diff --git a/types/src/number/math.rs b/types/src/number/math.rs
index bf9aef2..a5ef5b7 100644
--- a/types/src/number/math.rs
+++ b/types/src/number/math.rs
@@ -2,7 +2,7 @@
  * Eryn Wells <eryn@erynwells.me>
  */
 
-use number::Int;
+use number::{Int, Flt};
 
 pub trait GCD {
     /// Find the greatest common divisor of `self` and another number.
@@ -14,6 +14,11 @@ pub trait LCM {
     fn lcm(self, other: Self) -> Self;
 }
 
+pub trait Rational {
+    /// Convert `self` into a rational number -- the quotient of two whole numbers.
+    fn to_rational(self) -> (Int, Int);
+}
+
 impl GCD for Int {
     fn gcd(self, other: Int) -> Int {
 		let (mut a, mut b) = if self > other {
@@ -43,6 +48,30 @@ impl LCM for Int {
     }
 }
 
+impl Rational for Int {
+    fn to_rational(self) -> (Int, Int) { (self, 1) }
+}
+
+impl Rational for Flt {
+    fn to_rational(self) -> (Int, Int) {
+        // Convert the float to a fraction by iteratively multiplying by 10 until the fractional part of the float is 0.0.
+        let whole_part = self.trunc();
+        let mut p = self.fract();
+        let mut q = 1.0;
+        while p.fract() != 0.0 {
+            p *= 10.0;
+            q *= 10.0;
+        }
+        p += whole_part * q;
+
+        // Integers from here down. Reduce the fraction before returning.
+        let p = p as Int;
+        let q = q as Int;
+        let gcd = p.gcd(q);
+        (p / gcd, q / gcd)
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::{LCM, GCD};
diff --git a/types/src/number/real.rs b/types/src/number/real.rs
index f8b7f3c..19a98ed 100644
--- a/types/src/number/real.rs
+++ b/types/src/number/real.rs
@@ -24,13 +24,19 @@ impl Real {
     ///
     /// assert_eq!(Real::Integer(12).reduce(), Real::Integer(12));
     /// assert_eq!(Real::Rational(2, 4).reduce(), Real::Rational(1, 2));
+    /// assert_eq!(Real::Rational(3, 7).reduce(), Real::Rational(3, 7));
     /// assert_eq!(Real::Irrational(2.4).reduce(), Real::Irrational(2.4));
     /// ```
     pub fn reduce(self) -> Real {
         match self {
             Real::Rational(p, q) => {
                 let gcd = p.gcd(q);
-                Real::Rational(p / gcd, q / gcd)
+                if gcd == 1 {
+                    self
+                }
+                else {
+                    Real::Rational(p / gcd, q / gcd)
+                }
             },
             _ => self
         }
@@ -75,6 +81,23 @@ impl Real {
     }
 
     /// Demote a Real to the next lowest type, if possible.
+    ///
+    /// # Examples
+    ///
+    /// Integers can't reduce.
+    ///
+    /// ```
+    /// use sibiltypes::number::Real;
+    /// assert!(Real::Integer(3).demote_once().is_none());
+    /// ```
+    ///
+    /// Rationals can be demoted in certain cases.
+    ///
+    /// ```
+    /// use sibiltypes::number::Real;
+    /// assert_eq!(Real::Rational(4, 1).demote_once(), Some(Real::Integer(4)));
+    /// assert!(Real::Rational(4, 7).demote_once().is_none());
+    /// ```
     pub fn demote_once(self) -> Option<Real> {
         match self {
             Real::Integer(_) => None,
@@ -84,17 +107,10 @@ impl Real {
             else {
                 None
             },
-            // TODO: Convert an irrational into a fraction.
             Real::Irrational(v) => {
-                let whole_part = v.trunc();
-                let mut p = v.fract();
-                let mut q = 1.0;
-                while p.fract() != 0.0 {
-                    p *= 10.0;
-                    q *= 10.0;
-                }
-                p += whole_part * q;
-                Some(Real::Rational(p as Int, q as Int).reduce())
+                let (p, q) = v.to_rational();
+                // No need to reduce here since p/q is already reduced.
+                Some(Real::Rational(p, q))
             }
         }
     }