Fraction Class Calculator

/*
 * Problem : Process lines.
 * Input   : Several lines.
 * Output  : One result per line.
 * Approach: A Fraction class.
 * Time    : O(n log V)
 * Space   : O(n)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
        // Step 1: A Fraction keeps a numerator and a denominator. The constructor reduces it and keeps the sign on top.
        static final class Fraction {
            private final long numerator;
            private final long denominator;

            Fraction(long numerator, long denominator) {
                if (denominator == 0) {
                    throw new ArithmeticException("zero denominator");
                }
                long divisor = gcd(Math.abs(numerator), Math.abs(denominator));
                if (divisor == 0) {
                    divisor = 1;
                }
                long sign = denominator < 0 ? -1 : 1;
                this.numerator = sign * numerator / divisor;
                this.denominator = sign * denominator / divisor;
            }

            private static long gcd(long a, long b) {
                return b == 0 ? a : gcd(b, a % b);
            }

            // Step 2: Each operation returns a new Fraction. The old objects do not change (immutable).
            Fraction add(Fraction other) {
                return new Fraction(numerator * other.denominator + other.numerator * denominator, denominator * other.denominator);
            }

            Fraction subtract(Fraction other) {
                return new Fraction(numerator * other.denominator - other.numerator * denominator, denominator * other.denominator);
            }

            Fraction multiply(Fraction other) {
                return new Fraction(numerator * other.numerator, denominator * other.denominator);
            }

            Fraction divide(Fraction other) {
                return new Fraction(numerator * other.denominator, denominator * other.numerator);
            }

            @Override
            public String toString() {
                return denominator == 1 ? String.valueOf(numerator) : numerator + "/" + denominator;
            }
        }

    // This method solves the task. It receives the input and returns the answer.
    static String[] solve(String[] lines) {
        String[] output = new String[lines.length];
        for (int i = 0; i < lines.length; i++) {
            String[] part = lines[i].split(" ");

            // Step 3: Make the fractions and choose the operation. A zero denominator throws an exception, and we print error.
            try {
                Fraction first = new Fraction(Long.parseLong(part[1]), Long.parseLong(part[2]));
                Fraction second = new Fraction(Long.parseLong(part[3]), Long.parseLong(part[4]));
                Fraction result;
                if (part[0].equals("add")) {
                    result = first.add(second);
                } else if (part[0].equals("sub")) {
                    result = first.subtract(second);
                } else if (part[0].equals("mul")) {
                    result = first.multiply(second);
                } else {
                    result = first.divide(second);
                }
                output[i] = result.toString();
            } catch (ArithmeticException error) {
                output[i] = "error";
            }
        }
        return output;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        java.util.List<String> all = new java.util.ArrayList<>();
        while (scanner.hasNextLine()) {
            String line = scanner.nextLine().trim();
            if (!line.isEmpty()) {
                all.add(line);
            }
        }
        String[] lines = all.toArray(new String[0]);
        System.out.println(String.join("\n", solve(lines)));
    }
}