diff --git a/lib/iris/analysis/maths.py b/lib/iris/analysis/maths.py
index 0de97b02f3..46efe76689 100644
--- a/lib/iris/analysis/maths.py
+++ b/lib/iris/analysis/maths.py
@@ -944,6 +944,10 @@ def _math_op_common(
         new_cube.data = ma.masked_array(0, 1, dtype=new_dtype)
 
     iris.analysis.clear_phenomenon_identity(new_cube)
+    for cm in cube.cell_measures():
+        new_cube.remove_cell_measure(cm)
+    for av in cube.ancillary_variables():
+        new_cube.remove_ancillary_variable(av)
     new_cube.units = new_unit
     return new_cube
 
diff --git a/lib/iris/tests/unit/analysis/maths/__init__.py b/lib/iris/tests/unit/analysis/maths/__init__.py
index e706e53292..64065e420b 100644
--- a/lib/iris/tests/unit/analysis/maths/__init__.py
+++ b/lib/iris/tests/unit/analysis/maths/__init__.py
@@ -11,7 +11,7 @@
 from numpy import ma
 
 from iris.analysis import MEAN
-from iris.coords import DimCoord
+from iris.coords import DimCoord, CellMeasure, AncillaryVariable
 from iris.cube import Cube
 import iris.tests as tests
 import iris.tests.stock as stock
@@ -212,3 +212,36 @@ def test_masked_constant_not_in_place(self):
         self.assertMaskedArrayEqual(ma.masked_array(0, 1), res.data)
         self.assertEqual(dtype, res.dtype)
         self.assertIsNot(res, cube)
+
+
+class CubeArithmeticAncillaryHandlingTestMixin(metaclass=ABCMeta):
+    @property
+    @abstractmethod
+    def cube_func(self):
+        # Define an iris arithmetic function to be called
+        # I.E. 'iris.analysis.maths.xx'.
+        pass
+
+    def test_cell_measure_removal(self):
+        cube1 = Cube([0])
+        cm = CellMeasure([0], long_name="cm")
+        cube1.add_cell_measure(cm)
+        cube2 = Cube([0])
+        res1 = cube1 + cube2
+        res2 = cube2 + cube1
+        res3 = cube1 + cube1
+        self.assertEqual(res1.cell_measures(), [])
+        self.assertEqual(res2.cell_measures(), [])
+        self.assertEqual(res3.cell_measures(), [])
+
+    def test_ancillary_removal(self):
+        cube1 = Cube([0])
+        av = AncillaryVariable([0], long_name="av")
+        cube1.add_ancillary_variable(av)
+        cube2 = Cube([0])
+        res1 = cube1 + cube2
+        res2 = cube2 + cube1
+        res3 = cube1 + cube1
+        self.assertEqual(res1.ancillary_variables(), [])
+        self.assertEqual(res2.ancillary_variables(), [])
+        self.assertEqual(res3.ancillary_variables(), [])
diff --git a/lib/iris/tests/unit/analysis/maths/test_add.py b/lib/iris/tests/unit/analysis/maths/test_add.py
index 22f54e0a91..3a39c17447 100644
--- a/lib/iris/tests/unit/analysis/maths/test_add.py
+++ b/lib/iris/tests/unit/analysis/maths/test_add.py
@@ -17,6 +17,7 @@
     CubeArithmeticCoordsTest,
     CubeArithmeticMaskedConstantTestMixin,
     CubeArithmeticMaskingTestMixin,
+    CubeArithmeticAncillaryHandlingTestMixin,
 )
 
 
@@ -70,5 +71,14 @@ def cube_func(self):
         return add
 
 
+@tests.iristest_timing_decorator
+class TestAncillaryHandling(
+    tests.IrisTest_nometa, CubeArithmeticAncillaryHandlingTestMixin
+):
+    @property
+    def cube_func(self):
+        return add
+
+
 if __name__ == "__main__":
     tests.main()
diff --git a/lib/iris/tests/unit/analysis/maths/test_divide.py b/lib/iris/tests/unit/analysis/maths/test_divide.py
index c184a2cacc..305f58ca60 100644
--- a/lib/iris/tests/unit/analysis/maths/test_divide.py
+++ b/lib/iris/tests/unit/analysis/maths/test_divide.py
@@ -18,6 +18,7 @@
     CubeArithmeticBroadcastingTestMixin,
     CubeArithmeticMaskingTestMixin,
     CubeArithmeticCoordsTest,
+    CubeArithmeticAncillaryHandlingTestMixin,
 )
 
 
@@ -86,5 +87,14 @@ def test_reversed_points(self):
             divide(cube1, cube2)
 
 
+@tests.iristest_timing_decorator
+class TestAncillaryHandling(
+    tests.IrisTest_nometa, CubeArithmeticAncillaryHandlingTestMixin
+):
+    @property
+    def cube_func(self):
+        return divide
+
+
 if __name__ == "__main__":
     tests.main()
diff --git a/lib/iris/tests/unit/analysis/maths/test_multiply.py b/lib/iris/tests/unit/analysis/maths/test_multiply.py
index ed19f5bf09..6dfeb17056 100644
--- a/lib/iris/tests/unit/analysis/maths/test_multiply.py
+++ b/lib/iris/tests/unit/analysis/maths/test_multiply.py
@@ -17,6 +17,7 @@
     CubeArithmeticCoordsTest,
     CubeArithmeticMaskedConstantTestMixin,
     CubeArithmeticMaskingTestMixin,
+    CubeArithmeticAncillaryHandlingTestMixin,
 )
 
 
@@ -70,5 +71,14 @@ def cube_func(self):
         return multiply
 
 
+@tests.iristest_timing_decorator
+class TestAncillaryHandling(
+    tests.IrisTest_nometa, CubeArithmeticAncillaryHandlingTestMixin
+):
+    @property
+    def cube_func(self):
+        return multiply
+
+
 if __name__ == "__main__":
     tests.main()