Fraction Class in Java: Solution, Explanation & Practice

Problem summary

Create a Fraction class that can add two fractions and simplify the result.

Starter code

// Create Fraction class with:
// - int numerator, denominator
// - Fraction add(Fraction other)
// - void simplify() using GCD
// - String toString() as "num/den"

public class Main {
    public static void main(String[] args) {
        // Test case 1: 1/2 + 1/3
        // Print: <result>
    }
}

Expected output and test cases

• 1/2 + 1/3 = 5/6

  5/6

• 1/2 + 1/2 = 1

  1/1

• 1/4 + 1/2 = 3/4

  3/4

Hints

1. Common denominator: a*d + b*c / b*d
2. Find GCD to simplify
3. Divide both by GCD

Validated solution

class Fraction {
    final int numerator, denominator;
    Fraction(int numerator, int denominator) {
        if (denominator == 0) throw new IllegalArgumentException("zero denominator");
        int gcd = gcd(Math.abs(numerator), Math.abs(denominator));
        this.numerator = numerator / gcd; this.denominator = denominator / gcd;
    }
    Fraction add(Fraction other) { return new Fraction(numerator * other.denominator + other.numerator * denominator, denominator * other.denominator); }
    static int gcd(int a, int b) { while (b != 0) { int r = a % b; a = b; b = r; } return a; }
    public String toString() { return numerator + "/" + denominator; }
}
public class Main { public static void main(String[] args) { System.out.println(new Fraction(1, 2).add(new Fraction(1, 3))); } }

How to approach the problem

Fraction addition uses a common denominator, then the constructor normalizes the result with GCD. Keeping normalization in one place means every new Fraction has the same representation invariant.

Approach

1. Reject a zero denominator.
2. Cross-multiply to add numerators.
3. Reduce the new fraction in the constructor.

Time and space complexity

Time: O(log(min(a, b))) for normalization. Space: O(1).

Edge cases to test

• A negative denominator should be normalized consistently in a fuller implementation.
• Cross-products can overflow int for large inputs.

Common mistakes

• Adding numerators and denominators directly.
• Allowing a denominator of zero.

Follow-up challenge

Normalize signs and compare fractions without converting to double.

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