diff --git a/pandas/core/ops.py b/pandas/core/ops.py
index 9bf952633ccff..dc139a8e14f66 100644
--- a/pandas/core/ops.py
+++ b/pandas/core/ops.py
@@ -27,6 +27,7 @@
 from pandas.core.dtypes.common import (
     needs_i8_conversion,
     is_datetimelike_v_numeric,
+    is_period_dtype,
     is_integer_dtype, is_categorical_dtype,
     is_object_dtype, is_timedelta64_dtype,
     is_datetime64_dtype, is_datetime64tz_dtype,
@@ -41,7 +42,7 @@
 from pandas.core.dtypes.generic import (
     ABCSeries,
     ABCDataFrame, ABCPanel,
-    ABCIndex,
+    ABCIndex, ABCIndexClass,
     ABCSparseSeries, ABCSparseArray)
 
 
@@ -788,6 +789,57 @@ def mask_cmp_op(x, y, op, allowed_types):
     return result
 
 
+def masked_arith_op(x, y, op):
+    """
+    If the given arithmetic operation fails, attempt it again on
+    only the non-null elements of the input array(s).
+
+    Parameters
+    ----------
+    x : np.ndarray
+    y : np.ndarray, Series, Index
+    op : binary operator
+    """
+    # For Series `x` is 1D so ravel() is a no-op; calling it anyway makes
+    # the logic valid for both Series and DataFrame ops.
+    xrav = x.ravel()
+    assert isinstance(x, (np.ndarray, ABCSeries)), type(x)
+    if isinstance(y, (np.ndarray, ABCSeries, ABCIndexClass)):
+        dtype = find_common_type([x.dtype, y.dtype])
+        result = np.empty(x.size, dtype=dtype)
+
+        # PeriodIndex.ravel() returns int64 dtype, so we have
+        # to work around that case.  See GH#19956
+        yrav = y if is_period_dtype(y) else y.ravel()
+        mask = notna(xrav) & notna(yrav)
+
+        if yrav.shape != mask.shape:
+            # FIXME: GH#5284, GH#5035, GH#19448
+            # Without specifically raising here we get mismatched
+            # errors in Py3 (TypeError) vs Py2 (ValueError)
+            # Note: Only = an issue in DataFrame case
+            raise ValueError('Cannot broadcast operands together.')
+
+        if mask.any():
+            with np.errstate(all='ignore'):
+                result[mask] = op(xrav[mask],
+                                  com.values_from_object(yrav[mask]))
+
+    else:
+        assert is_scalar(y), type(y)
+        assert isinstance(x, np.ndarray), type(x)
+        # mask is only meaningful for x
+        result = np.empty(x.size, dtype=x.dtype)
+        mask = notna(xrav)
+        if mask.any():
+            with np.errstate(all='ignore'):
+                result[mask] = op(xrav[mask], y)
+
+    result, changed = maybe_upcast_putmask(result, ~mask, np.nan)
+    result = result.reshape(x.shape)  # 2D compat
+    return result
+
+
 def invalid_comparison(left, right, op):
     """
     If a comparison has mismatched types and is not necessarily meaningful,
@@ -880,8 +932,7 @@ def _get_method_wrappers(cls):
     return arith_flex, comp_flex, arith_special, comp_special, bool_special
 
 
-def _create_methods(cls, arith_method, comp_method, bool_method,
-                    special=False):
+def _create_methods(cls, arith_method, comp_method, bool_method, special):
     # creates actual methods based upon arithmetic, comp and bool method
     # constructors.
 
@@ -1136,19 +1187,7 @@ def na_op(x, y):
         try:
             result = expressions.evaluate(op, str_rep, x, y, **eval_kwargs)
         except TypeError:
-            if isinstance(y, (np.ndarray, ABCSeries, pd.Index)):
-                dtype = find_common_type([x.dtype, y.dtype])
-                result = np.empty(x.size, dtype=dtype)
-                mask = notna(x) & notna(y)
-                result[mask] = op(x[mask], com.values_from_object(y[mask]))
-            else:
-                assert isinstance(x, np.ndarray)
-                assert is_scalar(y)
-                result = np.empty(len(x), dtype=x.dtype)
-                mask = notna(x)
-                result[mask] = op(x[mask], y)
-
-            result, changed = maybe_upcast_putmask(result, ~mask, np.nan)
+            result = masked_arith_op(x, y, op)
 
         result = missing.fill_zeros(result, x, y, op_name, fill_zeros)
         return result
@@ -1675,40 +1714,7 @@ def na_op(x, y):
         try:
             result = expressions.evaluate(op, str_rep, x, y, **eval_kwargs)
         except TypeError:
-            xrav = x.ravel()
-            if isinstance(y, (np.ndarray, ABCSeries)):
-                dtype = find_common_type([x.dtype, y.dtype])
-                result = np.empty(x.size, dtype=dtype)
-                yrav = y.ravel()
-                mask = notna(xrav) & notna(yrav)
-                xrav = xrav[mask]
-
-                if yrav.shape != mask.shape:
-                    # FIXME: GH#5284, GH#5035, GH#19448
-                    # Without specifically raising here we get mismatched
-                    # errors in Py3 (TypeError) vs Py2 (ValueError)
-                    raise ValueError('Cannot broadcast operands together.')
-
-                yrav = yrav[mask]
-                if xrav.size:
-                    with np.errstate(all='ignore'):
-                        result[mask] = op(xrav, yrav)
-
-            elif isinstance(x, np.ndarray):
-                # mask is only meaningful for x
-                result = np.empty(x.size, dtype=x.dtype)
-                mask = notna(xrav)
-                xrav = xrav[mask]
-                if xrav.size:
-                    with np.errstate(all='ignore'):
-                        result[mask] = op(xrav, y)
-            else:
-                raise TypeError("cannot perform operation {op} between "
-                                "objects of type {x} and {y}"
-                                .format(op=op_name, x=type(x), y=type(y)))
-
-            result, changed = maybe_upcast_putmask(result, ~mask, np.nan)
-            result = result.reshape(x.shape)
+            result = masked_arith_op(x, y, op)
 
         result = missing.fill_zeros(result, x, y, op_name, fill_zeros)