Rational

import java.math.BigInteger;

public class Rational implements Comparable<Rational> {
  BigInteger num;
  BigInteger den;

  public static final Rational ZERO = new Rational(0);
  public static final Rational ONE = new Rational(1);
  public static final Rational TWO = new Rational(2);
  public static final Rational POSITIVE_INFINITY = new Rational(1, 0);
  public static final Rational NEGATIVE_INFINITY = new Rational(-1, 0);

  public Rational(long num) {
    this.num = BigInteger.valueOf(num);
    this.den = BigInteger.ONE;
  }

  public Rational(long num, long den) {
    this(BigInteger.valueOf(num), BigInteger.valueOf(den));
  }

  public Rational(BigInteger num, BigInteger den) {
    this.num = num;
    this.den = den;
    reduce();
  }

  void reduce() {
    if (!den.abs().equals(BigInteger.ONE)) {
      BigInteger gcd = num.gcd(den);
      if (gcd.signum() != 0 && !gcd.equals(BigInteger.ONE)) {
        num = num.divide(gcd);
        den = den.divide(gcd);
      }
    }
    if (den.signum() < 0 || den.signum() == 0 && num.signum() < 0) {
      num = num.negate();
      den = den.negate();
    }
  }

  public Rational add(Rational r) {
    return new Rational(num.multiply(r.den).add(r.num.multiply(den)), den.multiply(r.den));
  }

  public Rational sub(Rational r) {
    return new Rational(num.multiply(r.den).subtract(r.num.multiply(den)), den.multiply(r.den));
  }

  public Rational mul(Rational r) {
    return new Rational(num.multiply(r.num), den.multiply(r.den));
  }

  public Rational div(Rational r) {
    return new Rational(num.multiply(r.den), den.multiply(r.num));
  }

  public Rational negate() {
    return new Rational(num.negate(), den);
  }

  public Rational inverse() {
    return new Rational(den, num);
  }

  public Rational abs() {
    return new Rational(num.abs(), den);
  }

  public int signum() {
    return num.signum();
  }

  public double doubleValue() {
    return num.doubleValue() / den.doubleValue();
  }

  public double longValue() {
    return num.longValue() / den.longValue();
  }

  public int compareTo(Rational other) {
    return (num.multiply(other.den).compareTo(other.num.multiply(den)));
  }

  public boolean equals(Object obj) {
    return num.equals(((Rational) obj).num) && den.equals(((Rational) obj).den);
  }

  public int hashCode() {
    return num.hashCode() * 31 + den.hashCode();
  }

  public String toString() {
    return num + "/" + den;
  }

  // Usage example
  public static void main(String[] args) {
    Rational a = new Rational(1, 3);
    Rational b = new Rational(1, 6);
    Rational c = new Rational(1, 2);
    System.out.println(true == c.equals(a.add(b)));
  }
}