python
diff --git a/Doc/library/math.rst b/Doc/library/math.rst
@@ -29,6 +29,17 @@ noted otherwise, all return values are floats.
 Number-theoretic and representation functions
 ---------------------------------------------
 
+.. function:: as_integer_ratio(number)
+
+   Return integer ratio.
+
+   This function returns ``number.as_integer_ratio()`` if the argument has
+   the ``as_integer_ratio()`` method, otherwise it returns a pair
+   ``(number.numerator, number.denominator)``.
+
+   .. versionadded:: 3.9
+
+
 .. function:: ceil(x)
 
    Return the ceiling of *x*, the smallest integer greater than or equal to *x*.

diff --git a/Doc/whatsnew/3.9.rst b/Doc/whatsnew/3.9.rst
@@ -109,6 +109,14 @@ New Modules
 Improved Modules
 ================
 
+
+math
+----
+
+Added new function :func:`math.as_integer_ratio`.
+(Contributed by Serhiy Storchaka in :issue:``.)
+
+
 threading
 ---------
 

diff --git a/Lib/fractions.py b/Lib/fractions.py
@@ -115,22 +115,7 @@ def __new__(cls, numerator=0, denominator=None, *, _normalize=True):
         self = super(Fraction, cls).__new__(cls)
 
         if denominator is None:
-            if type(numerator) is int:
-                self._numerator = numerator
-                self._denominator = 1
-                return self
-
-            elif isinstance(numerator, numbers.Rational):
-                self._numerator = numerator.numerator
-                self._denominator = numerator.denominator
-                return self
-
-            elif isinstance(numerator, (float, Decimal)):
-                # Exact conversion
-                self._numerator, self._denominator = numerator.as_integer_ratio()
-                return self
-
-            elif isinstance(numerator, str):
+            if isinstance(numerator, str):
                 # Handle construction from strings.
                 m = _RATIONAL_FORMAT.match(numerator)
                 if m is None:
@@ -156,10 +141,13 @@ def __new__(cls, numerator=0, denominator=None, *, _normalize=True):
                             denominator *= 10**-exp
                 if m.group('sign') == '-':
                     numerator = -numerator
-
             else:
-                raise TypeError("argument should be a string "
-                                "or a Rational instance")
+                try:
+                    self._numerator, self._denominator = math.as_integer_ratio(numerator)
+                    return self
+                except TypeError:
+                    raise TypeError("argument should be a string or a number, "
+                                    "not %s" % type(numerator).__name__) from None
 
         elif type(numerator) is int is type(denominator):
             pass # *very* normal case

diff --git a/Lib/statistics.py b/Lib/statistics.py
@@ -225,27 +225,11 @@ def _exact_ratio(x):
     x is expected to be an int, Fraction, Decimal or float.
     """
     try:
-        # Optimise the common case of floats. We expect that the most often
-        # used numeric type will be builtin floats, so try to make this as
-        # fast as possible.
-        if type(x) is float or type(x) is Decimal:
-            return x.as_integer_ratio()
-        try:
-            # x may be an int, Fraction, or Integral ABC.
-            return (x.numerator, x.denominator)
-        except AttributeError:
-            try:
-                # x may be a float or Decimal subclass.
-                return x.as_integer_ratio()
-            except AttributeError:
-                # Just give up?
-                pass
+        return math.as_integer_ratio(x)
     except (OverflowError, ValueError):
         # float NAN or INF.
         assert not _isfinite(x)
         return (x, None)
-    msg = "can't convert type '{}' to numerator/denominator"
-    raise TypeError(msg.format(type(x).__name__))
 
 
 def _convert(value, T):

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
@@ -12,6 +12,8 @@
 import random
 import struct
 import sys
+from decimal import Decimal
+from fractions import Fraction
 
 
 eps = 1E-05
@@ -293,6 +295,33 @@ def testAcosh(self):
         self.assertRaises(ValueError, math.acosh, NINF)
         self.assertTrue(math.isnan(math.acosh(NAN)))
 
