diff --git a/types/src/number/frac.rs b/types/src/number/frac.rs
index b175e79..ad0d746 100644
--- a/types/src/number/frac.rs
+++ b/types/src/number/frac.rs
@@ -5,28 +5,40 @@
 use std::any::Any;
 use std::fmt;
 use std::ops::{Add, Mul};
+use number::arith::GCD;
 use number::{Int, Number};
 use object::{Obj, Object};
 
 /// A fraction consisting of a numerator and denominator.
-#[derive(Debug, Eq, PartialEq)]
-pub struct Frac(pub i64, pub u64);
+#[derive(Debug, Eq, Ord, PartialEq, PartialOrd)]
+pub struct Frac(Int, Int);
 
 impl Frac {
+    pub fn new(p: Int, q: Int) -> Result<Frac, ()> {
+        if q == Int(0) {
+            // TODO: Return a more specific error about dividing by zero.
+            Err(())
+        } else {
+            Ok(Frac(p, q).reduced())
+        }
+    }
+
+    fn reduced(self) -> Frac {
+        let gcd = self.0.gcd(self.1);
+        Frac(self.0 / gcd, self.1 / gcd)
+    }
 }
 
 impl Number for Frac {
     fn as_int(&self) -> Option<Int> {
-        if self.1 == 1 {
-            Some(Int(self.0))
+        if self.1 == Int(1) {
+            Some(self.0)
         } else {
             None
         }
     }
 
-    fn as_frac(&self) -> Option<Frac> {
-        Some(Frac(self.0, self.1))
-    }
+    fn as_frac(&self) -> Option<Frac> { Frac::new(self.0, self.1).ok() }
 }
 
 impl fmt::Display for Frac {
@@ -64,25 +76,25 @@ mod tests {
 
     #[test]
     fn equal_fracs_are_equal() {
-        assert_eq!(Frac(3, 2), Frac(3, 2));
-        assert_ne!(Frac(12, 4), Frac(9, 7));
+        assert_eq!(Frac(Int(3), Int(2)), Frac(Int(3), Int(2)));
+        assert_ne!(Frac(Int(12), Int(4)), Frac(Int(9), Int(7)));
     }
 
     #[test]
     fn fracs_should_reduce_to_ints_where_possible() {
-        let rational_as_integer = Frac(3, 1).as_int();
+        let rational_as_integer = Frac(Int(3), Int(1)).as_int();
         assert!(rational_as_integer.is_some());
         // Oh my god this line is so dumb.
     }
 
     #[test]
     fn fracs_should_not_reduce_to_ints_where_impossible() {
-        let rational_as_integer = Frac(3, 2).as_int();
+        let rational_as_integer = Frac(Int(3), Int(2)).as_int();
         assert!(rational_as_integer.is_none());
     }
 
     #[test]
     fn fracs_are_exact() {
-        assert!(Frac(4, 2).is_exact());
+        assert!(Frac(Int(4), Int(2)).is_exact());
     }
 }
diff --git a/types/src/number/integer.rs b/types/src/number/integer.rs
index 98ff532..d075035 100644
--- a/types/src/number/integer.rs
+++ b/types/src/number/integer.rs
@@ -4,12 +4,12 @@
 
 use std::any::Any;
 use std::fmt;
-use std::ops::{Add, Mul, Rem};
+use std::ops::{Add, Div, Mul, Rem};
 use number::arith::{GCD, LCM};
 use number::{Frac, Number};
 use object::{Obj, Object};
 
-#[derive(Copy, Clone, Debug, Eq, PartialEq)]
+#[derive(Copy, Clone, Debug, Eq, Ord, PartialEq, PartialOrd)]
 pub struct Int(pub i64);
 
 impl Add for Int {
@@ -39,6 +39,27 @@ impl fmt::Display for Int {
     }
 }
 
+impl Div for Int {
+    type Output = Int;
+    fn div(self, rhs: Self) -> Self::Output {
+        Int(self.0 / rhs.0)
+    }
+}
+
+impl<'a> Div<Int> for &'a Int {
+    type Output = Int;
+    fn div(self, rhs: Int) -> Self::Output {
+        Int(self.0 / rhs.0)
+    }
+}
+
+impl<'a, 'b> Div<&'a Int> for &'b Int {
+    type Output = Int;
+    fn div(self, rhs: &Int) -> Self::Output {
+        Int(self.0 / rhs.0)
+    }
+}
+
 impl GCD for Int {
     fn gcd(self, other: Int) -> Int {
 		let (mut a, mut b) = if self.0 > other.0 {
@@ -72,7 +93,7 @@ impl Object for Int {
 
 impl Number for Int {
     fn as_int(&self) -> Option<Int> { Some(*self) }
-    fn as_frac(&self) -> Option<Frac> { Some(Frac(self.0, 1)) }
+    fn as_frac(&self) -> Option<Frac> { Frac::new(*self, Int(1)).ok() }
 }
 
 impl Mul for Int {