Rational.scala

class Rational(x: Int, y: Int) {
  
  // private method  
  private def gcd(x: Int, y: Int): Int = if (y == 0) x else gcd(y, x % y)
  
  // private value
  private val g = gcd(x, y)
  
  // accessor methods
  def numer = x / g // normalize using gcd
  def denom = y / g // normalize using gcd
  
  // methods can be used as infix operators
  // e.g. r1 < r2 will rewrite to r1.<(r2)
  def < (that: Rational) = numer * that.denom < that.numer * denom
  
  // addition
  def + (that: Rational) = new Rational(
    numer * that.denom + that.numer * denom,
    denom * that.denom
  )
  
  // symbolic prefix operators
  // use <unary_><symbol>
  def unary_- : Rational = new Rational(-numer, denom)
  
  // subtraction
  def - (that: Rational) = this + -that
  
  // override modifier needed here
  override def toString = numer + "/" + denom
  
}

val r1 = new Rational(1,2)
val r2 = new Rational(1,3)

println(
  r1,
  r2,
  -r1,
  -r2,
  r1 < r2,
  r2 < r1,
  r1 + r2,
  r1 - r2
)