Addition of two fractions
Detailed guide and Python implementation for the 'Addition of two fractions' problem.
Problem Statement
Write a function add_fractions(a, b, c, d) that takes four integers representing two fractions a/b and c/d, and returns the result as a tuple (numerator, denominator) in its simplest form (reduced by GCD).
The formula for adding fractions is: a/b + c/d = (a*d + b*c) / (b*d), then simplify by dividing both numerator and denominator by their GCD.
- •1 <= b, d <= 1000
- •-1000 <= a, c <= 1000
- •b and d are not zero
Examples
add_fractions(1, 2, 1, 3)
(5, 6)
1/2 + 1/3 = (1×3 + 2×1) / (2×3) = 5/6. GCD(5,6) = 1, so result is 5/6.
add_fractions(2, 4, 3, 6)
(1, 1)
2/4 + 3/6 = (2×6 + 4×3) / (4×6) = 24/24 = 1/1.
add_fractions(1, 3, 2, 3)
(1, 1)
1/3 + 2/3 = 3/3 = 1/1.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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