diff --git a/docs/CMakeLists.txt b/docs/CMakeLists.txt
index a26079df..79f5b1ad 100644
--- a/docs/CMakeLists.txt
+++ b/docs/CMakeLists.txt
@@ -49,6 +49,7 @@ set(unitsSphinxDocs
     "${CMAKE_CURRENT_SOURCE_DIR}/design/directories.rst"
     "${CMAKE_CURRENT_SOURCE_DIR}/design/downcasting.rst"
     "${CMAKE_CURRENT_SOURCE_DIR}/design/quantity.rst"
+    "${CMAKE_CURRENT_SOURCE_DIR}/design/quantity_kind.rst"
 
     "${CMAKE_CURRENT_SOURCE_DIR}/examples.rst"
     "${CMAKE_CURRENT_SOURCE_DIR}/examples/avg_speed.rst"
diff --git a/docs/design/quantity_kind.rst b/docs/design/quantity_kind.rst
new file mode 100644
index 00000000..78505d1d
--- /dev/null
+++ b/docs/design/quantity_kind.rst
@@ -0,0 +1,52 @@
+.. namespace:: units
+
+quantity_kind
+=============
+
+The ``quantity_kind`` class template provides a similar interface to ``quantity``.
+
+Kinds
+-----
+
+The first template parameter of ``quantity_kind`` is a ``Kind``.
+
+``Kind``s, by themselves:
+
+    * Wrap a ``Dimension``, and
+    * opt into the downcasting facility.
+
+If a dimensional analysis operator on a quantity of kind *A*
+can result on a quantity of kind *B*,
+*A* and *B* are *related*.
+
+The library provides two ``Kind`` bases, ``kind`` and ``derived_kind``.
+
+``kind`` is an entry point, and there's only one per set of related kinds.
+
+``derived_kind`` is used to explicitly name other related kinds.
+Unnamed, they look like ``detail::_kind_base<the-entry-kind, some_dimension>``.
+
+Unnamed kinds, like unnamed units and dimensions,
+allows (intermediate) results in formulas without having to name them.
+
+Quantity kinds
+--------------
+
+``quantity_kind`` wraps a ``quantity`` and layers over its dimensional analysis.
+While all properties of the ``quantity`` apply transparently,
+results are always ``quantity_kind``s related to the kind(s) of the argument(s).
+
+One of the arguments to the dimensional analysis operators can also be ``Quantity``.
+
+The way back to ``quantity`` is through the ``.common()`` observer.
+
+Intra-kind operations
+---------------------
+
+``quantity_kind`` takes care of operators between related quantity kinds.
+Intra-kind operations can be opted into as follows::
+
+    struct width : kind<width, dim_length> {};
+    struct height : kind<height, dim_length> {};
+
+    size2d operator+(QuantityKindOf<width> auto, QuantityKindOf<height> auto);
diff --git a/docs/framework/dimensions.rst b/docs/framework/dimensions.rst
index bde6378a..d81c8258 100644
--- a/docs/framework/dimensions.rst
+++ b/docs/framework/dimensions.rst
@@ -67,23 +67,40 @@ dimension, than we will end up with just a dimensionless quantity:
 Quantity Kinds
 ++++++++++++++
 
-Quantity kinds behave the same as quantities for addition and subtraction.
-The same behavior is also provided for multiplication with, and division by
-a :term:`scalable number`.
-
-Multiplication and division with a quantity (but not a quantity kind) is allowed.
-The result is a quantity kind with the appropriate dimension
-and related to the original quantity kind:
+Quantity kinds behave the same as quantities for all operations,
+except that the quantity types in the operators' declarations
+are quantity kind types instead.
+Additionally, for the dimensional analysis operators,
+you can use a quantity argument instead of a quantity kind.
 
 .. code-block::
-    :emphasize-lines: 5-6
+    :emphasize-lines: 8-9
 
-    struct height : kind<height, dim_length> {};
-    struct rate_of_climb : derived_kind<rate_of_climb, height, dim_speed> {};
+    struct height_kind : kind<height_kind, dim_length> {};
+    struct rate_of_climb_kind : derived_kind<rate_of_climb_kind, height_kind, dim_speed> {};
 
-    quantity_kind h(height{}, 100 * m);
-    quantity_point_kind rate = h / (25 * s);
-      // quantity_point_kind<rate_of_climb, si::metre_per_second, int>(4 * m / s)
+    template <Unit U, QuantityValue Rep = double> using height = quantity_kind<height_kind, U, Rep>;
+    template <Unit U, QuantityValue Rep = double> using rate_of_climb = quantity_kind<rate_of_climb_kind, U, Rep>;
+
+    height h{100 * m};
+    rate_of_climb rate = h / (25 * s);
+      // quantity_kind<rate_of_climb_kind, si::metre_per_second, int>(4 * m / s)
+
+.. code-block::
+    :emphasize-lines: 8-12
+
+    struct width_kind : kind<width_kind, dim_length> {};
+    struct horizontal_area_kind : derived_kind<horizontal_area_kind, width_kind, dim_area> {};
+
+    template <Unit U, QuantityValue Rep = double> using width = quantity_kind<width_kind, U, Rep>;
+    template <Unit U, QuantityValue Rep = double> using horizontal_area = quantity_kind<horizontal_area_kind, U, Rep>;
+
+    width w{5 * m};
+    horizontal_area area1 = w * w;
+      // quantity_kind<horizontal_area_kind, si::metre_per_second, int>(25 * m * m)
+    width w2 = area1 / w; // quantity_kind<width_kind, si::metre, int>(5 * m)
+    auto q1 = w / w; // Dimensionless quantity kinds related to width
+    auto q2 = w / (5 * m); // with .common() equal to quantity{1}
 
