how to convert a fraction to float in ruby

Use Rational

>> (Rational(*("1/16".split('/').map( &:to_i )))*45).to_f
=> 2.8125

Looks like you're going to have to parse the fraction yourself. This will work on fractions and whole numbers, but not mixed numbers (ie: 1½ will not work.)

class String
  def to_frac
    numerator, denominator = split('/').map(&:to_f)
    denominator ||= 1
    numerator/denominator
  end
end

"1/16".to_frac * 45