diff --git a/freezegun/api.py b/freezegun/api.py
index 0f11e0c..d235292 100644
--- a/freezegun/api.py
+++ b/freezegun/api.py
@@ -509,10 +509,11 @@ def __init__(self, time_to_freeze: datetime.datetime, start: datetime.datetime):
     def __call__(self) -> datetime.datetime:
         return self.time_to_freeze + (real_datetime.now() - self.start)
 
-    def tick(self, delta: Union[datetime.timedelta, int]=datetime.timedelta(seconds=1)) -> datetime.datetime:
-        if isinstance(delta, numbers.Real):
-            # noinspection PyTypeChecker
-            self.move_to(self.time_to_freeze + datetime.timedelta(seconds=delta))
+    def tick(self, delta: Union[datetime.timedelta, float]=datetime.timedelta(seconds=1)) -> datetime.datetime:
+        if isinstance(delta, numbers.Integral):
+            self.move_to(self.time_to_freeze + datetime.timedelta(seconds=int(delta)))
+        elif isinstance(delta, numbers.Real):
+            self.move_to(self.time_to_freeze + datetime.timedelta(seconds=float(delta)))
         else:
             self.move_to(self.time_to_freeze + delta)  # type: ignore
         return self.time_to_freeze
@@ -531,10 +532,11 @@ def __init__(self, time_to_freeze: datetime.datetime):
     def __call__(self) -> datetime.datetime:
         return self.time_to_freeze
 
-    def tick(self, delta: Union[datetime.timedelta, int]=datetime.timedelta(seconds=1)) -> datetime.datetime:
-        if isinstance(delta, numbers.Real):
-            # noinspection PyTypeChecker
-            self.time_to_freeze += datetime.timedelta(seconds=delta)
+    def tick(self, delta: Union[datetime.timedelta, float]=datetime.timedelta(seconds=1)) -> datetime.datetime:
+        if isinstance(delta, numbers.Integral):
+            self.move_to(self.time_to_freeze + datetime.timedelta(seconds=int(delta)))
+        elif isinstance(delta, numbers.Real):
+            self.move_to(self.time_to_freeze + datetime.timedelta(seconds=float(delta)))
         else:
             self.time_to_freeze += delta  # type: ignore
         return self.time_to_freeze
@@ -557,9 +559,13 @@ def __call__(self) -> datetime.datetime:
         self.tick()
         return return_time
 
-    def tick(self, delta: Union[datetime.timedelta, int, None]=None) -> datetime.datetime:
+    def tick(self, delta: Union[datetime.timedelta, float, None]=None) -> datetime.datetime:
         if not delta:
             delta = datetime.timedelta(seconds=self.step_width)
+        elif isinstance(delta, numbers.Integral):
+            delta = datetime.timedelta(seconds=int(delta))
+        elif isinstance(delta, numbers.Real):
+            delta = datetime.timedelta(seconds=float(delta))
         self.time_to_freeze += delta  # type: ignore
         return self.time_to_freeze
 
diff --git a/tests/test_datetimes.py b/tests/test_datetimes.py
index 12e5949..a6f1989 100644
--- a/tests/test_datetimes.py
+++ b/tests/test_datetimes.py
@@ -1,6 +1,7 @@
 import time
 import calendar
 import datetime
+import fractions
 import unittest
 import locale
 import sys
@@ -180,6 +181,17 @@ def test_manual_increment() -> None:
         assert frozen_datetime.tick(delta=datetime.timedelta(seconds=10)) == expected
         assert frozen_datetime() == expected
 
+        expected = initial_datetime + datetime.timedelta(seconds=22.5)
+        ticked_time = frozen_datetime.tick(
+            delta=fractions.Fraction(3, 2)  # type: ignore
+            # type hints follow the recommendation of
+            # https://peps.python.org/pep-0484/#the-numeric-tower
+            # which means for instance `Fraction`s work at runtime, but not
+            # during static type analysis
+        )
+        assert ticked_time == expected
+        assert frozen_datetime() == expected
+
 
 def test_move_to() -> None:
     initial_datetime = datetime.datetime(year=1, month=7, day=12,
diff --git a/tests/test_operations.py b/tests/test_operations.py
index d34f3dd..49b703d 100644
--- a/tests/test_operations.py
+++ b/tests/test_operations.py
@@ -1,9 +1,11 @@
 import datetime
+import fractions
+import pytest
 from freezegun import freeze_time
 from dateutil.relativedelta import relativedelta
 from datetime import timedelta, tzinfo
 from tests import utils
-from typing import Any
+from typing import Any, Union
 
 
 @freeze_time("2012-01-14")
@@ -102,3 +104,38 @@ def test_auto_tick() -> None:
     auto_incremented_time = datetime.datetime.now()
     assert first_time + datetime.timedelta(seconds=15) == auto_incremented_time
 
+
+@pytest.mark.parametrize(
+    "tick,expected_diff",
+    (
+        (datetime.timedelta(milliseconds=1500), 1.5),
+        (1, 1),
+        (1.5, 1.5),
+        (fractions.Fraction(3, 2), 1.5),
+    )
+)
+def test_auto_and_manual_tick(
+    tick: Union[
+        datetime.timedelta,
+        int,
+        float,
+        # fractions.Fraction,
+        # Fraction works at runtime, but not at type-checking time
+        # cf. https://peps.python.org/pep-0484/#the-numeric-tower
+    ],
+    expected_diff: float
+) -> None:
+    first_time = datetime.datetime(2020, 1, 14, 0, 0, 0, 1)
+
+    with freeze_time(first_time, auto_tick_seconds=2) as frozen_time:
+        frozen_time.tick(tick)
+        incremented_time = datetime.datetime.now()
+        expected_time = first_time + datetime.timedelta(seconds=expected_diff)
+        assert incremented_time == expected_time
+
+        expected_time += datetime.timedelta(seconds=2)  # auto_tick_seconds
+
+        frozen_time.tick(tick)
+        incremented_time = datetime.datetime.now()
+        expected_time += datetime.timedelta(seconds=expected_diff)
+        assert incremented_time == expected_time