 Quantity Points
 +++++++++++++++
diff --git a/docs/framework/quantity_kinds.rst b/docs/framework/quantity_kinds.rst
index 73528afd..36b67913 100644
--- a/docs/framework/quantity_kinds.rst
+++ b/docs/framework/quantity_kinds.rst
@@ -41,7 +41,7 @@ the value to the `quantity_kind` class template constructor::
 Differences To Quantity
 -----------------------
 
-Unlike `quantity`, the library provides:
+The library provides:
 
 - no kinds, such as ``radius`` or ``width``, therefore
 
@@ -49,7 +49,7 @@ Unlike `quantity`, the library provides:
     * no kind-specific concepts, such as ``Radius``,
       (there's the generic `QuantityKind` and kind-specifiable `QuantityKindOf`),
 
-- a slightly different set of operations on quantity kinds
+- a slightly larger set of operations on quantity kinds
   (see the :ref:`framework/dimensions:Quantity Kinds` chapter).
 
 
diff --git a/example/glide_computer.cpp b/example/glide_computer.cpp
index d3576ac9..be410b8b 100644
--- a/example/glide_computer.cpp
+++ b/example/glide_computer.cpp
@@ -100,8 +100,8 @@ using namespace si::international::literals;
 using namespace si::unit_constants;
 
 template<QuantityKind QK1, QuantityKind QK2>
-constexpr Quantity auto operator/(const QK1& lhs, const QK2& rhs)
-  requires requires { lhs.common() / rhs.common(); } {
+constexpr Dimensionless auto operator/(const QK1& lhs, const QK2& rhs)
+  requires (!units::QuantityKindRelatedTo<QK1, QK2>) && requires { lhs.common() / rhs.common(); } {
   return lhs.common() / rhs.common();
 }
 
@@ -258,7 +258,7 @@ struct flight_point {
 constexpr altitude terrain_level_alt(const task& t, distance dist)
 {
   const height alt_diff = t.finish.alt - t.start.alt;
-  return t.start.alt + alt_diff * (dist / t.dist);
+  return t.start.alt + alt_diff * (dist / t.dist).common();
 }
 
 constexpr height agl(altitude glider_alt, altitude terrain_level)
@@ -283,7 +283,7 @@ void print(std::string_view phase_name, const flight_point& point, const flight_
 
 flight_point tow(const flight_point& point, const aircraft_tow& at)
 {
-  const duration d = at.height_agl / at.performance;
+  const duration d = (at.height_agl / at.performance).common();
   const flight_point new_point{point.dur + d, point.dist, point.alt + at.height_agl};
 
   print("Tow", point, new_point);
@@ -295,7 +295,7 @@ flight_point circle(const flight_point& point, const glider& g, const weather& w
   const height h_agl = agl(point.alt, terrain_level_alt(t, point.dist));
   const height circle_height = std::min(w.cloud_base - h_agl, height_to_gain);
   const rate_of_climb circling_rate = w.thermal_strength + g.polar[0].climb;
-  const duration d = circle_height / circling_rate;
+  const duration d = (circle_height / circling_rate).common();
   const flight_point new_point{point.dur + d, point.dist, point.alt + circle_height};
 
   height_to_gain -= circle_height;
diff --git a/src/include/units/quantity.h b/src/include/units/quantity.h
index 4aef869f..9ea29b5a 100644
--- a/src/include/units/quantity.h
+++ b/src/include/units/quantity.h
@@ -246,6 +246,16 @@ public:
     return *this;
   }
 
+  template<typename Rep2>
+  constexpr quantity& operator%=(const dimensionless<units::one, Rep2>& rhs)
+    requires (!floating_point_<rep>) && (!floating_point_<Rep2>) &&
+             requires(rep a, const Rep2 b) { { a %= b } -> std::same_as<rep&>; }
+  {
+    gsl_ExpectsAudit(rhs.count() != quantity_values<Rep2>::zero());
+    value_ %= rhs.count();
+    return *this;
+  }
+
   constexpr quantity& operator%=(const quantity& q)
     requires (!floating_point_<rep>) &&
              requires(rep a, rep b) { { a %= b } -> std::same_as<rep&>; }
diff --git a/src/include/units/quantity_kind.h b/src/include/units/quantity_kind.h
index e8ec9fb5..2e40d978 100644
--- a/src/include/units/quantity_kind.h
+++ b/src/include/units/quantity_kind.h
@@ -53,6 +53,15 @@ inline constexpr auto& downcasted_kind = downcasted_kind_fn<typename QK::kind_ty
 
