Division by subtraction example in F#

DivisionBySubtraction.fs

type DivisionProblem =
    {
        Dividend : int
        Divisor : int
    }
type DivisionSolution =
    {
        Quotient : int
        Remainder : int
        Divisor : int
    }
    member solution.AsString =
        if solution.Remainder = 0 then string solution.Quotient
        else String.Format ("{0}-{1}/{2}", solution.Quotient, solution.Remainder, solution.Divisor)
let divide (problem:DivisionProblem) =
    let rec divisionBySubtraction (solutionSoFar:DivisionSolution) =
        if solutionSoFar.Remainder > problem.Divisor then
            divisionBySubtraction
                { solutionSoFar with
                    Quotient = solutionSoFar.Quotient + 1
                    Remainder = solutionSoFar.Remainder - problem.Divisor }
        elif solutionSoFar.Remainder = problem.Divisor then
            { solutionSoFar with
                Quotient = solutionSoFar.Quotient + 1
                Remainder = 0 }
        else
            solutionSoFar
    divisionBySubtraction { Quotient = 0; Remainder = problem.Dividend; Divisor = problem.Divisor }

[<Fact>]
let tryDivision () =
    let five = divide { Dividend = 55; Divisor = 11 }
    let sixAndSevenEighths = divide { Dividend = 55; Divisor = 8 }
    let one = divide { Dividend=10; Divisor=10 }
    Assert.Equal(5, five.Quotient)
    Assert.Equal(0, five.Remainder)
    Assert.Equal(6, sixAndSevenEighths.Quotient)
    Assert.Equal(7, sixAndSevenEighths.Remainder)
    Assert.Equal(8, sixAndSevenEighths.Divisor)
    Assert.Equal(1, one.Quotient)
    Assert.Equal(0, one.Remainder)