diff -r cb911e1fb3dc Lib/datetime.py
--- a/Lib/datetime.py	Wed Feb 25 18:14:47 2015 +0200
+++ b/Lib/datetime.py	Wed Feb 25 18:59:32 2015 -0500
@@ -297,6 +297,17 @@
     raise TypeError("can't compare '%s' to '%s'" % (
                     type(x).__name__, type(y).__name__))
 
+def _divide_and_round(a, b):
+    """divide a by b and round result to nearest even integer"""
+    d, r = divmod(a, b)
+    r2 = r * 2
+    if r2 > b:
+        return d + 1
+    if r2 < b:
+        return d
+    # resolve ties to even
+    return d + (d & 1)
+
 class timedelta:
     """Represent the difference between two datetime objects.
 
@@ -515,8 +526,9 @@
                              self._seconds * other,
                              self._microseconds * other)
         if isinstance(other, float):
+            ms = self._to_microseconds()
             a, b = other.as_integer_ratio()
-            return self * a / b
+            return timedelta(microseconds=_divide_and_round(ms * a, b))
         return NotImplemented
 
     __rmul__ = __mul__
@@ -544,7 +556,7 @@
             return timedelta(0, 0, usec / other)
         if isinstance(other, float):
             a, b = other.as_integer_ratio()
-            return timedelta(0, 0, b * usec / a)
+            return timedelta(0, 0, _divide_and_round(b * usec, a))
 
     def __mod__(self, other):
         if isinstance(other, timedelta):
diff -r cb911e1fb3dc Lib/test/datetimetester.py
--- a/Lib/test/datetimetester.py	Wed Feb 25 18:14:47 2015 +0200
+++ b/Lib/test/datetimetester.py	Wed Feb 25 18:59:32 2015 -0500
@@ -394,6 +394,9 @@
         eq((-3*us) * 0.5, -2*us)
         eq((-5*us) * 0.5, -2*us)
 
+        eq(td(seconds=1) * 0.123456, td(microseconds=123456))
+        eq(td(seconds=1) * 0.6112295, td(microseconds=611229))
+
         # Division by int and float
         eq((3*us) / 2, 2*us)
         eq((5*us) / 2, 2*us)
@@ -408,6 +411,8 @@
         for i in range(-10, 10):
             eq((i*us/-3)//us, round(i/-3))
 
+        eq(td(seconds=1) / (1 / 0.6112295), td(microseconds=611229))
+
         # Issue #11576
         eq(td(999999999, 86399, 999999) - td(999999999, 86399, 999998),
            td(0, 0, 1))