 }  // namespace detail
 
+/**
+ * @brief A concept matching two related quantity kinds
+ *
+ * Satisfied by quantity kinds having equivalent base kinds.
+ */
+template<typename QK1, typename QK2>
+concept QuantityKindRelatedTo = QuantityKind<QK1> && QuantityKind<QK2> &&
+  equivalent<typename QK1::kind_type::base_kind, typename QK2::kind_type::base_kind>;
+
 /**
  * @brief A quantity kind
  *
@@ -180,6 +189,13 @@ public:
     q_ *= rhs;
     return *this;
   }
+  template<typename Rep2>
+  constexpr quantity_kind& operator*=(const quantity_kind<downcast_kind<K, dim_one>, units::one, Rep2>& rhs)
+    requires requires(quantity_type q) { q *= rhs.common(); }
+  {
+    q_ *= rhs.common();
+    return *this;
+  }
 
   template<typename Rep2>
   constexpr quantity_kind& operator/=(const Rep2& rhs)
@@ -189,15 +205,29 @@ public:
     q_ /= rhs;
     return *this;
   }
+  template<typename Rep2>
+  constexpr quantity_kind& operator/=(const quantity_kind<downcast_kind<K, dim_one>, units::one, Rep2>& rhs)
+    requires requires(quantity_type q) { q /= rhs.common(); }
+  {
+    q_ /= rhs.common();
+    return *this;
+  }
 
   template<typename Rep2>
   constexpr quantity_kind& operator%=(const Rep2& rhs)
-    requires (!Quantity<Rep2>) && requires(quantity_type q, const Rep2 r) { q %= r; }
+    requires (!Quantity<Rep2> || Dimensionless<Rep2>) && requires(quantity_type q, const Rep2 r) { q %= r; }
   {
     gsl_ExpectsAudit(rhs != quantity_values<Rep2>::zero());
     q_ %= rhs;
     return *this;
   }
+  template<typename Rep2>
+  constexpr quantity_kind& operator%=(const quantity_kind<downcast_kind<K, dim_one>, units::one, Rep2>& rhs)
+    requires requires(quantity_type q) { q %= rhs.common(); }
+  {
+    q_ %= rhs.common();
+    return *this;
+  }
 
   constexpr quantity_kind& operator%=(const quantity_kind& qk)
     requires requires(quantity_type q) { q %= qk.common(); }
@@ -256,9 +286,6 @@ public:
   [[nodiscard]] friend constexpr bool operator==(const quantity_kind&, const quantity_kind&) = default;
 };
 
-template<Kind K, QuantityValue V>
-explicit(false) quantity_kind(K, V) -> quantity_kind<K, one, V>;
-
 template<QuantityKind QK1, QuantityKindEquivalentTo<QK1> QK2>
 [[nodiscard]] constexpr QuantityKind auto operator+(const QK1& lhs, const QK2& rhs)
   requires requires { lhs.common() + rhs.common(); }
@@ -287,6 +314,13 @@ template<Quantity Q, QuantityKind QK>
   return detail::downcasted_kind<QK>(lhs * rhs.common());
 }
 
+template<QuantityKind QK1, QuantityKindRelatedTo<QK1> QK2>
+[[nodiscard]] constexpr QuantityKind auto operator*(const QK1& lhs, const QK2& rhs)
+  requires requires { lhs.common() * rhs.common(); }
+{
+  return detail::downcasted_kind<QK1>(lhs.common() * rhs.common());
+}
+
 template<QuantityKind QK, Quantity Q>
 [[nodiscard]] constexpr QuantityKind auto operator/(const QK& lhs, const Q& rhs)
   requires requires { lhs.common() / rhs; }
@@ -303,6 +337,13 @@ template<Quantity Q, QuantityKind QK>
   return detail::downcasted_kind<QK>(lhs / rhs.common());
 }
 
+template<QuantityKind QK1, QuantityKindRelatedTo<QK1> QK2>
+[[nodiscard]] constexpr QuantityKind auto operator/(const QK1& lhs, const QK2& rhs)
+  requires requires { lhs.common() / rhs.common(); }
+{
+  return detail::downcasted_kind<QK1>(lhs.common() / rhs.common());
+}
+
 template<QuantityKind QK, Dimensionless D>
 [[nodiscard]] constexpr QuantityKind auto operator%(const QK& lhs, const D& rhs)
   requires requires { lhs.common() % rhs; }
diff --git a/src/include/units/quantity_point_kind.h b/src/include/units/quantity_point_kind.h
index 94847c7e..0503bba1 100644
--- a/src/include/units/quantity_point_kind.h
+++ b/src/include/units/quantity_point_kind.h
@@ -182,9 +182,6 @@ public:
 
