diff --git a/example/kalman_filter/kalman.h b/example/kalman_filter/kalman.h
index 4d844b36..09867fa2 100644
--- a/example/kalman_filter/kalman.h
+++ b/example/kalman_filter/kalman.h
@@ -124,7 +124,7 @@ constexpr state<Q1, Q2, Q3> state_update(const state<Q1, Q2, Q3>& predicted, QM
 template<mp_units::Quantity Q, mp_units::QuantityOf<mp_units::dimensionless> K>
 constexpr Q covariance_update(Q uncertainty, K gain)
 {
-  return (1 - gain) * uncertainty;
+  return (1 * mp_units::one - gain) * uncertainty;
 }
 
 // state extrapolation
diff --git a/example/storage_tank.cpp b/example/storage_tank.cpp
index 4dccdcd6..ec74e3e4 100644
--- a/example/storage_tank.cpp
+++ b/example/storage_tank.cpp
@@ -121,7 +121,7 @@ int main()
 
   const QuantityOf<isq::mass_change_rate> auto input_flow_rate = measured_mass / fill_time;
   const QuantityOf<isq::speed> auto float_rise_rate = fill_level / fill_time;
-  const QuantityOf<isq::time> auto fill_time_left = (height / fill_level - 1) * fill_time;
+  const QuantityOf<isq::time> auto fill_time_left = (height / fill_level - 1 * one) * fill_time;
 
   const auto fill_ratio = fill_level / height;
 
diff --git a/src/core/include/mp-units/quantity.h b/src/core/include/mp-units/quantity.h
index 850cf624..3d3642b3 100644
--- a/src/core/include/mp-units/quantity.h
+++ b/src/core/include/mp-units/quantity.h
@@ -147,13 +147,6 @@ public:
   {
   }
 
-  template<typename Value>
-    requires(dimension == dimension_one) &&
-            (unit == ::mp_units::one) && detail::RepSafeConstructibleFrom<rep, Value&&, unit>
-  constexpr explicit(!std::convertible_to<Value, Rep>) quantity(Value&& v) : number_(std::forward<Value>(v))
-  {
-  }
-
   quantity& operator=(const quantity&) = default;
   quantity& operator=(quantity&&) = default;
 
@@ -433,65 +426,6 @@ template<auto R1, typename Rep1, auto R2, typename Rep2>
   return ct(lhs).number() <=> ct(rhs).number();
 }
 
