Rational.scala

object Rational {
  implicit def rationalInt(n: Int): Rational =
    Rational(n, 1)

  def gcd(a: Int, b: Int): Int =
    if (b == 0) a else gcd(b, a % b)
}

case class Rational(p: Int, q: Int) {
  require(q != 0, "Denominator 'q' cannot be 0")

  def + (that: Rational) =
    Rational(
      this.p * that.q + that.p * this.q,
      this.q * that.q
    )

  def - (that: Rational) =
    Rational(
      this.p * that.q - that.p * this.q,
      this.q * that.q
    )

  def * (that: Rational) =
    Rational(
      this.p * that.p,
      this.q * that.q
    )

  def / (that: Rational) =
    Rational(
      this.p * that.q,
      this.q * that.p
    )

  def normalized: Rational = {
    val gcd = Rational.gcd(p, q)
    val lcm = p * q / gcd

    Rational(p / gcd, q / gcd)
  }
}

val r1 = Rational(1,5) + Rational(6,4)