Fraction Module in Python

The fractions module in Python allows you to perform arithmetic operations with rational numbers while maintaining precision.

Why use the fractions module?

Unlike floating-point numbers (float type), which may cause precision errors, the Fraction class provides exact arithmetic with rational numbers.
It supports addition, subtraction, multiplication, and division without rounding errors.

1. Importing the `fractions` Module

To use Fraction, first import the module:

from fractions import Fraction

2. Creating Fractions

The Fraction class allows you to create fractions in multiple ways.

2.1 From Integers (Numerator/Denominator)

You can create a fraction by passing two integers, where the first number is the numerator and the second is the denominator.

from fractions import Fraction

f1 = Fraction(3, 4)  # Represents 3/4
print(f1)

Output:

3/4

The fraction 3/4 remains unchanged.

2.2 From a String

You can also create a Fraction using a string representation:

f2 = Fraction("5/8")
print(f2)

Output:

5/8

This is useful when reading fractions from user input or text files.

2.3 From a Floating-Point Number

When you pass a floating-point number, Python converts it into an exact fraction.

f3 = Fraction(0.75)
print(f3)

Output:

3/4

Python automatically simplifies 0.75 to 3/4 using the greatest common divisor (GCD).

2.4 From a Decimal Number

When using floating-point numbers, precision issues can occur. Instead, you can use decimal.Decimal for more accurate conversions.

from decimal import Decimal

f4 = Fraction(Decimal('0.1'))  # Using Decimal instead of float
print(f4)

Output:

1/10

Decimal('0.1') is an exact representation, unlike Fraction(0.1), which can lead to floating-point inaccuracies.

3. Fraction Arithmetic Operations

Fractions in Python support all arithmetic operations.

3.1 Addition of Fractions

f1 = Fraction(1, 4)
f2 = Fraction(1, 2)

result = f1 + f2
print(result)

Output:

3/4

The sum of 1/4 and 1/2 is 3/4 because:

\frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4} ]

3.2 Subtraction of Fractions

result = f2 - f1
print(result)

Output:

1/4

The difference between 1/2 and 1/4 is 1/4 because:

\frac{1}{2} – \frac{1}{4} = \frac{2}{4} – \frac{1}{4} = \frac{1}{4} ]

3.3 Multiplication of Fractions

result = f1 * f2
print(result)

Output:

1/8

Multiplication formula:

\frac{1}{4} \times \frac{1}{2} = \frac{1 \times 1}{4 \times 2} = \frac{1}{8} ]

3.4 Division of Fractions

result = f1 / f2
print(result)

Output:

1/2

Division formula:

\frac{1}{4} \div \frac{1}{2} = \frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2} ]

4. Properties of a Fraction

Each fraction has two properties:

numerator → The top part of the fraction
denominator → The bottom part of the fraction

f = Fraction(5, 10)

print(f.numerator)    
print(f.denominator)

Output:

1
2

Python simplifies 5/10 to 1/2, so the numerator is 1 and the denominator is 2.

5. Limiting the Denominator

Sometimes, fractions derived from floats have very large denominators. Use limit_denominator() to find an approximate fraction.

f = Fraction(3.14159)  # Creates a fraction close to π
print(f)

approx = f.limit_denominator(1000)
print(approx)

Output:

314159/100000
355/113

355/113 is a common approximation of π.

6. Mixed Operations with Integers and Floats

Fractions can interact with other data types.

print(Fraction(1, 3) + 1)      # Adds an integer
print(Fraction(1, 3) + 0.5)    # Adds a float

Output:

4/3
0.8333333333333333

If a fraction is added to a float, the result is converted to a float.

7. Comparing Fractions

Fractions can be compared using standard operators.

print(Fraction(1, 2) > Fraction(1, 3))  
print(Fraction(3, 4) == Fraction(6, 8))

Output:

True
True

1/2 is greater than 1/3
3/4 and 6/8 are equivalent.

8. Converting Fractions

8.1 Convert to Float

print(float(Fraction(3, 4)))

Output:

0.75

8.2 Convert to Integer

print(int(Fraction(5, 2)))

Output:

The integer part of 5/2 is 2 (truncates the decimal).

9. Greatest Common Divisor (GCD) Calculation

Python automatically simplifies fractions using GCD.

import math
print(math.gcd(12, 16))

Output:

The GCD of 12 and 16 is 4.

Summary

Feature	Example Usage
Create fraction from numbers	`Fraction(3, 4)` → `3/4`
Create from string	`Fraction("5/8")` → `5/8`
Arithmetic operations	`Fraction(1, 2) + Fraction(1, 3)` → `5/6`
Convert to float	`float(Fraction(3, 4))` → `0.75`
Limit denominator	`Fraction(3.14159).limit_denominator(1000)` → `355/113`
Access numerator/denominator	`f.numerator`, `f.denominator`