-// binary operators on dimensionless quantities
-template<auto R, typename Rep, typename Value>
-  requires(!Quantity<Value>) && (quantity<R, Rep>::dimension == dimension_one) &&
-          detail::InvokeResultOf<get_quantity_spec(R).character, std::plus<>, Rep, Value>
-[[nodiscard]] constexpr Quantity auto operator+(const quantity<R, Rep>& q, const Value& v)
-{
-  return q + make_quantity<::mp_units::one>(v);
-}
-
-template<typename Value, auto R, typename Rep>
-  requires(!Quantity<Value>) && (quantity<R, Rep>::dimension == dimension_one) &&
-          detail::InvokeResultOf<get_quantity_spec(R).character, std::plus<>, Value, Rep>
-[[nodiscard]] constexpr Quantity auto operator+(const Value& v, const quantity<R, Rep>& q)
-{
-  return make_quantity<::mp_units::one>(v) + q;
-}
-
-template<auto R, typename Rep, typename Value>
-  requires(!Quantity<Value>) && (quantity<R, Rep>::dimension == dimension_one) &&
-          detail::InvokeResultOf<get_quantity_spec(R).character, std::minus<>, Rep, Value>
-[[nodiscard]] constexpr Quantity auto operator-(const quantity<R, Rep>& q, const Value& v)
-{
-  return q - make_quantity<::mp_units::one>(v);
-}
-
-template<typename Value, auto R, typename Rep>
-  requires(!Quantity<Value>) && (quantity<R, Rep>::dimension == dimension_one) &&
-          detail::InvokeResultOf<get_quantity_spec(R).character, std::minus<>, Value, Rep>
-[[nodiscard]] constexpr Quantity auto operator-(const Value& v, const quantity<R, Rep>& q)
-{
-  return make_quantity<::mp_units::one>(v) - q;
-}
-
-template<typename Value, auto R, typename Rep>
-  requires(!Quantity<Value>) && (quantity<R, Rep>::dimension == dimension_one) && (get_unit(R) == ::mp_units::one) &&
-          (!treat_as_floating_point<Value>) && (!treat_as_floating_point<Rep>) &&
-          detail::InvokeResultOf<get_quantity_spec(R).character, std::modulus<>, Value, Rep>
-[[nodiscard]] constexpr Quantity auto operator%(const Value& v, const quantity<R, Rep>& q)
-{
-  gsl_ExpectsAudit(q.number() != quantity_values<Rep>::zero());
-  return make_quantity<R>(v % q.number());
-}
-
-template<auto R, typename Rep, typename Value>
-  requires(!Quantity<Value>) &&
-          (quantity<R, Rep>::dimension == dimension_one) && std::equality_comparable_with<Rep, Value>
-[[nodiscard]] constexpr bool operator==(const quantity<R, Rep>& q, const Value& v)
-{
-  return q == make_quantity<::mp_units::one>(v);
-}
-
-template<auto R, typename Rep, typename Value>
-  requires(!Quantity<Value>) &&
-          (quantity<R, Rep>::dimension == dimension_one) && std::three_way_comparable_with<Rep, Value>
-[[nodiscard]] constexpr auto operator<=>(const quantity<R, Rep>& q, const Value& v)
-{
-  return q <=> make_quantity<::mp_units::one>(v);
-}
-
 // make_quantity
 template<Reference auto R, typename Rep>
   requires quantity<R, std::remove_cvref_t<Rep>>::_rep_safe_constructible_
diff --git a/test/unit_test/runtime/math_test.cpp b/test/unit_test/runtime/math_test.cpp
index 12d2c209..dbaf0907 100644
--- a/test/unit_test/runtime/math_test.cpp
+++ b/test/unit_test/runtime/math_test.cpp
@@ -37,7 +37,7 @@ using namespace mp_units::si::unit_symbols;
 
 TEST_CASE("'pow<N>()' on quantity changes the value and the dimension accordingly", "[math][pow]")
 {
-  SECTION("'pow<0>(q)' returns '1'") { CHECK(pow<0>(2 * isq::length[m]) == 1); }
+  SECTION("'pow<0>(q)' returns '1'") { CHECK(pow<0>(2 * isq::length[m]) == 1 * one); }
 
   SECTION("'pow<1>(q)' returns 'q'") { CHECK(pow<1>(2 * isq::length[m]) == 2 * isq::length[m]); }
 
diff --git a/test/unit_test/static/custom_rep_test_min_impl.cpp b/test/unit_test/static/custom_rep_test_min_impl.cpp
index 1f140b39..eabd54e5 100644
--- a/test/unit_test/static/custom_rep_test_min_impl.cpp
+++ b/test/unit_test/static/custom_rep_test_min_impl.cpp
@@ -80,45 +80,6 @@ concept creates_quantity = Unit<std::remove_cvref_t<decltype(U)>> && requires {
 static_assert(creates_quantity<min_impl<int>, si::metre>);
 static_assert(creates_quantity<min_impl<double>, si::metre>);
 
