diff --git a/pint/quantity.py b/pint/quantity.py
index d9286ba..eb10207 100644
--- a/pint/quantity.py
+++ b/pint/quantity.py
@@ -44,6 +44,25 @@ class _Exception(Exception):            # pragma: no cover
         self.internal = internal
 
 
+def reduce_dimensions(f):
+    def wrapped(self, *args, **kwargs):
+        result = f(self, *args, **kwargs)
+        if result._REGISTRY.auto_reduce_dimensions:
+            return result.to_root_units()
+        else:
+            return result
+    return wrapped
+
+
+def ireduce_dimensions(f):
+    def wrapped(self, *args, **kwargs):
+        result = f(self, *args, **kwargs)
+        if result._REGISTRY.auto_reduce_dimensions:
+            result.ito_root_units()
+        return result
+    return wrapped
+
+
 @fix_str_conversions
 class _Quantity(SharedRegistryObject):
     """Implements a class to describe a physical quantity:
@@ -657,6 +676,7 @@ class _Quantity(SharedRegistryObject):
     def __rsub__(self, other):
         return -self._add_sub(other, operator.sub)
 
+    @ireduce_dimensions
     def _imul_div(self, other, magnitude_op, units_op=None):
         """Perform multiplication or division operation in-place and return the
         result.
@@ -714,6 +734,7 @@ class _Quantity(SharedRegistryObject):
 
         return self
 
+    @reduce_dimensions
     def _mul_div(self, other, magnitude_op, units_op=None):
         """Perform multiplication or division operation and return the result.
 
diff --git a/pint/registry.py b/pint/registry.py
index a5b74c6..b778fd8 100644
--- a/pint/registry.py
+++ b/pint/registry.py
@@ -96,6 +96,7 @@ class BaseRegistry(meta.with_metaclass(_Meta)):
     :param on_redefinition: action to take in case a unit is redefined.
                             'warn', 'raise', 'ignore'
     :type on_redefinition: str
+    :param auto_reduce_dimensions: If True, reduce dimensionality on appropriate operations.
     """
 
     #: Map context prefix to function
@@ -111,7 +112,7 @@ class BaseRegistry(meta.with_metaclass(_Meta)):
             'parse_unit_name', 'parse_units', 'parse_expression',
             'convert']
 
-    def __init__(self, filename='', force_ndarray=False, on_redefinition='warn'):
+    def __init__(self, filename='', force_ndarray=False, on_redefinition='warn', auto_reduce_dimensions=False):
 
         self._register_parsers()
 
@@ -129,6 +130,9 @@ class BaseRegistry(meta.with_metaclass(_Meta)):
         #: Action to take in case a unit is redefined. 'warn', 'raise', 'ignore'
         self._on_redefinition = on_redefinition
 
+        #: Determines if dimensionality should be reduced on appropriate operations.
+        self.auto_reduce_dimensions = auto_reduce_dimensions
+
         #: Map between name (string) and value (string) of defaults stored in the definitions file.
         self._defaults = {}
 
@@ -1435,17 +1439,20 @@ class UnitRegistry(SystemRegistry, ContextRegistry, NonMultiplicativeRegistry):
     :param on_redefinition: action to take in case a unit is redefined.
                             'warn', 'raise', 'ignore'
     :type on_redefinition: str
+    :param auto_reduce_dimensions: If True, reduce dimensionality on appropriate operations.
     """
 
     def __init__(self, filename='', force_ndarray=False, default_as_delta=True,
                  autoconvert_offset_to_baseunit=False,
-                 on_redefinition='warn', system=None):
+                 on_redefinition='warn', system=None,
+                 auto_reduce_dimensions=False):
 
         super(UnitRegistry, self).__init__(filename=filename, force_ndarray=force_ndarray,
                                            on_redefinition=on_redefinition,
                                            default_as_delta=default_as_delta,
                                            autoconvert_offset_to_baseunit=autoconvert_offset_to_baseunit,
-                                           system=system)
+                                           system=system,
+                                           auto_reduce_dimensions=auto_reduce_dimensions)
 
     def pi_theorem(self, quantities):
         """Builds dimensionless quantities using the Buckingham π theorem
diff --git a/pint/testsuite/test_quantity.py b/pint/testsuite/test_quantity.py
index 7a184a1..e83abec 100644
--- a/pint/testsuite/test_quantity.py
+++ b/pint/testsuite/test_quantity.py
@@ -1168,3 +1168,40 @@ class TestOffsetUnitMath(QuantityTestCase, ParameterizedTestCase):
 
                 in1_cp = copy.copy(in1)
                 self.assertQuantityAlmostEqual(op.ipow(in1_cp, in2), expected)
+
+
+class TestDimensionReduction(QuantityTestCase):
+    def _calc_mass(self, ureg):
+        density = 3 * ureg.g / ureg.L
+        volume = 32 * ureg.milliliter
+        return density * volume
+
+    def _icalc_mass(self, ureg):
+        res = ureg.Quantity(3.0, 'gram/liter')
+        res *= ureg.Quantity(32.0, 'milliliter')
+        return res
+
+    def test_mul_and_div_reduction(self):
+        ureg = UnitRegistry(auto_reduce_dimensions=True)
+        mass = self._calc_mass(ureg)
+        self.assertEqual(mass.units, ureg.g)
+        ureg = UnitRegistry(auto_reduce_dimensions=False)
+        mass = self._calc_mass(ureg)
+        self.assertEqual(mass.units, ureg.g / ureg.L * ureg.milliliter)
+
+    @helpers.requires_numpy()
+    def test_imul_and_div_reduction(self):
+        ureg = UnitRegistry(auto_reduce_dimensions=True, force_ndarray=True)
+        mass = self._icalc_mass(ureg)
+        self.assertEqual(mass.units, ureg.g)
+        ureg = UnitRegistry(auto_reduce_dimensions=False, force_ndarray=True)
+        mass = self._icalc_mass(ureg)
+        self.assertEqual(mass.units, ureg.g / ureg.L * ureg.milliliter)
+
+    def test_reduction_to_dimensionless(self):
+        ureg = UnitRegistry(auto_reduce_dimensions=True)
+        x = (10 * ureg.feet) / (3 * ureg.inches)
+        self.assertEqual(x.units, UnitsContainer({}))
+        ureg = UnitRegistry(auto_reduce_dimensions=False)
+        x = (10 * ureg.feet) / (3 * ureg.inches)
+        self.assertEqual(x.units, ureg.feet / ureg.inches)