= Solution
Place an <implicit conversion> in the companion object and import it into the client scope, so it is available for both an integer argument and an integer receiver:
``
import scala.language.implicitConversions
class Rational(n0: BigInt, d0: BigInt) {
def this(n: Int, d: Int) = this(BigInt(n), BigInt(d))
require(d0 != 0)
private val g = n0.abs.gcd(d0.abs)
val num: BigInt = (if (d0 < 0) -n0 else n0) / g
val den: BigInt = d0.abs / g
def *(r: Rational): Rational =
new Rational(num*r.num, den*r.den)
override def toString: String =
if (den == 1) num.toString else num.toString + "/" + den.toString
}
object Rational {
implicit def fromInt(n: Int): Rational = new Rational(n,1)
}
import Rational._
val r1 = new Rational(3,7)
val r2 = new Rational(-11,-5)
println(r1*r2)
println(r1*3)
println(7*r1)
``
Normalization gives $r_2=11/5$. The output lines are \b[`33/35`, `9/7`, `3`]. For `r1*3`, the argument is converted; for `7*r1`, conversion supplies the receiver's rational multiplication method. `BigInt` keeps the exact <rational arithmetic> independent of fixed-width product overflow.
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