-// dimensionless quantity is constructible and convertible from a value
-static_assert(std::constructible_from<quantity<one, min_impl<int>>, min_impl<int>>);
-static_assert(std::convertible_to<min_impl<int>, quantity<one, min_impl<int>>>);
-
-static_assert(std::constructible_from<quantity<one, min_impl<double>>, min_impl<double>>);
-static_assert(std::convertible_to<min_impl<double>, quantity<one, min_impl<double>>>);
-
-static_assert(std::constructible_from<quantity<one, min_impl<double>>, min_impl<int>>);
-static_assert(std::convertible_to<min_impl<int>, quantity<one, min_impl<double>>>);
-
-static_assert(!std::constructible_from<quantity<one, min_impl<int>>, min_impl<double>>);  // narrowing conversion
-static_assert(!std::convertible_to<min_impl<double>, quantity<one, min_impl<int>>>);
-
-// and underlying type
-static_assert(std::constructible_from<quantity<one, min_impl<int>>, int>);
-static_assert(std::convertible_to<int, quantity<one, min_impl<int>>>);
-
-static_assert(std::constructible_from<quantity<one, min_impl<double>>, double>);
-static_assert(std::convertible_to<double, quantity<one, min_impl<double>>>);
-
-static_assert(std::constructible_from<quantity<one, min_impl<double>>, int>);
-static_assert(std::convertible_to<int, quantity<one, min_impl<double>>>);
-
-static_assert(!std::constructible_from<quantity<one, min_impl<int>>, double>);  // narrowing conversion
-static_assert(!std::convertible_to<double, quantity<one, min_impl<int>>>);
-
-// but only for ratio(1)
-static_assert(!std::constructible_from<quantity<percent, min_impl<int>>, min_impl<int>>);
-static_assert(!std::convertible_to<min_impl<int>, quantity<percent, min_impl<int>>>);
-
-static_assert(!std::constructible_from<quantity<percent, min_impl<double>>, min_impl<double>>);
-static_assert(!std::convertible_to<min_impl<double>, quantity<percent, min_impl<double>>>);
-
-static_assert(!std::constructible_from<quantity<percent, min_impl<double>>, min_impl<int>>);
-static_assert(!std::convertible_to<min_impl<int>, quantity<percent, min_impl<double>>>);
-
-static_assert(!std::constructible_from<quantity<percent, min_impl<int>>, min_impl<double>>);  // narrowing conversion
-static_assert(!std::convertible_to<min_impl<double>, quantity<percent, min_impl<int>>>);
-
 // multiply syntax
 static_assert(creates_quantity<min_impl<int>, one>);
 static_assert(creates_quantity<min_impl<double>, one>);
@@ -258,9 +219,9 @@ static_assert(min_impl<int>{123} * si::metre / (min_impl<double>(2.) * one) == m
 static_assert(min_impl<int>{123} * si::metre / (2. * one) == min_impl<double>{61.5} * si::metre);
 static_assert(123 * si::metre / (min_impl<double>(2.) * one) == min_impl<double>{61.5} * si::metre);
 
-static_assert(min_impl<int>{123} * si::metre / (min_impl<double>{2.} * si::metre) == 61.5);
-static_assert(min_impl<int>{123} * si::metre / (double{2.} * si::metre) == 61.5);
-static_assert(123 * si::metre / (min_impl<double>{2.} * si::metre) == 61.5);
+static_assert(min_impl<int>{123} * si::metre / (min_impl<double>{2.} * si::metre) == 61.5 * one);
+static_assert(min_impl<int>{123} * si::metre / (double{2.} * si::metre) == 61.5 * one);
+static_assert(123 * si::metre / (min_impl<double>{2.} * si::metre) == 61.5 * one);
 
 static_assert(min_impl<int>{123} * si::metre % (min_impl<int>(100) * si::metre) == 23 * si::metre);
 static_assert(min_impl<int>{123} * si::metre % (100 * si::metre) == 23 * si::metre);
diff --git a/test/unit_test/static/quantity_test.cpp b/test/unit_test/static/quantity_test.cpp
index 5486b74c..a20f92e9 100644
--- a/test/unit_test/static/quantity_test.cpp
+++ b/test/unit_test/static/quantity_test.cpp
@@ -131,43 +131,11 @@ static_assert(!std::convertible_to<double, quantity<isq::length[m]>>);
 static_assert(!std::constructible_from<quantity<isq::length[m], int>, int>);
 static_assert(!std::convertible_to<int, quantity<isq::length[m], int>>);
 
-// exception, implicit construction from a value allowed for a dimensionless quantity
-static_assert(std::constructible_from<quantity<dimensionless[one]>, double>);
-static_assert(std::convertible_to<double, quantity<dimensionless[one]>>);
+static_assert(!std::constructible_from<quantity<dimensionless[one]>, double>);
+static_assert(!std::convertible_to<double, quantity<dimensionless[one]>>);
 
