diff --git a/Lib/test/test_datetime.py b/Lib/test/test_datetime.py
index b751820..7c5fa9f 100644
--- a/Lib/test/test_datetime.py
+++ b/Lib/test/test_datetime.py
@@ -25,6 +25,16 @@
 OTHERSTUFF = (10, 34.5, "abc", {}, [], ())
 
 
+# XXX Copied from test_float.
+INF = float("inf")
+NAN = float("nan")
+
+# decorator for skipping tests on non-IEEE 754 platforms
+requires_IEEE_754 = unittest.skipUnless(
+    float.__getformat__("double").startswith("IEEE"),
+    "test requires IEEE 754 doubles")
+
+
 #############################################################################
 # module tests
 
@@ -225,6 +235,36 @@
         eq(c//1000, td(0, 0, 1))
         eq(a//10, td(0, 7*24*360))
         eq(a//3600000, td(0, 0, 7*24*1000))
+        eq(a/0.5, td(14))
+        eq(b/0.5, td(0, 120))
+        eq(a/7, td(1))
+        eq(b/10, td(0, 6))
+        eq(c/1000, td(0, 0, 1))
+        eq(a/10, td(0, 7*24*360))
+        eq(a/3600000, td(0, 0, 7*24*1000))
+
+        # Multiplication by float
+        us = td(microseconds=1)
+        eq((3*us) * 0.5, 2*us)
+        eq((5*us) * 0.5, 2*us)
+        eq(0.5 * (3*us), 2*us)
+        eq(0.5 * (5*us), 2*us)
+        eq((-3*us) * 0.5, -2*us)
+        eq((-5*us) * 0.5, -2*us)
+
+        # Division by int and float
+        eq((3*us) / 2, 2*us)
+        eq((5*us) / 2, 2*us)
+        eq((-3*us) / 2.0, -2*us)
+        eq((-5*us) / 2.0, -2*us)
+        eq((3*us) / -2, -2*us)
+        eq((5*us) / -2, -2*us)
+        eq((3*us) / -2.0, -2*us)
+        eq((5*us) / -2.0, -2*us)
+        for i in range(-10, 10):
+            eq((i*us/3)//us, round(i/3))
+        for i in range(-10, 10):
+            eq((i*us/-3)//us, round(i/-3))
 
     def test_disallowed_computations(self):
         a = timedelta(42)
@@ -236,20 +276,19 @@
             self.assertRaises(TypeError, lambda: i+a)
             self.assertRaises(TypeError, lambda: i-a)
 
-        # Mul/div by float isn't supported.
-        x = 2.3
-        self.assertRaises(TypeError, lambda: a*x)
-        self.assertRaises(TypeError, lambda: x*a)
-        self.assertRaises(TypeError, lambda: a/x)
-        self.assertRaises(TypeError, lambda: x/a)
-        self.assertRaises(TypeError, lambda: a // x)
-        self.assertRaises(TypeError, lambda: x // a)
-
         # Division of int by timedelta doesn't make sense.
         # Division by zero doesn't make sense.
         zero = 0
         self.assertRaises(TypeError, lambda: zero // a)
         self.assertRaises(ZeroDivisionError, lambda: a // zero)
+        self.assertRaises(ZeroDivisionError, lambda: a / zero)
+        self.assertRaises(ZeroDivisionError, lambda: a / 0.0)
+
+    @requires_IEEE_754
+    def test_disallowed_special(self):
+        a = timedelta(42)
+        self.assertRaises(ValueError, a.__mul__, NAN)
+        self.assertRaises(ValueError, a.__truediv__, NAN)
 
     def test_basic_attributes(self):
         days, seconds, us = 1, 7, 31
@@ -410,6 +449,19 @@
 
         self.assertRaises(OverflowError, lambda: -timedelta.max)
 
+        day = timedelta(1)
+        self.assertRaises(OverflowError, day.__mul__, 10**9)
+        self.assertRaises(OverflowError, day.__mul__, 1e9)
+        self.assertRaises(OverflowError, day.__truediv__, 1e-20)
+        self.assertRaises(OverflowError, day.__truediv__, 1e-10)
+        self.assertRaises(OverflowError, day.__truediv__, 9e-10)
+
+    @requires_IEEE_754
+    def _test_overflow_special(self):
+        day = timedelta(1)
+        self.assertRaises(OverflowError, day.__mul__, INF)
+        self.assertRaises(OverflowError, day.__mul__, -INF)
+
     def test_microsecond_rounding(self):
         td = timedelta
         eq = self.assertEqual
@@ -489,7 +541,7 @@
         self.assertRaises(ZeroDivisionError, truediv, t, zerotd)
         self.assertRaises(ZeroDivisionError, floordiv, t, zerotd)
 
-        self.assertRaises(TypeError, truediv, t, 2)
+        # self.assertRaises(TypeError, truediv, t, 2)
         # note: floor division of a timedelta by an integer *is*
         # currently permitted.