 };
 
-template<PointKind PK, QuantityValue V>
-explicit(false) quantity_point_kind(PK, V) -> quantity_point_kind<PK, one, V>;
-
 template<QuantityKind QK>
 quantity_point_kind(QK) ->
   quantity_point_kind<downcast_point_kind<typename QK::kind_type>, typename QK::unit, typename QK::rep>;
diff --git a/test/unit_test/static/quantity_kind_test.cpp b/test/unit_test/static/quantity_kind_test.cpp
index 301e687d..b10b7e8a 100644
--- a/test/unit_test/static/quantity_kind_test.cpp
+++ b/test/unit_test/static/quantity_kind_test.cpp
@@ -309,6 +309,7 @@ static_assert(construct_from_only<width<cgs::centimetre, double>>(1.0 * cm).comm
 static_assert(construct_and_convert_from<width<metre, int>>(width<metre, int>(1 * m)).common() == 1 * m);
 static_assert(construct_and_convert_from<width<centimetre, int>>(width<cgs::centimetre, int>(1 * cgs_cm)).common() == 1 * cm);
 static_assert(construct_and_convert_from<width<fps::foot, double>>(width<cgs::centimetre, int>(1 * cgs_cm)).common() == 1 * cm);
+// clang-format on
 
 static_assert(construct_and_convert_from<width<metre, double>>(width<metre, int>(1 * m)).common() == 1 * m);
 static_assert(!constructible_or_convertible_from<width<metre, int>>(width<metre, double>(1.0 * m)));
@@ -322,7 +323,6 @@ static_assert(construct_and_convert_from<width<kilometre, double>>(width<metre,
 static_assert(!constructible_or_convertible_from<width<metre, int>>(height<metre, int>(1 * m)));
 static_assert(!constructible_or_convertible_from<apples<one, int>>(width<metre, int>(1 * m) / m));
 static_assert(!constructible_or_convertible_from<apples<one, int>>(oranges<one, int>(1)));
-// clang-format on
 
 
 //////////////////////////////////
@@ -380,23 +380,42 @@ static_assert([]() {
   assert(&(w -= w) == &w && w.common() == 0 * m);
   w = width<metre, int>(3 * m);
   assert(&(w *= 3) == &w && w.common() == 9 * m);
+  assert(&(w *= quantity(1)) == &w && w.common() == 9 * m);
+  assert(&(w *= (w / w)) == &w && w.common() == 9 * m);
   assert(&(w /= 2) == &w && w.common() == 4 * m);
+  assert(&(w /= quantity(1)) == &w && w.common() == 4 * m);
+  assert(&(w /= (w / w)) == &w && w.common() == 4 * m);
   assert(&(w %= 3) == &w && w.common() == 1 * m);
+  assert(&(w %= quantity(3)) == &w && w.common() == 1 * m);
+  assert(&(w %= 3 * (w / w)) == &w && w.common() == 1 * m);
   assert(&(w %= w) == &w && w.common() == 0 * m);
   w = width<metre, int>(3 * m);
   assert(&(w *= 3.9) == &w && w.common() == 11 * m);
+  assert(&(w *= quantity(1.0)) == &w && w.common() == 11 * m);
+  assert(&(w *= 1.0 * (w / w)) == &w && w.common() == 11 * m);
   assert(&(w /= 3.9) == &w && w.common() == 2 * m);
+  assert(&(w /= quantity(1.0)) == &w && w.common() == 2 * m);
+  assert(&(w /= 1.0 * (w / w)) == &w && w.common() == 2 * m);
   return true;
 }());
 #endif
 
 static_assert((std::uint8_t(255) * m %= 256) == (width<metre, std::uint8_t>(255 * m) %= 256).common());
+static_assert((std::uint8_t(255) * m %= quantity(256)) ==
+              (width<metre, std::uint8_t>(255 * m) %= quantity(256)).common());
+// static_assert((std::uint8_t(255) * m %= 256 * m) ==
+//               (width<metre, std::uint8_t>(255 * m) %=
+//                 quantity_kind<downcast_kind<width_kind, dim_one>, one, std::uint8_t>(256)).common());  // UB
 // static_assert((std::uint8_t(255) * m %= 256 * m) !=
-//   (width<metre, std::uint8_t>(255 * m) %= width<metre, std::uint8_t>(256 * m)).common());  // UB
+//               (width<metre, std::uint8_t>(255 * m) %= width<metre, std::uint8_t>(256 * m)).common());  // UB
 static_assert((std::uint8_t(255) * m %= 257) == (width<metre, std::uint8_t>(255 * m) %= 257).common());
-// TODO: Fix
+static_assert((std::uint8_t(255) * m %= quantity(257)) ==
+              (width<metre, std::uint8_t>(255 * m) %= quantity(257)).common());
 static_assert((std::uint8_t(255) * m %= 257 * m) ==
-  (width<metre, std::uint8_t>(255 * m) %= width<metre, std::uint8_t>(257 * m)).common());
+              (width<metre, std::uint8_t>(255 * m) %=
+                quantity_kind<downcast_kind<width_kind, dim_one>, one, std::uint8_t>(257)).common());
+static_assert((std::uint8_t(255) * m %= 257 * m) ==
+              (width<metre, std::uint8_t>(255 * m) %= width<metre, std::uint8_t>(257 * m)).common());
 
 static_assert(same((-width<metre, short>(short{1} * m)).common(), int{-1} * m));
 
