diff --git a/Makefile.am b/Makefile.am
index 814c1e6e..8e0067cb 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -334,6 +334,7 @@ TEST_BIN = 			\
     test/pool			\
     test/rand			\
     test/range 			\
+    test/rational		\
     test/region			\
     test/ripemd			\
     test/sha1			\
diff --git a/rational.cpp b/rational.cpp
index bee06132..9fe513d2 100644
--- a/rational.cpp
+++ b/rational.cpp
@@ -16,85 +16,151 @@
 
 #include "rational.hpp"
 
+#include "maths.hpp"
+
 #include <cstdint>
 
 using util::rational;
 
 
-//-----------------------------------------------------------------------------
+///////////////////////////////////////////////////////////////////////////////
 template <typename T>
 rational<T>::rational (T _n, T _d):
     n (_n),
     d (_d)
-{ ; }
+{
+    if (n < 0 && d < 0) {
+        n *= -1;
+        d *= -1;
+    }
+}
 
 
 //-----------------------------------------------------------------------------
 template <typename T>
+rational<T>::rational (T v):
+    n (v),
+    d (1)
+{ ; }
+
+
+///////////////////////////////////////////////////////////////////////////////
+template <typename T>
 bool
-rational<T>::operator== (const rational<T> &rhs) {
+rational<T>::operator== (const rational<T> rhs) const
+{
     return rhs.n == n && rhs.d == d;
 }
 
 
 //-----------------------------------------------------------------------------
 template <typename T>
-rational<T>::operator float (void) const {
+bool
+rational<T>::operator!= (const rational<T> rhs) const
+{
+    return !operator== (rhs);
+}
+
+
+//-----------------------------------------------------------------------------
+template <typename T>
+bool
+rational<T>::operator< (const rational<T> rhs) const
+{
+    return n * rhs.d < rhs.n * d;
+}
+
+
+//-----------------------------------------------------------------------------
+template <typename T>
+bool
+rational<T>::operator>= (const rational<T> rhs) const
+{
+    return n * rhs.d >= rhs.n * d;
+}
+
+
+///////////////////////////////////////////////////////////////////////////////
+template <typename T>
+rational<T>::operator float (void) const
+{
     return static_cast<float> (n) / d;
 }
 
 
 //-----------------------------------------------------------------------------
 template <typename T>
-rational<T>::operator double (void) const {
+rational<T>::operator double (void) const
+{
     return static_cast<double> (n) / d;
 }
 
 
-//-----------------------------------------------------------------------------
+///////////////////////////////////////////////////////////////////////////////
 template <typename T>
-rational<T>::operator int (void) const {
-    return n / d;
+rational<T>
+rational<T>::reduced (void) const
+{
+    auto x = gcd (abs (n), abs (d));
+
+    return { n / x, d / x };
 }
 
 
-//-----------------------------------------------------------------------------
+///////////////////////////////////////////////////////////////////////////////
 template <typename T>
 rational<T>
-rational<T>::inverse (void) const {
+rational<T>::inverse (void) const
+{
     return rational<T> { d, n };
 }
 
 
 //-----------------------------------------------------------------------------
 template <typename T>
-template <typename U>
 rational<T>
-rational<T>::operator* (const U &rhs) const {
+rational<T>::operator+ (const T rhs) const
+{
+    return { n + rhs * d, d };
+}
+
+
+//-----------------------------------------------------------------------------
+template <typename T>
+rational<T>
+rational<T>::operator- (const T rhs) const
+{
+    return { n - rhs * d, d };
+}
+
+
+//-----------------------------------------------------------------------------
+template <typename T>
+rational<T>
+rational<T>::operator* (const T rhs) const
+{
     return { rhs * n, d };
 }
 
 
 //-----------------------------------------------------------------------------
 template <typename T>
-template <typename U>
 rational<T>
-rational<T>::operator/ (const U &rhs) const {
+rational<T>::operator/ (const T rhs) const
+{
     return { n, rhs * d };
 }
 
 
 //-----------------------------------------------------------------------------
-template <typename T, typename U>
+template <typename T>
 rational<T>
-util::operator/ (U lhs, rational<T> rhs) {
+util::operator/ (T lhs, rational<T> rhs) {
     return rhs.inverse () * lhs;
 }
 
 //-----------------------------------------------------------------------------
-namespace util {
-    template struct rational<uint32_t>;
-    template struct rational<int32_t>;
+template struct util::rational<uint32_t>;
+template struct util::rational< int32_t>;
 
-    template rational<uint32_t> operator/ (int, rational<uint32_t>);
-}
+template util::rational<uint32_t> util::operator/ (uint32_t, util::rational<uint32_t>);
diff --git a/rational.hpp b/rational.hpp
index eff6d575..7c30b2cf 100644
--- a/rational.hpp
+++ b/rational.hpp
@@ -17,30 +17,41 @@
 #ifndef __UTIL_RATIONAL_HPP
 #define __UTIL_RATIONAL_HPP
 
+#include <type_traits>
+
 namespace util {
     template <typename T>
     struct rational {
-        rational (T _n, T _d);
-        rational& operator=  (const rational&) = default;
+        static_assert (std::is_integral<T>::value, "only defined for integer types");
 
-        bool operator== (const rational&);
+        rational (T n, T d);
+        explicit rational (T);
+        rational& operator= (const rational&) = default;
+
+        bool operator== (rational) const;
+        bool operator!= (rational) const;
+        bool operator<  (rational) const;
+        bool operator>= (rational) const;
 
         explicit operator float  (void) const;
         explicit operator double (void) const;
-        explicit operator int    (void) const;
+
+        rational<T> reduced (void) const;
 
         rational<T>  inverse (void) const;
         rational<T>& invert  (void);
 
-        template <typename U> rational<T> operator* (const U&) const;
-        template <typename U> rational<T> operator/ (const U&) const;
+        rational<T> operator+ (T) const;
+        rational<T> operator- (T) const;
+        rational<T> operator* (T) const;
+        rational<T> operator/ (T) const;
 
         T n;
         T d;
     };
 
-    template <typename T, typename U>
-    rational<T> operator/ (U, rational<T>);
+    template <typename T>
+    rational<T> operator/ (T, rational<T>);
 }
 
 #endif
diff --git a/test/rational.cpp b/test/rational.cpp
new file mode 100644
index 00000000..31740bba
--- /dev/null
+++ b/test/rational.cpp
@@ -0,0 +1,35 @@
+#include "rational.hpp"
+#include "tap.hpp"
+
+using util::rational;
+
+
+int
+main (void)
+{
+    util::TAP::logger tap;
+
+    {
+        rational<int> val { -3, -2 };
+        tap.expect (val.n == 3 && val.d == 2, "reduce double negatives at construction");
+    }
+
+    {
+        rational<int> val { 5 };
+        tap.expect (val.n == 5 && val.d == 1, "scalar construction");
+    }
+
+    {
+        rational<int> a { 2, 3 };
+        rational<int> b { 3, 2 };
+
+        tap.expect_eq (a.inverse (), b, "inversion and equality");
+    }
+
+    {
+        rational<int> val { 8, 12 };
+        tap.expect_eq (val.reduced (), rational<int> { 2, 3 }, "factorisation");
+    }
+
+    return tap.status ();
+}