diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 7153f5c2e7007..fcd1e3db46f3a 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -4935,6 +4935,33 @@ def reorder_levels(self, order, axis=0):
     # ----------------------------------------------------------------------
     # Arithmetic / combination related
 
+    def _wrap_dispatched_op(self, result, other, func, axis=None):
+        """
+        Wrap the result of an arithmetic/comparison operation performed
+        via ops.dispatch_to_series in a properly-indexed DataFrame.
+
+        Parameters
+        ----------
+        result : dict[int:Series]
+        other : DataFrame, Series, or scalar
+        func : binary operator
+        axis : {0, 1, "index", "columns"}
+
+        Returns
+        -------
+        DataFrame
+
+        Notes
+        -----
+        The `other`, `func`, and `axis` arguments are not used here but are
+        included to keep the signature consistent with that in SparseDataFrame.
+        """
+        result = self._constructor(result, index=self.index, copy=False)
+        # Pin columns instead of passing to constructor for compat with
+        # non-unique columns case
+        result.columns = self.columns
+        return result
+
     def _combine_frame(self, other, func, fill_value=None, level=None):
         this, other = self.align(other, join='outer', level=level, copy=False)
         new_index, new_columns = this.index, this.columns
diff --git a/pandas/core/ops.py b/pandas/core/ops.py
index fbfdfb9c01237..3f299d1585ce7 100644
--- a/pandas/core/ops.py
+++ b/pandas/core/ops.py
@@ -792,7 +792,7 @@ def fill_binop(left, right, fill_value):
     return left, right
 
 
-def mask_cmp_op(x, y, op, allowed_types):
+def mask_cmp_op(x, y, op):
     """
     Apply the function `op` to only non-null points in x and y.
 
@@ -801,16 +801,15 @@ def mask_cmp_op(x, y, op, allowed_types):
     x : array-like
     y : array-like
     op : binary operation
-    allowed_types : class or tuple of classes
 
     Returns
     -------
     result : ndarray[bool]
     """
-    # TODO: Can we make the allowed_types arg unnecessary?
+    # TODO: can we do this without casting to list?
     xrav = x.ravel()
     result = np.empty(x.size, dtype=bool)
-    if isinstance(y, allowed_types):
+    if isinstance(y, (np.ndarray, ABCSeries)):
         yrav = y.ravel()
         mask = notna(xrav) & notna(yrav)
         result[mask] = op(np.array(list(xrav[mask])),
@@ -1006,12 +1005,7 @@ def column_op(a, b):
         raise NotImplementedError(right)
 
     new_data = expressions.evaluate(column_op, str_rep, left, right)
-
-    result = left._constructor(new_data, index=left.index, copy=False)
-    # Pin columns instead of passing to constructor for compat with
-    # non-unique columns case
-    result.columns = left.columns
-    return result
+    return left._wrap_dispatched_op(new_data, right, func, axis=axis)
 
 
 def dispatch_to_index_op(op, left, right, index_class):
@@ -1896,7 +1890,7 @@ def na_op(x, y):
             with np.errstate(invalid='ignore'):
                 result = op(x, y)
         except TypeError:
-            result = mask_cmp_op(x, y, op, (np.ndarray, ABCSeries))
+            result = mask_cmp_op(x, y, op)
         return result
 
     @Appender('Wrapper for flexible comparison methods {name}'
@@ -1948,7 +1942,7 @@ def f(self, other):
         else:
 
             # straight boolean comparisons we want to allow all columns
-            # (regardless of dtype to pass thru) See #4537 for discussion.
+            # (regardless of dtype to pass thru) See GH#4537 for discussion.
             res = self._combine_const(other, func)
             return res.fillna(True).astype(bool)
 
@@ -1986,7 +1980,7 @@ def na_op(x, y):
         try:
             result = expressions.evaluate(op, str_rep, x, y)
         except TypeError:
-            result = mask_cmp_op(x, y, op, np.ndarray)
+            result = mask_cmp_op(x, y, op)
         return result
 
     @Appender('Wrapper for comparison method {name}'.format(name=op_name))
diff --git a/pandas/core/sparse/frame.py b/pandas/core/sparse/frame.py
index ee7de49bc1bce..7ebedd02a5ff3 100644
--- a/pandas/core/sparse/frame.py
+++ b/pandas/core/sparse/frame.py
@@ -339,9 +339,10 @@ def _apply_columns(self, func):
         for col, series in compat.iteritems(self):
             new_data[col] = func(series)
 
-        return self._constructor(
-            data=new_data, index=self.index, columns=self.columns,
-            default_fill_value=self.default_fill_value).__finalize__(self)
+        # pass dummy arguments for func and axis; `other` just needs to be
+        #  a scalar.
+        return self._wrap_dispatched_op(new_data, other=None,
+                                        func=None, axis=None)
 
     def astype(self, dtype):
         return self._apply_columns(lambda x: x.astype(dtype))
@@ -547,6 +548,31 @@ def xs(self, key, axis=0, copy=False):
     # ----------------------------------------------------------------------
     # Arithmetic-related methods
 