@@ -409,11 +428,20 @@ concept invalid_compound_assignments_ = requires(quantity_kind<K, U, int> w, Qx
   requires !requires { w %= q; };
 };
 template<typename Width>
-concept invalid_compound_assignments = requires(quantity_kind<Width, metre, int> w) {
+concept invalid_compound_assignments = requires(quantity_kind<Width, metre, int> w, height<metre, int> h) {
   requires !requires { w += 1; };
   requires !requires { w -= 1; };
+  requires !requires { w *= 1 * km / m; };
+  requires !requires { w /= 1 * km / m; };
+  requires !requires { w %= 1 * km / m; };
+  requires !requires { w *= quantity_kind<downcast_kind<Width, dim_one>, scaled_unit<ratio{1, 1, 3}, one>, int>{1}; };
+  requires !requires { w /= quantity_kind<downcast_kind<Width, dim_one>, scaled_unit<ratio{1, 1, 3}, one>, int>{1}; };
+  requires !requires { w %= quantity_kind<downcast_kind<Width, dim_one>, scaled_unit<ratio{1, 1, 3}, one>, int>{1}; };
   requires !requires { w %= 1.0; };
-  requires !requires { w %= w * 1.0; };
+  requires !requires { w %= quantity(1.0); };
+  requires !requires { w %= 1.0 * (w / w); };
+  requires !requires { w %= 1.0 * w; };
+  requires !requires { w %= h / h; };
   requires invalid_compound_assignments_<Width, metre, length<metre, int>>;
   requires invalid_compound_assignments_<Width, metre, height<metre, int>>;
   requires invalid_compound_assignments_<Width, metre, horizontal_area<square_metre, int>>;
@@ -477,6 +505,26 @@ static_assert(same(2 * width<metre, int>(3 * m), width<metre, int>(6 * m)));
 static_assert(same(2 * width<metre, double>(3. * m), width<metre, double>(6. * m)));
 static_assert(same(2. * width<metre, int>(3 * m), width<metre, double>(6. * m)));
 
+static_assert(same(width<metre, int>(2 * m) * quantity(3), width<metre, int>(6 * m)));
+static_assert(same(width<metre, int>(2 * m) * quantity(3.), width<metre, double>(6. * m)));
+static_assert(same(width<metre, double>(2. * m) * quantity(3), width<metre, double>(6. * m)));
+static_assert(same(quantity(2) * width<metre, int>(3 * m), width<metre, int>(6 * m)));
+static_assert(same(quantity(2) * width<metre, double>(3. * m), width<metre, double>(6. * m)));
+static_assert(same(quantity(2.) * width<metre, int>(3 * m), width<metre, double>(6. * m)));
+
+static_assert(same(width<metre, int>(2 * m) * quantity_kind<downcast_kind<width_kind, dim_one>, one, int>(3),
+                   width<metre, int>(6 * m)));
+static_assert(same(width<metre, int>(2 * m) * quantity_kind<downcast_kind<width_kind, dim_one>, one, double>(3.),
+                   width<metre, double>(6. * m)));
+static_assert(same(width<metre, double>(2. * m) * quantity_kind<downcast_kind<width_kind, dim_one>, one, int>(3),
+                   width<metre, double>(6. * m)));
+static_assert(same(quantity_kind<downcast_kind<width_kind, dim_one>, one, int>(2) * width<metre, int>(3 * m),
+                   width<metre, int>(6 * m)));
+static_assert(same(quantity_kind<downcast_kind<width_kind, dim_one>, one, int>(2) * width<metre, double>(3. * m),
+                   width<metre, double>(6. * m)));
+static_assert(same(quantity_kind<downcast_kind<width_kind, dim_one>, one, double>(2.) * width<metre, int>(3 * m),
+                   width<metre, double>(6. * m)));
+
 static_assert(same(height<metre, int>(2 * m) * (3 * Hz), rate_of_climb<metre_per_second, int>(6 * m / s)));
 static_assert(same(height<metre, int>(2 * m) * (3. * Hz), rate_of_climb<metre_per_second, double>(6. * m / s)));
 static_assert(same(height<metre, double>(2. * m) * (3 * Hz), rate_of_climb<metre_per_second, double>(6. * m / s)));
@@ -484,13 +532,65 @@ static_assert(same((2 * Hz) * height<metre, int>(3 * m), rate_of_climb<metre_per
 static_assert(same((2 * Hz) * height<metre, double>(3. * m), rate_of_climb<metre_per_second, double>(6. * m / s)));
 static_assert(same((2. * Hz) * height<metre, int>(3 * m), rate_of_climb<metre_per_second, double>(6. * m / s)));
 