-static_assert(std::constructible_from<quantity<dimensionless[one]>, float>);
-static_assert(std::convertible_to<float, quantity<dimensionless[one]>>);
-
-static_assert(std::constructible_from<quantity<dimensionless[one], float>, double>);
-static_assert(std::convertible_to<double, quantity<dimensionless[one], float>>);
-
-static_assert(std::constructible_from<quantity<dimensionless[one]>, int>);
-static_assert(std::convertible_to<int, quantity<dimensionless[one]>>);
-
-static_assert(std::constructible_from<quantity<dimensionless[one]>, short>);
-static_assert(std::convertible_to<short, quantity<dimensionless[one]>>);
-
-static_assert(std::constructible_from<quantity<dimensionless[one], short>, int>);
-static_assert(std::convertible_to<int, quantity<dimensionless[one], short>>);
-
-// but only if a dimensionless quantity has a ratio(1)
-static_assert(!std::constructible_from<quantity<dimensionless[percent]>, double>);
-static_assert(!std::convertible_to<double, quantity<dimensionless[percent]>>);
-
-static_assert(!std::constructible_from<quantity<dimensionless[percent]>, float>);
-static_assert(!std::convertible_to<float, quantity<dimensionless[percent]>>);
-
-static_assert(!std::constructible_from<quantity<dimensionless[percent], float>, double>);
-static_assert(!std::convertible_to<double, quantity<dimensionless[percent], float>>);
-
-static_assert(!std::constructible_from<quantity<dimensionless[percent]>, int>);
-static_assert(!std::convertible_to<int, quantity<dimensionless[percent]>>);
-
-static_assert(!std::constructible_from<quantity<dimensionless[percent]>, short>);
-static_assert(!std::convertible_to<short, quantity<dimensionless[percent]>>);
-
-static_assert(!std::constructible_from<quantity<dimensionless[percent], short>, int>);
-static_assert(!std::convertible_to<int, quantity<dimensionless[percent], short>>);
+static_assert(!std::constructible_from<quantity<dimensionless[one]>, int>);
+static_assert(!std::convertible_to<int, quantity<dimensionless[one]>>);
 
 
 ///////////////////////////////////////
@@ -715,29 +683,20 @@ static_assert(1 * si::si2019::speed_of_light_in_vacuum + 10 * isq::speed[m / s]
 // Implicit conversions allowed between quantities of `convertible` references
 constexpr quantity<isq::speed[km / h]> speed = 120 * isq::length[km] / (2 * isq::time[h]);
 
-
 // dimensionless
-
-static_assert((3 * one *= 2 * one) == 6);
-static_assert((6 * one /= 2 * one) == 3);
-static_assert(1 * one + 1 * one == 2);
-static_assert(1 + 1 * one == 2);
-static_assert(1 * one + 1 == 2);
-static_assert(2 * one - 1 * one == 1);
-static_assert(2 - 1 * one == 1);
-static_assert(2 * one - 1 == 1);
-static_assert(2 * one * (2 * one) == 4);
-static_assert(2 * (2 * one) == 4);
-static_assert(2 * one * 2 == 4);
-static_assert(4 * one / (2 * one) == 2);
-static_assert(4 / (2 * one) == 2);
-static_assert(4 * one / 2 == 2);
-static_assert(4 * one % (2 * one) == 0);
-static_assert(4 % (2 * one) == 0);
-static_assert(4 % (2 * one) == 0);
+static_assert((3 * one *= 2 * one) == 6 * one);
+static_assert((6 * one /= 2 * one) == 3 * one);
+static_assert(1 * one + 1 * one == 2 * one);
+static_assert(2 * one - 1 * one == 1 * one);
+static_assert(2 * one * (2 * one) == 4 * one);
+static_assert(2 * (2 * one) == 4 * one);
+static_assert(2 * one * 2 == 4 * one);
+static_assert(4 * one / (2 * one) == 2 * one);
+static_assert(4 / (2 * one) == 2 * one);
+static_assert(4 * one / 2 == 2 * one);
+static_assert(4 * one % (2 * one) == 0 * one);
 
 // modulo arithmetics
-
 static_assert(5 * h % (120 * min) == 60 * min);
 static_assert(300 * min % (2 * h) == 60 * min);
 static_assert(300 * min % (120 * min) == 60 * min);
@@ -754,17 +713,13 @@ constexpr auto quotient_remainder_theorem(auto q1, auto q2)
 static_assert(quotient_remainder_theorem(7 * m, 3 * m) == 7 * m);
 static_assert(quotient_remainder_theorem(3'000 * m, 400 * m) == 3'000 * m);
 
