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:

1. numerator → The top part of the fraction
2. 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:

2

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:

4

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