diff --git a/artiq/compiler/ir_values.py b/artiq/compiler/ir_values.py
index 72b209a37..ac34d3c3f 100644
--- a/artiq/compiler/ir_values.py
+++ b/artiq/compiler/ir_values.py
@@ -188,6 +188,22 @@ class VBool(VInt):
 
 # Fraction type
 
+def _gcd64(builder, a, b):
+	gcd_f = builder.module.get_function_named("__gcd64")
+	return builder.call(gcd_f, [a, b])
+
+def _frac_normalize(builder, numerator, denominator):
+	gcd = _gcd64(numerator, denominator)
+	numerator = builder.sdiv(numerator, gcd)
+	denominator = builder.sdiv(denominator, gcd)
+	return numerator, denominator
+
+def _frac_make_ssa(builder, numerator, denominator):
+	value = lc.Constant.undef(lc.Type.vector(lc.Type.int(64), 2))
+	value = builder.insert_element(value, numerator, lc.Constant.int(lc.Type.int(), 0))
+	value = builder.insert_element(value, denominator, lc.Constant.int(lc.Type.int(), 1))
+	return value
+
 class VFraction(_Value):
 	def get_llvm_type(self):
 		return lc.Type.vector(lc.Type.int(64), 2)
@@ -202,25 +218,20 @@ class VFraction(_Value):
 		if not isinstance(other, VFraction):
 			raise TypeError
 
-	def _nd(self, builder):
+	def _nd(self, builder, invert=False):
 		ssa_value = self.get_ssa_value(builder)
 		numerator = builder.extract_element(ssa_value, lc.Constant.int(lc.Type.int(), 0))
 		denominator = builder.extract_element(ssa_value, lc.Constant.int(lc.Type.int(), 1))
-		return numerator, denominator
+		if invert:
+			return denominator, numerator
+		else:
+			return numerator, denominator
 
 	def set_value_nd(self, builder, numerator, denominator):
 		numerator = numerator.o_int64(builder).get_ssa_value(builder)
 		denominator = denominator.o_int64(builder).get_ssa_value(builder)
-
-		gcd_f = builder.module.get_function_named("__gcd64")
-		gcd = builder.call(gcd_f, [numerator, denominator])
-		numerator = builder.sdiv(numerator, gcd)
-		denominator = builder.sdiv(denominator, gcd)
-
-		value = lc.Constant.undef(lc.Type.vector(lc.Type.int(64), 2))
-		value = builder.insert_element(value, numerator, lc.Constant.int(lc.Type.int(), 0))
-		value = builder.insert_element(value, denominator, lc.Constant.int(lc.Type.int(), 1))
-		self.set_ssa_value(builder, value)
+		numerator, denominator = _frac_normalize(builder, numerator, denominator)
+		self.set_ssa_value(builder, _frac_make_ssa(builder, numerator, denominator))
 
 	def set_value(self, builder, n):
 		if not isinstance(n, VFraction):
@@ -255,7 +266,7 @@ class VFraction(_Value):
 			r.set_ssa_value(builder, builder.sdiv(r_numerator, denominator))
 			return r.o_intx(target_bits, builder)
 
-	def _o_eq_inv(self, other, builder, invert):
+	def _o_eq_inv(self, other, builder, ne):
 		if isinstance(other, VFraction):
 			r = VBool()
 			if builder is not None:
@@ -265,7 +276,7 @@ class VFraction(_Value):
 					eo = builder.extract_element(other.get_ssa_value(builder), lc.Constant.int(lc.Type.int(), i))
 					ee.append(builder.icmp(lc.ICMP_EQ, es, eo))
 				ssa_r = builder.and_(ee[0], ee[1])
-				if invert:
+				if ne:
 					ssa_r = builder.xor(ssa_r, lc.Constant.int(lc.Type.int(1), 1))
 				r.set_ssa_value(builder, ssa_r)
 			return r
@@ -278,6 +289,68 @@ class VFraction(_Value):
 	def o_ne(self, other, builder):
 		return self._o_eq_inv(other, builder, True)
 
+	def _o_muldiv(self, other, builder, div, invert=False):
+		r = VFraction()
+		if isinstance(other, VInt):
+			if builder is None:
+				return r
+			else:
+				numerator, denominator = self._nd(builder, invert)
+				i = other.get_ssa_value(builder)
+				if div:
+					gcd = _gcd64(i, numerator)
+					i = builder.sdiv(i, gcd)
+					numerator = builder.sdiv(numerator, gcd)
+					denominator = builder.mul(denominator, i)
+				else:
+					gcd = _gcd64(i, denominator)
+					i = builder.sdiv(i, gcd)
+					denominator = builder.sdiv(denominator, gcd)
+					numerator = builder.mul(numerator, i)
+				self.set_ssa_value(builder, _frac_make_ssa(builder, numerator, denominator))
+		elif isinstance(other, VFraction):
+			if builder is None:
+				return r
+			else:
+				numerator, denominator = self._nd(builder, invert)
+				onumerator, odenominator = other._nd(builder)
+				if div:
+					numerator = builder.mul(numerator, odenominator)
+					denominator = builder.mul(denominator, onumerator)
+				else:
+					numerator = builder.mul(numerator, onumerator)
+					denominator = builder.mul(denominator, odenominator)
+				numerator, denominator = _frac_normalize(builder, numerator, denominator)
+				self.set_ssa_value(builder, _frac_make_ssa(builder, numerator, denominator))
+		else:
+			return NotImplemented
+
+	def o_mul(self, other, builder):
+		return self._o_muldiv(other, builder, False)
+
+	def o_truediv(self, other, builder):
+		return self._o_muldiv(other, builder, True)
+
+	def or_mul(self, other, builder):
+		return self._o_muldiv(other, builder, False)
+
+	def or_truediv(self, other, builder):
+		return self._o_muldiv(other, builder, False, True)
+
+	def o_floordiv(self, other, builder):
+		r = self.o_truediv(other, builder)
+		if r is NotImplemented:
+			return r
+		else:
+			return r.o_int(builder)
+
+	def or_floordiv(self, other, builder):
+		r = self.or_truediv(other, builder)
+		if r is NotImplemented:
+			return r
+		else:
+			return r.o_int(builder)
+
 # Operators
 
 def _make_unary_operator(op_name):