The Fractions module in Python is a built-in module that provides support for rational number arithmetic. It allows you to work with fractions (like 1/2, 3/4, etc.) exactly, without the precision issues that can occur with floating-point numbers.
What Problems Does It Solve?
Problem with Floating-Point Numbers:
python
# Floating-point precision issue print(0.1 + 0.2) # Output: 0.30000000000000004 (not exact!)
Solution with Fractions:
python
from fractions import Fraction # Exact arithmetic print(Fraction(1, 10) + Fraction(2, 10)) # Output: 3/10 (exact!)
Key Features
1. Exact Representation
python
from fractions import Fraction # Fractions represent numbers exactly f1 = Fraction(1, 3) # Exactly 1/3 f2 = Fraction(2, 3) # Exactly 2/3 print(f1 + f2) # Output: 1 (exactly)
2. Automatic Simplification
python
# Fractions are automatically reduced f = Fraction(4, 8) # Becomes 1/2 print(f) # Output: 1/2 f = Fraction(9, 12) # Becomes 3/4 print(f) # Output: 3/4
3. Multiple Ways to Create Fractions
python
from fractions import Fraction
# Different creation methods
a = Fraction(1, 2) # From numerator/denominator
b = Fraction('3/4') # From string
c = Fraction(0.25) # From float (be careful!)
d = Fraction(5) # From integer (5/1)
print(a) # 1/2
print(b) # 3/4
print(c) # 1/4
print(d) # 5
Importing the Module
python
from fractions import Fraction
Creating Fractions
1. From integers (numerator/denominator)
python
# Create fraction 1/2 f1 = Fraction(1, 2) print(f1) # Output: 1/2 # Create fraction 3/4 f2 = Fraction(3, 4) print(f2) # Output: 3/4
2. From strings
python
# From string representation
f3 = Fraction('1/3')
print(f3) # Output: 1/3
f4 = Fraction('2/5')
print(f4) # Output: 2/5
3. From floats (be careful with this!)
python
# From float - may have precision issues f5 = Fraction(0.5) print(f5) # Output: 1/2 f6 = Fraction(0.25) print(f6) # Output: 1/4
4. From single number (numerator with denominator 1)
python
f7 = Fraction(5) # 5/1 print(f7) # Output: 5 f8 = Fraction(-3) # -3/1 print(f8) # Output: -3
Basic Arithmetic Operations
python
# Create some fractions a = Fraction(1, 2) # 1/2 b = Fraction(1, 4) # 1/4 # Addition print(a + b) # Output: 3/4 # Subtraction print(a - b) # Output: 1/4 # Multiplication print(a * b) # Output: 1/8 # Division print(a / b) # Output: 2
Accessing Numerator and Denominator
python
f = Fraction(3, 8) print(f.numerator) # Output: 3 print(f.denominator) # Output: 8 print(float(f)) # Output: 0.375
Automatic Simplification
python
# Fractions are automatically simplified f1 = Fraction(2, 4) # Becomes 1/2 print(f1) # Output: 1/2 f2 = Fraction(4, 8) # Becomes 1/2 print(f2) # Output: 1/2 f3 = Fraction(6, 9) # Becomes 2/3 print(f3) # Output: 2/3
Comparing Fractions
python
f1 = Fraction(1, 2) f2 = Fraction(2, 4) f3 = Fraction(3, 4) print(f1 == f2) # Output: True (both are 1/2) print(f1 < f3) # Output: True (1/2 < 3/4) print(f3 > f1) # Output: True (3/4 > 1/2)
Practical Examples
Example 1: Recipe Scaling
python
# Original recipe: 3/4 cup flour, 1/2 cup sugar
# Double the recipe
flour = Fraction(3, 4)
sugar = Fraction(1, 2)
double_flour = flour * 2
double_sugar = sugar * 2
print(f"Double flour: {double_flour} cups") # 3/2 cups
print(f"Double sugar: {double_sugar} cups") # 1 cup
Example 2: Pizza Sharing
python
# 3 friends sharing 2 pizzas
pizzas = Fraction(2, 1)
friends = 3
each_gets = pizzas / friends
print(f"Each friend gets: {each_gets}") # Output: 2/3 of a pizza
Example 3: Mixed Numbers
python
# Convert improper fraction to mixed number
def to_mixed_number(fraction):
whole = fraction.numerator // fraction.denominator
remainder = fraction.numerator % fraction.denominator
if whole == 0:
return f"{remainder}/{fraction.denominator}"
elif remainder == 0:
return str(whole)
else:
return f"{whole} {remainder}/{fraction.denominator}"
f = Fraction(7, 3) # 7/3 = 2 1/3
print(to_mixed_number(f)) # Output: 2 1/3
Important Notes
- Fractions are automatically reduced to their simplest form
- Use strings instead of floats when possible to avoid precision issues
- You can mix fractions with integers in calculations
- Negative fractions work as expected
python
# Mixing with integers f = Fraction(1, 3) result = f + 1 # 1/3 + 1 = 4/3 print(result) # Output: 4/3 # Negative fractions neg_f = Fraction(-1, 2) print(neg_f) # Output: -1/2
The fractions module is perfect when you need exact rational arithmetic without the rounding errors that can occur with floating-point numbers!