+static_assert(same(quantity_kind<time_kind, second, int>(2 * s) * (3 * Hz),
+                   quantity_kind<downcast_kind<time_kind, dim_one>, one, int>(6)));
+static_assert(same((3 * Hz) * quantity_kind<time_kind, second, int>(2 * s),
+                   quantity_kind<downcast_kind<time_kind, dim_one>, one, int>(6)));
+
+static_assert(same(apples<one, int>(2) * quantity(2), apples<one, int>(4)));
+static_assert(same(quantity(2) * apples<one, int>(2), apples<one, int>(4)));
+
+// clang-format off
+static_assert(same(width<metre, int>(2 * m) * width<metre, int>(2 * m), horizontal_area<square_metre, int>(4 * m * m)));
+static_assert(same(width<metre, int>(2 * m) * width<metre, double>(2 * m), horizontal_area<square_metre, double>(4 * m * m)));
+static_assert(same(width<metre, double>(2 * m) * width<metre, int>(2 * m), horizontal_area<square_metre, double>(4 * m * m)));
+// clang-format on
+
+static_assert(same(apples<one, int>(2) * apples<one, int>(2), apples<one, int>(4)));
+static_assert(same(apples<one, int>(2) * (2 / apples<one, int>(1)), apples<one, int>(4)));
+
+static_assert(same(width<kilometre>(2 * m) * width<millimetre>(2 * m), horizontal_area<square_metre>(4 * m * m)));
+static_assert(same(width<metre>(2 * m) * (1 / width<metre>(2 * m)),
+                   quantity_kind<downcast_kind<width_kind, dim_one>, one>(1)));
+
 static_assert(same(width<metre, int>(2 * m) / 3, width<metre, int>(0 * m)));
 static_assert(same(width<metre, int>(2 * m) / 3., width<metre, double>(2 / 3. * m)));
 static_assert(same(width<metre, double>(2. * m) / 3, width<metre, double>(2. / 3 * m)));
 
-static_assert(same((2 / width<metre, int>(3 * m)).common(), 2 / 3 / m));
-static_assert(same((2 / width<metre, double>(3. * m)).common(), 2 / 3. / m));
-static_assert(same((2. / width<metre, int>(3 * m)).common(), 2. / 3 / m));
+static_assert(same(width<metre, int>(2 * m) / quantity(3), width<metre, int>(0 * m)));
+static_assert(same(width<metre, int>(2 * m) / quantity(3.), width<metre, double>(2 / 3. * m)));
+static_assert(same(width<metre, double>(2. * m) / quantity(3), width<metre, double>(2. / 3 * m)));
+
+static_assert(same(width<metre, int>(2 * m) / quantity_kind<downcast_kind<width_kind, dim_one>, one, int>(3),
+                   width<metre, int>(0 * m)));
+static_assert(same(width<metre, int>(2 * m) / quantity_kind<downcast_kind<width_kind, dim_one>, one, double>(3.),
+                   width<metre, double>(2 / 3. * m)));
+static_assert(same(width<metre, double>(2. * m) / quantity_kind<downcast_kind<width_kind, dim_one>, one, double>(3),
+                   width<metre, double>(2. / 3 * m)));
+
+static_assert(same(2 / quantity_kind<time_kind, second, int>(3 * s),
+                   quantity_kind<downcast_kind<time_kind, dim_frequency>, hertz, int>(2 / 3 / s)));
+static_assert(same(2 / quantity_kind<time_kind, second, double>(3. * s),
+                   quantity_kind<downcast_kind<time_kind, dim_frequency>, hertz, double>(2 / 3. / s)));
+static_assert(same(2. / quantity_kind<time_kind, second, int>(3 * s),
+                   quantity_kind<downcast_kind<time_kind, dim_frequency>, hertz, double>(2 / 3. / s)));
+
+static_assert(same(quantity(2) / quantity_kind<time_kind, second, int>(3 * s),
+                   quantity_kind<downcast_kind<time_kind, dim_frequency>, hertz, int>(2 / 3 / s)));
+static_assert(same(quantity(2) / quantity_kind<time_kind, second, double>(3. * s),
+                   quantity_kind<downcast_kind<time_kind, dim_frequency>, hertz, double>(2 / 3. / s)));
+static_assert(same(quantity(2.) / quantity_kind<time_kind, second, int>(3 * s),
+                   quantity_kind<downcast_kind<time_kind, dim_frequency>, hertz, double>(2 / 3. / s)));
+
+static_assert(
+  same(quantity_kind<downcast_kind<time_kind, dim_one>, one, int>(2) / quantity_kind<time_kind, second, int>(3 * s),
+       quantity_kind<downcast_kind<time_kind, dim_frequency>, hertz, int>(2 / 3 / s)));
+static_assert(
+  same(quantity_kind<downcast_kind<time_kind, dim_one>, one, int>(2) / quantity_kind<time_kind, second, double>(3. * s),
+       quantity_kind<downcast_kind<time_kind, dim_frequency>, hertz, double>(2 / 3. / s)));
+static_assert(
+  same(quantity_kind<downcast_kind<time_kind, dim_one>, one, double>(2.) / quantity_kind<time_kind, second, int>(3 * s),
+       quantity_kind<downcast_kind<time_kind, dim_frequency>, hertz, double>(2 / 3. / s)));
 