+    def _wrap_dispatched_op(self, result, other, func, axis=None):
+        """
+        Wrap the result of an arithmetic/comparison operation performed
+        via ops.dispatch_to_series in a properly-indexed DataFrame.
+
+        Parameters
+        ----------
+        result : dict[int:Series]
+        other : DataFrame, Series, scalar
+        func : binary function
+        axis : {None, "columns"}
+
+        Returns
+        -------
+        SparseDataFrame
+        """
+
+        fill_value = self._get_op_result_fill_value(other, func, axis)
+
+        res = self._constructor(result, index=self.index,
+                                columns=self.columns,
+                                default_fill_value=fill_value)
+
+        return res.__finalize__(self)
+
     def _combine_frame(self, other, func, fill_value=None, level=None):
         if level is not None:
             raise NotImplementedError("'level' argument is not supported")
@@ -557,31 +583,22 @@ def _combine_frame(self, other, func, fill_value=None, level=None):
         if self.empty and other.empty:
             return self._constructor(index=new_index).__finalize__(self)
 
-        new_data = {}
-        if fill_value is not None:
-            # TODO: be a bit more intelligent here
-            for col in new_columns:
-                if col in this and col in other:
-                    dleft = this[col].to_dense()
-                    dright = other[col].to_dense()
-                    result = dleft._binop(dright, func, fill_value=fill_value)
-                    result = result.to_sparse(fill_value=this[col].fill_value)
-                    new_data[col] = result
-        else:
+        def _arith_op(left, right):
+            # analogous to _arith_op defined in DataFrame._combine_frame
+            dleft = left.to_dense()
+            dright = right.to_dense()
+            result = dleft._binop(dright, func, fill_value=fill_value)
+            result = result.to_sparse(fill_value=left.fill_value)
+            return result
 
-            for col in new_columns:
-                if col in this and col in other:
-                    new_data[col] = func(this[col], other[col])
+        assert all(col in this and col in other for col in new_columns)
 
-        new_fill_value = self._get_op_result_fill_value(other, func)
+        new_data = {col: _arith_op(this[col], other[col])
+                    for col in new_columns}
 
-        return self._constructor(data=new_data, index=new_index,
-                                 columns=new_columns,
-                                 default_fill_value=new_fill_value
-                                 ).__finalize__(self)
+        return this._wrap_dispatched_op(new_data, other, func, axis=None)
 
     def _combine_match_index(self, other, func, level=None):
-        new_data = {}
 
         if level is not None:
             raise NotImplementedError("'level' argument is not supported")
@@ -589,14 +606,10 @@ def _combine_match_index(self, other, func, level=None):
         this, other = self.align(other, join='outer', axis=0, level=level,
                                  copy=False)
 
-        for col, series in compat.iteritems(this):
-            new_data[col] = func(series.values, other.values)
+        new_data = {col: func(this[col].values, other.values)
+                    for col in this.columns}
 
-        fill_value = self._get_op_result_fill_value(other, func)
-
-        return self._constructor(
-            new_data, index=this.index, columns=self.columns,
-            default_fill_value=fill_value).__finalize__(self)
+        return self._wrap_dispatched_op(new_data, other, func, axis=None)
 
     def _combine_match_columns(self, other, func, level=None):
         # patched version of DataFrame._combine_match_columns to account for
@@ -611,29 +624,33 @@ def _combine_match_columns(self, other, func, level=None):
                                  copy=False)
         assert left.columns.equals(right.index)
 
-        new_data = {}
-
-        for col in left.columns:
-            new_data[col] = func(left[col], float(right[col]))
+        new_data = {col: func(left[col], float(right[col]))
+                    for col in left.columns}
 
-        return self._constructor(
-            new_data, index=left.index, columns=left.columns,
-            default_fill_value=self.default_fill_value).__finalize__(self)
+        return self._wrap_dispatched_op(new_data, other, func, "columns")
 
     def _combine_const(self, other, func):
-        return self._apply_columns(lambda x: func(x, other))
+        new_data = {col: func(self[col], other) for col in self.columns}
+
+        return self._wrap_dispatched_op(new_data, other, func, axis=None)
 
-    def _get_op_result_fill_value(self, other, func):
+    def _get_op_result_fill_value(self, other, func, axis=None):
         own_default = self.default_fill_value
 
-        if isinstance(other, DataFrame):
+        axis = self._get_axis_name(axis) if axis is not None else None
+
+        if axis == "columns":
+            # i.e. called via _combine_match_columns
+            fill_value = self.default_fill_value
+
+        elif isinstance(other, DataFrame):
             # i.e. called from _combine_frame
 
             other_default = getattr(other, 'default_fill_value', np.nan)
 
             # if the fill values are the same use them? or use a valid one
             if own_default == other_default:
-                # TOOD: won't this evaluate as False if both are np.nan?
+                # TODO: won't this evaluate as False if both are np.nan?
                 fill_value = own_default
             elif np.isnan(own_default) and not np.isnan(other_default):
                 fill_value = other_default
@@ -652,6 +669,10 @@ def _get_op_result_fill_value(self, other, func):
                 fill_value = func(np.float64(own_default),
                                   np.float64(other.fill_value))
 
+        elif np.ndim(other) == 0:
+            # i.e. called via _combine_const
+            fill_value = self.default_fill_value
+
         else:
             raise NotImplementedError(type(other))