diff --git a/pandas/tests/frame/test_arithmetic.py b/pandas/tests/frame/test_arithmetic.py
index 7c022106c9104..706bc122c6d9e 100644
--- a/pandas/tests/frame/test_arithmetic.py
+++ b/pandas/tests/frame/test_arithmetic.py
@@ -642,3 +642,14 @@ def test_arith_non_pandas_object(self):
         val3 = np.random.rand(*df.shape)
         added = pd.DataFrame(df.values + val3, index=df.index, columns=df.columns)
         tm.assert_frame_equal(df.add(val3), added)
+
+    def test_operations_with_interval_categories_index(self, all_arithmetic_operators):
+        # GH#27415
+        op = all_arithmetic_operators
+        ind = pd.CategoricalIndex(pd.interval_range(start=0.0, end=2.0))
+        data = [1, 2]
+        df = pd.DataFrame([data], columns=ind)
+        num = 10
+        result = getattr(df, op)(num)
+        expected = pd.DataFrame([[getattr(n, op)(num) for n in data]], columns=ind)
+        tm.assert_frame_equal(result, expected)