diff --git a/Makefile.am b/Makefile.am
index 9e9b9196..aba8a38d 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -210,6 +210,7 @@ UTIL_FILES   =			\
     range.ipp			\
     rational.cpp		\
     rational.hpp		\
+    rational.ipp		\
     ray.cpp			\
     ray.hpp			\
     region.cpp			\
diff --git a/rational.cpp b/rational.cpp
index 771b2d43..b64ff473 100644
--- a/rational.cpp
+++ b/rational.cpp
@@ -160,13 +160,6 @@ rational<T>::operator/ (const T rhs) const
 }
 
 
-//-----------------------------------------------------------------------------
-template <typename T>
-rational<T>
-util::operator/ (T lhs, rational<T> rhs) {
-    return rhs.inverse () * lhs;
-}
-
 //-----------------------------------------------------------------------------
 template struct util::rational<uint32_t>;
 template struct util::rational< int32_t>;
diff --git a/rational.hpp b/rational.hpp
index b85b12ff..332a0908 100644
--- a/rational.hpp
+++ b/rational.hpp
@@ -51,8 +51,15 @@ namespace util {
         T d;
     };
 
-    template <typename T>
-    rational<T> operator/ (T, rational<T>);
+    template <typename T, typename U>
+    rational<typename std::common_type<T,U>::type>
+    operator/ (U, rational<T>);
+
+    template <typename T, typename U>
+    rational<typename std::common_type<T,U>::type>
+    operator* (U, rational<T>);
 }
 
+#include "rational.ipp"
+
 #endif
diff --git a/rational.ipp b/rational.ipp
new file mode 100644
index 00000000..7412af26
--- /dev/null
+++ b/rational.ipp
@@ -0,0 +1,38 @@
+/*
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Copyright 2015 Danny Robson <danny@nerdcruft.net>
+ */
+
+#ifdef __UTIL_RATIONAL_IPP
+#error
+#endif
+#define __UTIL_RATIONAL_IPP
+
+
+//-----------------------------------------------------------------------------
+template <typename T, typename U>
+util::rational<typename std::common_type<T,U>::type>
+util::operator/ (U lhs, rational<T> rhs)
+{
+    return rhs.inverse () * lhs;
+}
+
+
+//-----------------------------------------------------------------------------
+template <typename T, typename U>
+util::rational<typename std::common_type<T,U>::type>
+util::operator* (U lhs, rational<T> rhs)
+{
+    return rhs * lhs;
+}