diff --git a/Lib/fractions.py b/Lib/fractions.py
index f9ac882ec002fa..738a0d4c301d43 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -245,14 +245,16 @@ def limit_denominator(self, max_denominator=1000000):
break
p0, q0, p1, q1 = p1, q1, p0+a*p1, q2
n, d = d, n-a*d
-
k = (max_denominator-q0)//q1
- bound1 = Fraction(p0+k*p1, q0+k*q1)
- bound2 = Fraction(p1, q1)
- if abs(bound2 - self) <= abs(bound1-self):
- return bound2
+
+ # Determine which of the candidates (p0+k*p1)/(q0+k*q1) and p1/q1 is
+ # closer to self. The distance between them is 1/(q1*(q0+k*q1)), while
+ # the distance from p1/q1 to self is d/(q1*self._denominator). So we
+ # need to compare 2*(q0+k*q1) with self._denominator/d.
+ if 2*d*(q0+k*q1) <= self._denominator:
+ return Fraction(p1, q1, _normalize=False)
else:
- return bound1
+ return Fraction(p0+k*p1, q0+k*q1, _normalize=False)
@property
def numerator(a):
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