-static_assert(is_same_v<decltype(0 * one + 0.0), decltype(0.0 * one)>);
-static_assert(is_same_v<decltype(0 * one - 0.0), decltype(0.0 * one)>);
-static_assert(is_same_v<decltype(0.0 + 0 * one), decltype(0.0 * one)>);
-static_assert(is_same_v<decltype(0.0 + 0 * one), decltype(0.0 * one)>);
-static_assert(1 * one + 2.3 == (1 + 2.3) * one);
-static_assert(1 * one - 2.3 == (1 - 2.3) * one);
-static_assert(1.2 + 3 * one == (1.2 + 3) * one);
-static_assert(1.2 - 3 * one == (1.2 - 3) * one);
+static_assert(is_same_v<decltype(0 * one + 0.0 * one), decltype(0.0 * one)>);
+static_assert(is_same_v<decltype(0 * one - 0.0 * one), decltype(0.0 * one)>);
+static_assert(is_same_v<decltype(0.0 * one + 0 * one), decltype(0.0 * one)>);
+static_assert(is_same_v<decltype(0.0 * one - 0 * one), decltype(0.0 * one)>);
 
-static_assert(1 - 30 * percent == (100 - 30) * percent);
-static_assert(1 + 30 * percent == (100 + 30) * percent);
+static_assert(1 * one - 30 * percent == (100 - 30) * percent);
+static_assert(1 * one + 30 * percent == (100 + 30) * percent);
 
 static_assert(is_same_v<decltype((std::uint8_t(0) * one + std::uint8_t(0) * one).number()), int&&>);
 static_assert(is_same_v<decltype((std::uint8_t(0) * one - std::uint8_t(0) * one).number()), int&&>);
@@ -821,17 +776,6 @@ static_assert(321 * km != 123'000 * m);
 static_assert(!(123 * km == 321'000 * m));
 static_assert(!(123 * km != 123'000 * m));
 
-// dimensionless
-static_assert(std::equality_comparable_with<quantity<dimensionless[one]>, double>);
-static_assert(std::equality_comparable_with<quantity<dimensionless[one]>, int>);
-static_assert(std::equality_comparable_with<quantity<dimensionless[one], int>, int>);
-static_assert(std::equality_comparable_with<quantity<dimensionless[one], int>, double>);
-
-static_assert(123 * one == 123);
-static_assert(321 * one != 123);
-static_assert(123 == 123 * one);
-static_assert(123 != 321 * one);
-
 // Named and derived dimensions (same units)
 static_assert(10 * isq::length[m] / (2 * isq::time[s]) == 5 * isq::speed[m / s]);
 static_assert(5 * isq::speed[m / s] == 10 * isq::length[m] / (2 * isq::time[s]));
@@ -908,21 +852,6 @@ static_assert(!(123 * km > 321'000 * m));
 static_assert(!(123 * km > 123'000 * m));
 static_assert(!(123 * km >= 321'000 * m));
 
-// dimensionless
-static_assert(123 * one < 321);
-static_assert(123 * one <= 123);
-static_assert(123 * one <= 321);
-static_assert(321 * one > 123);
-static_assert(123 * one >= 123);
-static_assert(321 * one >= 123);
-
-static_assert(123 < 321 * one);
-static_assert(123 <= 123 * one);
-static_assert(123 <= 321 * one);
-static_assert(321 > 123 * one);
-static_assert(123 >= 123 * one);
-static_assert(321 >= 123 * one);
-
 
 //////////////////
 // dimensionless
diff --git a/test/unit_test/static/reference_test.cpp b/test/unit_test/static/reference_test.cpp
index 923cfb5a..83e2cc60 100644
--- a/test/unit_test/static/reference_test.cpp
+++ b/test/unit_test/static/reference_test.cpp
@@ -285,60 +285,39 @@ static_assert(no_common_reference<radian, solid_angular_measure[steradian]>);
 static_assert(no_common_reference<angular_measure[radian], solid_angular_measure[steradian]>);
 
 // addition of various dimensionless quantities
-static_assert(is_of_type<1 * one + 1, quantity<one, int>>);
-static_assert(is_of_type<dimensionless(1 * one) + 1, quantity<dimensionless[one], int>>);
-
-static_assert(is_of_type<1 * radian + 1, quantity<radian, int>>);
 static_assert(is_of_type<1 * radian + 1 * one, quantity<radian, int>>);
 static_assert(is_of_type<1 * radian + dimensionless(1 * one), quantity<angular_measure[radian], int>>);
-static_assert(is_of_type<angular_measure(1 * radian) + 1, quantity<angular_measure[radian], int>>);
 static_assert(is_of_type<angular_measure(1 * radian) + 1 * one, quantity<angular_measure[radian], int>>);
 static_assert(is_of_type<angular_measure(1 * radian) + dimensionless(1 * one), quantity<angular_measure[radian], int>>);
 
-static_assert(is_of_type<1 * steradian + 1, quantity<steradian, int>>);
 static_assert(is_of_type<1 * steradian + 1 * one, quantity<steradian, int>>);
 static_assert(is_of_type<1 * steradian + dimensionless(1 * one), quantity<solid_angular_measure[steradian], int>>);
-static_assert(is_of_type<solid_angular_measure(1 * steradian) + 1, quantity<solid_angular_measure[steradian], int>>);
 static_assert(
   is_of_type<solid_angular_measure(1 * steradian) + 1 * one, quantity<solid_angular_measure[steradian], int>>);
 static_assert(is_of_type<solid_angular_measure(1 * steradian) + dimensionless(1 * one),
                          quantity<solid_angular_measure[steradian], int>>);
 
 // subtraction of various dimensionless quantities
-static_assert(is_of_type<1 * one - 1, quantity<one, int>>);
-static_assert(is_of_type<dimensionless(1 * one) - 1, quantity<dimensionless[one], int>>);
-
-static_assert(is_of_type<1 * radian - 1, quantity<radian, int>>);
 static_assert(is_of_type<1 * radian - 1 * one, quantity<radian, int>>);
 static_assert(is_of_type<1 * radian - dimensionless(1 * one), quantity<angular_measure[radian], int>>);
-static_assert(is_of_type<angular_measure(1 * radian) - 1, quantity<angular_measure[radian], int>>);
 static_assert(is_of_type<angular_measure(1 * radian) - 1 * one, quantity<angular_measure[radian], int>>);
 static_assert(is_of_type<angular_measure(1 * radian) - dimensionless(1 * one), quantity<angular_measure[radian], int>>);
 
-static_assert(is_of_type<1 * steradian - 1, quantity<steradian, int>>);
 static_assert(is_of_type<1 * steradian - 1 * one, quantity<steradian, int>>);
 static_assert(is_of_type<1 * steradian - dimensionless(1 * one), quantity<solid_angular_measure[steradian], int>>);
-static_assert(is_of_type<solid_angular_measure(1 * steradian) - 1, quantity<solid_angular_measure[steradian], int>>);
 static_assert(
   is_of_type<solid_angular_measure(1 * steradian) - 1 * one, quantity<solid_angular_measure[steradian], int>>);
 static_assert(is_of_type<solid_angular_measure(1 * steradian) - dimensionless(1 * one),
                          quantity<solid_angular_measure[steradian], int>>);
 
 // comparison of various dimensionless quantities
-static_assert(1 * one == 1);
-static_assert(dimensionless(1 * one) == 1);
-
-static_assert(1 * radian == 1);
 static_assert(1 * radian == 1 * one);
 static_assert(1 * radian == dimensionless(1 * one));
-static_assert(angular_measure(1 * radian) == 1);
 static_assert(angular_measure(1 * radian) == 1 * one);
 static_assert(angular_measure(1 * radian) == dimensionless(1 * one));
 
-static_assert(1 * steradian == 1);
 static_assert(1 * steradian == 1 * one);
 static_assert(1 * steradian == dimensionless(1 * one));
-static_assert(solid_angular_measure(1 * steradian) == 1);
 static_assert(solid_angular_measure(1 * steradian) == 1 * one);
 static_assert(solid_angular_measure(1 * steradian) == dimensionless(1 * one));