diff -r 7c6e3358221a Lib/datetime.py
--- a/Lib/datetime.py	Thu Feb 26 15:27:57 2015 +0200
+++ b/Lib/datetime.py	Thu Feb 26 11:13:46 2015 -0500
@@ -297,6 +297,23 @@
     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 the nearest integer
+
+    When the ratio is exactly half-way between two integers,
+    the even integer is returned.
+    """
+    if b < 0:
+        return -_divide_and_round(a, -b)
+    q, r = divmod(a, b)
+    r2 = r * 2
+    if r2 > b:
+        return q + 1
+    if r2 < b:
+        return q
+    # resolve ties to even
+    return q + (q & 1)
+
 class timedelta:
     """Represent the difference between two datetime objects.
 
@@ -515,8 +532,9 @@
                              self._seconds * other,
                              self._microseconds * other)
         if isinstance(other, float):
+            usec = self._to_microseconds()
             a, b = other.as_integer_ratio()
-            return self * a / b
+            return timedelta(0, 0, _divide_and_round(usec * a, b))
         return NotImplemented
 
     __rmul__ = __mul__
@@ -541,10 +559,10 @@
         if isinstance(other, timedelta):
             return usec / other._to_microseconds()
         if isinstance(other, int):
-            return timedelta(0, 0, usec / other)
+            return timedelta(0, 0, _divide_and_round(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 7c6e3358221a Lib/test/datetimetester.py
--- a/Lib/test/datetimetester.py	Thu Feb 26 15:27:57 2015 +0200
+++ b/Lib/test/datetimetester.py	Thu Feb 26 11:13:46 2015 -0500
@@ -62,6 +62,17 @@
                        'tzinfo'])
         self.assertEqual(names - allowed, set([]))
 
+    def test_divide_and_round(self):
+        if '_Fast' in str(self):
+            return
+        dar = datetime_module._divide_and_round
+        self.assertEqual(dar(-10, -3), 3)
+        self.assertEqual(dar(5, -2), -2)
+        # ties to even
+        self.assertEqual(dar(10, -4), -2)
+        self.assertEqual(dar(-10, 4), -2)
+        self.assertEqual(dar(-10, -4), 2)
+        
 #############################################################################
 # tzinfo tests
 
@@ -394,6 +405,10 @@
         eq((-3*us) * 0.5, -2*us)
         eq((-5*us) * 0.5, -2*us)
 
+        # Issue #23521
+        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 +423,9 @@
         for i in range(-10, 10):
             eq((i*us/-3)//us, round(i/-3))
 
+        # Issue #23521
+        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))