 static_assert(same(height<metre, int>(2 * m) / (3 * s), rate_of_climb<metre_per_second, int>(0 * m / s)));
 static_assert(same(height<metre, int>(2 * m) / (3. * s), rate_of_climb<metre_per_second, double>(2 / 3. * m / s)));
@@ -501,11 +601,31 @@ static_assert(same(dimensionless<percent, int>(2) * width<metre, int>(3 * m), wi
 static_assert(same(width<metre, int>(2 * m) / dimensionless<percent, double>(3), width<hectometre, double>(2. / 3 * hm)));
 static_assert(same(width<metre, int>(2 * m) % dimensionless<percent, int>(3), width<centimetre, int>(2 * cm)));
 
-static_assert(same(((2 * m) / height<metre, int>(3 * m)), quantity_kind<downcast_kind<height_kind, dim_one>, one, int>(0)));
-static_assert(same(((2 * m) / height<metre, int>(3 * m)).common(), quantity(0)));
-static_assert(same(((2 * m) / height<metre, double>(3. * m)).common(), quantity(2 / 3.)));
-static_assert(same(((2. * m) / height<metre, int>(3 * m)).common(), quantity(2. / 3)));
-static_assert(same(((2 * m) / height<metre, int>(3 * m) * (0 * m)), height<metre, int>(0 * m)));
+static_assert(same(height<metre, int>(2 * m) / (3 * m),
+                   quantity_kind<downcast_kind<height_kind, dim_one>, one, int>(0)));
+static_assert(same(height<metre, int>(2 * m) / (3. * m),
+                   quantity_kind<downcast_kind<height_kind, dim_one>, one, double>(2 / 3.)));
+static_assert(same(height<metre, double>(2. * m) / (3 * m),
+                   quantity_kind<downcast_kind<height_kind, dim_one>, one, double>(2. / 3)));
+
+static_assert(same((2 * m) / height<metre, int>(3 * m),
+                   quantity_kind<downcast_kind<height_kind, dim_one>, one, int>(0)));
+static_assert(same((2 * m) / height<metre, double>(3. * m),
+                   quantity_kind<downcast_kind<height_kind, dim_one>, one, double>(2 / 3.)));
+static_assert(same((2. * m) / height<metre, int>(3 * m),
+                   quantity_kind<downcast_kind<height_kind, dim_one>, one, double>(2. / 3)));
+
+static_assert(same(width<metre, int>(8 * m) / width<metre, int>(2 * m),
+                   quantity_kind<downcast_kind<width_kind, dim_one>, one, int>(4)));
+static_assert(same(width<metre, int>(8 * m) / width<metre, double>(2 * m),
+                   quantity_kind<downcast_kind<width_kind, dim_one>, one, double>(4.0)));
+static_assert(same(width<metre, double>(8 * m) / width<metre, int>(2 * m),
+                   quantity_kind<downcast_kind<width_kind, dim_one>, one, double>(4.0)));
+
+static_assert(same(apples<one, int>(8) / apples<one, int>(2), apples<one, int>(4)));
+static_assert(same(apples<one, int>(8) / (2 / apples<one, int>(1)), apples<one, int>(4)));
+
+static_assert(same(horizontal_area<square_metre>(8 * m * m) / width<metre>(2 * m), width<metre>(4 * m)));
 
 static_assert(same(width<metre, int>(2 * m) % 3, width<metre, int>(2 * m)));
 static_assert(same(width<metre, int>(3 * m) % width<metre, int>(2 * m), width<metre, int>(1 * m)));
@@ -514,7 +634,6 @@ static_assert(is_same_v<
   decltype((width<metre, std::uint8_t>(0 * m) % width<metre, std::uint8_t>(0 * m)).common().count()),
   decltype(std::uint8_t(0) % std::uint8_t(0))>);
 
