
+    ):
         # when sp_index are the same
         op = all_arithmetic_functions
-        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])
-
-        a = self._klass(values, kind=kind)
-        b = self._klass(rvalues, kind=kind)
-        self._check_numeric_ops(a, b, values, rvalues, mix, op)
 
         values = self._base([0.0, 1.0, 2.0, 6.0, 0.0, 0.0, 1.0, 2.0, 1.0, 0.0])
         rvalues = self._base([0.0, 2.0, 3.0, 4.0, 0.0, 0.0, 1.0, 3.0, 2.0, 0.0])
@@ -159,6 +163,24 @@ def test_float_same_index(self, kind, mix, all_arithmetic_functions):
         b = self._klass(rvalues, kind=kind, fill_value=0)
         self._check_numeric_ops(a, b, values, rvalues, mix, op)
 
+    def test_float_same_index_with_nans(
+        self, kind, mix, all_arithmetic_functions, request
+    ):
+        # when sp_index are the same
+        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)
+
+        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])
+
+        a = self._klass(values, kind=kind)
+        b = self._klass(rvalues, kind=kind)
+        self._check_numeric_ops(a, b, values, rvalues, mix, op)
+
     def test_float_same_index_comparison(self, kind):
         # when sp_index are the same
         values = self._base([np.nan, 1, 2, 0, np.nan, 0, 1, 2, 1, np.nan])
@@ -324,9 +346,14 @@ def test_bool_array_logical(self, kind, fill_value):
         b = self._klass(rvalues, kind=kind, dtype=np.bool_, fill_value=fill_value)
         self._check_logical_ops(a, b, values, rvalues)
 
-    def test_mixed_array_float_int(self, kind, mix, all_arithmetic_functions):
+    def test_mixed_array_float_int(self, kind, mix, all_arithmetic_functions, request):
         op = all_arithmetic_functions
 
+        if not _np_version_under1p20:
+            if op in [operator.floordiv, ops.rfloordiv] and mix:
+                mark = pytest.mark.xfail(strict=True, reason="GH#38172")
+                request.node.add_marker(mark)
+
         rdtype = "int64"
 
         values = self._base([np.nan, 1, 2, 0, np.nan, 0, 1, 2, 1, np.nan])