+    def testAsIntegerRatio(self):
+        as_integer_ratio = math.as_integer_ratio
+        self.assertEqual(as_integer_ratio(0), (0, 1))
+        self.assertEqual(as_integer_ratio(3), (3, 1))
+        self.assertEqual(as_integer_ratio(-3), (-3, 1))
+        self.assertEqual(as_integer_ratio(False), (0, 1))
+        self.assertEqual(as_integer_ratio(True), (1, 1))
+        self.assertEqual(as_integer_ratio(0.0), (0, 1))
+        self.assertEqual(as_integer_ratio(-0.0), (0, 1))
+        self.assertEqual(as_integer_ratio(0.875), (7, 8))
+        self.assertEqual(as_integer_ratio(-0.875), (-7, 8))
+        self.assertEqual(as_integer_ratio(Decimal('0')), (0, 1))
+        self.assertEqual(as_integer_ratio(Decimal('0.875')), (7, 8))
+        self.assertEqual(as_integer_ratio(Decimal('-0.875')), (-7, 8))
+        self.assertEqual(as_integer_ratio(Fraction(0)), (0, 1))
+        self.assertEqual(as_integer_ratio(Fraction(7, 8)), (7, 8))
+        self.assertEqual(as_integer_ratio(Fraction(-7, 8)), (-7, 8))
+
+        self.assertRaises(OverflowError, as_integer_ratio, float('inf'))
+        self.assertRaises(OverflowError, as_integer_ratio, float('-inf'))
+        self.assertRaises(ValueError, as_integer_ratio, float('nan'))
+        self.assertRaises(OverflowError, as_integer_ratio, Decimal('inf'))
+        self.assertRaises(OverflowError, as_integer_ratio, Decimal('-inf'))
+        self.assertRaises(ValueError, as_integer_ratio, Decimal('nan'))
+
+        self.assertRaises(TypeError, as_integer_ratio, '0')
+
     def testAsin(self):
         self.assertRaises(TypeError, math.asin)
         self.ftest('asin(-1)', math.asin(-1), -math.pi/2)

diff --git a/Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst b/Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst
@@ -0,0 +1 @@
+Added :func:`math.as_integer_ratio`.
diff --git a/Modules/clinic/mathmodule.c.h b/Modules/clinic/mathmodule.c.h
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
@@ -3306,9 +3306,83 @@ math_comb_impl(PyObject *module, PyObject *n, PyObject *k)
 }
 
 
+/*[clinic input]
+math.as_integer_ratio
+    x: object
+    /
+greatest common divisor of x and y
-greatest common divisor of x and y
+Return the rational representation of x as the pair (numerator, denominator).
-greatest common divisor of x and y
+Return the rational representation of x as the pair (numerator, denominator).
+[clinic start generated code]*/
+
+static PyObject *
+math_as_integer_ratio(PyObject *module, PyObject *x)
+/*[clinic end generated code: output=1844868fd4efb2f1 input=d7f2e8ffd51c6599]*/
+{
+    _Py_IDENTIFIER(as_integer_ratio);
+    _Py_IDENTIFIER(numerator);
+    _Py_IDENTIFIER(denominator);
+    PyObject *ratio, *as_integer_ratio, *numerator, *denominator;
+
+    if (PyLong_CheckExact(x)) {
+        return PyTuple_Pack(2, x, _PyLong_One);
+    }
+
+    if (_PyObject_LookupAttrId(x, &PyId_as_integer_ratio, &as_integer_ratio) < 0) {
+        return NULL;
+    }
+    if (as_integer_ratio) {
+        ratio = _PyObject_CallNoArg(as_integer_ratio);
+        Py_DECREF(as_integer_ratio);
+        if (ratio == NULL) {
+            return NULL;
+        }
+        if (!PyTuple_Check(ratio)) {
+            PyErr_Format(PyExc_TypeError,
+                        "unexpected return type from as_integer_ratio(): "
+                        "expected tuple, got '%.200s'",
+                        Py_TYPE(ratio)->tp_name);
+            Py_DECREF(ratio);
+            return NULL;
+        }
+        if (PyTuple_GET_SIZE(ratio) != 2) {
+            PyErr_SetString(PyExc_ValueError,
+                            "as_integer_ratio() must return a 2-tuple");
+            Py_DECREF(ratio);
+            return NULL;
+        }
+    }
+    else {
+        if (_PyObject_LookupAttrId(x, &PyId_numerator, &numerator) < 0) {
+            return NULL;
+        }
+        if (numerator == NULL) {
+            PyErr_Format(PyExc_TypeError,
+                         "required a number, not '%.200s'",
+                         Py_TYPE(x)->tp_name);
+            return NULL;
+        }
+        if (_PyObject_LookupAttrId(x, &PyId_denominator, &denominator) < 0) {
+            Py_DECREF(numerator);
+            return NULL;
+        }
+        if (denominator == NULL) {
+            Py_DECREF(numerator);
+            PyErr_Format(PyExc_TypeError,
+                         "required a number, not '%.200s'",
+                         Py_TYPE(x)->tp_name);
+            return NULL;
+        }
+        ratio = PyTuple_Pack(2, numerator, denominator);
+        Py_DECREF(numerator);
+        Py_DECREF(denominator);
+    }
+    return ratio;
+}
+
+
 static PyMethodDef math_methods[] = {
     {"acos",            math_acos,      METH_O,         math_acos_doc},
     {"acosh",           math_acosh,     METH_O,         math_acosh_doc},
+    MATH_AS_INTEGER_RATIO_METHODDEF
     {"asin",            math_asin,      METH_O,         math_asin_doc},
     {"asinh",           math_asinh,     METH_O,         math_asinh_doc},
     {"atan",            math_atan,      METH_O,         math_atan_doc},