-static_assert(!std::is_invocable_v<std::multiplies<>, width<metre>, width<metre>>);
 static_assert(!std::is_invocable_v<std::multiplies<>, width<metre>, height<metre>>);
 static_assert(!std::is_invocable_v<std::multiplies<>, height<metre>, quantity_point<dim_length, metre>>);
 static_assert(!std::is_invocable_v<std::multiplies<>, quantity_point<dim_length, metre>, height<metre>>);
diff --git a/test/unit_test/static/quantity_point_kind_test.cpp b/test/unit_test/static/quantity_point_kind_test.cpp
index b5eba3d0..13e83165 100644
--- a/test/unit_test/static/quantity_point_kind_test.cpp
+++ b/test/unit_test/static/quantity_point_kind_test.cpp
@@ -336,7 +336,6 @@ static_assert(!constructible_or_convertible_from<nth_apple<percent, int>>(apples
 static_assert(!constructible_or_convertible_from<nth_apple<percent, int>>(apples<percent, double>(dimensionless<percent>(1))));
 static_assert(!constructible_or_convertible_from<nth_apple<one, int>>(apples<one, double>(1.0)));
 static_assert(!constructible_or_convertible_from<nth_apple<one, int>>(apples<percent, double>(dimensionless<percent>(1))));
-static_assert(!constructible_or_convertible_from<nth_apple<one, int>>(width<metre, int>(1 * m) / m));
 static_assert(!constructible_or_convertible_from<nth_apple<one, int>>(oranges<one, int>(1)));
 // clang-format on
 
diff --git a/test/unit_test/static/quantity_test.cpp b/test/unit_test/static/quantity_test.cpp
index 9952dfa5..6d945ec8 100644
--- a/test/unit_test/static/quantity_test.cpp
+++ b/test/unit_test/static/quantity_test.cpp
@@ -278,9 +278,10 @@ static_assert((1_q_m += 1_q_m).count() == 2);
 static_assert((2_q_m -= 1_q_m).count() == 1);
 static_assert((1_q_m *= 2).count() == 2);
 static_assert((2_q_m /= 2).count() == 1);
+static_assert((7_q_m %= 2).count() == 1);
 static_assert((1_q_m *= quantity(2)).count() == 2);
 static_assert((2_q_m /= quantity(2)).count() == 1);
-static_assert((7_q_m %= 2).count() == 1);
+static_assert((7_q_m %= quantity(2)).count() == 1);
 static_assert((7_q_m %= 2_q_m).count() == 1);
 
 // different types
@@ -295,8 +296,10 @@ static_assert((7.5_q_m /= quantity(3)).count() == 2.5);
 static_assert((3500_q_m %= 1_q_km).count() == 500);
 
 static_assert((std::uint8_t(255) * m %= 256).count() == [] { std::uint8_t ui(255); return ui %= 256; }());
+static_assert((std::uint8_t(255) * m %= quantity(256)).count() == [] { std::uint8_t ui(255); return ui %= 256; }());
 // static_assert((std::uint8_t(255) * m %= 256 * m).count() != [] { std::uint8_t ui(255); return ui %= 256; }());  // UB
 static_assert((std::uint8_t(255) * m %= 257).count() == [] { std::uint8_t ui(255); return ui %= 257; }());
+static_assert((std::uint8_t(255) * m %= quantity(257)).count() == [] { std::uint8_t ui(255); return ui %= 257; }());
 // TODO: Fix
 static_assert((std::uint8_t(255) * m %= 257 * m).count() != [] { std::uint8_t ui(255); return ui %= 257; }());
 
@@ -309,14 +312,21 @@ static_assert((22_q_m *= quantity(33.33)).count() == 733);
 static_assert((22_q_m /= quantity(3.33)).count() == 6);
 #endif
 
-template<typename Metre>
+template<typename Metre, typename Kilometre>
 concept invalid_compound_assignments = requires() {
   // truncating not allowed
   requires !requires(length<Metre, int> l) { l += 2.5_q_m; };
   requires !requires(length<Metre, int> l) { l -= 2.5_q_m; };
-  requires !requires(length<kilometre, int> l) { l += length<Metre, int>(2); };
-  requires !requires(length<kilometre, int> l) { l -= length<Metre, int>(2); };
-  requires !requires(length<kilometre, int> l) { l %= length<Metre, int>(2); };
+  requires !requires(length<Kilometre, int> l) { l += length<Metre, int>(2); };
+  requires !requires(length<Kilometre, int> l) { l -= length<Metre, int>(2); };
+  requires !requires(length<Kilometre, int> l) { l %= length<Metre, int>(2); };
+  requires !requires(length<Kilometre, int> l) { l %= dimensionless<percent, int>(2); };
+  requires !requires(length<Kilometre, int> l) { l %= dimensionless<percent, double>(2); };
+
+  // TODO: accept non-truncating argument
+  requires !requires(length<Kilometre, int> l) { l *= 1 * km / m; };
+  requires !requires(length<Kilometre, int> l) { l /= 1 * km / m; };
+  requires !requires(length<Kilometre, int> l) { l %= 1 * km / m; };
 
   // only quantities can be added or subtracted
   requires !requires(length<Metre, int> l) { l += 2; };
@@ -333,7 +343,7 @@ concept invalid_compound_assignments = requires() {
   requires !requires(length<Metre, double> l) { l %= 2_q_m; };
   requires !requires(length<Metre, int> l) { l %= 2._q_m; };
 };
-static_assert(invalid_compound_assignments<metre>);
+static_assert(invalid_compound_assignments<metre, kilometre>);
 
 
 ////////////////////