Using Python Fractions

Python
from fractions import Fraction

# Create fractions
f1 = Fraction(1, 3)          # 1/3
f2 = Fraction('3.14')        # 157/50 (from decimal string)
f3 = Fraction('22/7')        # from string ratio
f4 = Fraction(0.5)           # 1/2 (exact binary float conversion)
f5 = Fraction(Decimal('1.1'))  # from Decimal, exact

# Arithmetic stays exact
result = Fraction(1, 3) + Fraction(1, 6)  # Fraction(1, 2)
print(result)  # 1/2

1. Choose the right constructor input

   • Fraction(numerator, denominator) — two integers, auto-reduced via GCD
   • Fraction(other_fraction) — copy
   • Fraction(float) — exact value of the float (not the "nice" decimal you'd expect)
   • Fraction(decimal.Decimal) — exact value, preferred over float for decimal-like input
   • Fraction(string) — parses "3/4", "-3/4", "1.5", "1.5e3", with optional whitespace and underscores in numbers

2. Use arithmetic operators normally — + - * / ** all return Fraction (or complex/float when mixed with those types).

3. Access components when needed:

   Python
   f = Fraction(6, 8)   # auto-reduces to Fraction(3, 4)
   f.numerator          # 3
   f.denominator        # 4

4. Convert to/from other numeric types:

   Python
   float(Fraction(1, 3))          # 0.3333333333333333
   Fraction(1, 3).limit_denominator(10)  # Fraction(1, 3) — best approx with denom <= 10
   f.as_integer_ratio()           # (3, 4)

5. Round, floor, ceil — Fractions support round(), math.floor(), math.ceil(), math.trunc() natively.

Example 1: Avoiding float imprecision Input:

Python
0.1 + 0.2 == 0.3  # False due to float rounding
Fraction('0.1') + Fraction('0.2') == Fraction('0.3')

Output: True — exact decimal-string parsing avoids binary float error.

Example 2: Approximating an irrational-ish float as a simple fraction Input:

Python
import math
Fraction(math.pi).limit_denominator(1000)

Output: Fraction(355, 113) — best rational approximation with denominator ≤ 1000.

Example 3: Parsing user input safely Input:

Python
Fraction("  -3/4 ")
Fraction("1_000/2_000")

Output: Fraction(-3, 4), Fraction(1, 2)

Example 4: GCD reduction happens automatically Input: Fraction(10, 4) Output: Fraction(5, 2)