diff --git a/Tests/test_tiff_ifdrational.py b/Tests/test_tiff_ifdrational.py
index c16cd506e65..b38c418dd58 100644
--- a/Tests/test_tiff_ifdrational.py
+++ b/Tests/test_tiff_ifdrational.py
@@ -54,6 +54,16 @@ def test_float() -> None:
     assert math.isnan(float(IFDRational(0, 0)))
 
 
+def test_arithmetic_between_rationals() -> None:
+    a = IFDRational(1, 2)
+    b = IFDRational(1, 3)
+
+    assert a + b == Fraction(5, 6)
+    assert a - b == Fraction(1, 6)
+    assert a * b == Fraction(1, 6)
+    assert a / b == Fraction(3, 2)
+
+
 def test_ranges() -> None:
     for num in range(1, 10):
         for denom in range(1, 10):
diff --git a/src/PIL/TiffImagePlugin.py b/src/PIL/TiffImagePlugin.py
index df0173f2475..5a9cf6b850d 100644
--- a/src/PIL/TiffImagePlugin.py
+++ b/src/PIL/TiffImagePlugin.py
@@ -337,7 +337,10 @@ def _delegate(op: str) -> Any:
     def delegate(
         self: IFDRational, *args: tuple[float, ...]
     ) -> bool | float | Fraction:
-        return getattr(self._val, op)(*args)
+        func = getattr(self._val, op)
+        if len(args) == 1 and isinstance(args[0], IFDRational):
+            return func(args[0]._val)
+        return func(*args)
 
     return delegate
 
@@ -700,7 +703,12 @@ def _setitem(self, tag: int, value: Any, legacy_api: bool) -> None:
                 self.tagtype[tag] = TiffTags.UNDEFINED
                 if all(isinstance(v, IFDRational) for v in values):
                     for v in values:
-                        if v < IFDRational(0):
+                        value = (
+                            v.numerator
+                            if isinstance(v, IFDRational) and v.denominator == 0
+                            else v
+                        )
+                        if value < IFDRational(0):
                             self.tagtype[tag] = TiffTags.SIGNED_RATIONAL
                             break
                     else: