まちがった約分なのに、なぜか正しくなる分数

curious.rb

(1..9).each do |a|
  (1..9).each do |b|
    (1..9).each do |c|
      x = (10 * a + b).to_r
      y = (10 * b + c).to_r
      # puts "a = #{a}, b = #{b}, c = #{c}, x = #{x}, y = #{y}"
      if a != c and x / y == a.to_r / c.to_r
        puts "\\frac{#{x.to_i}}{#{y.to_i}} = \\frac{#{a}}{#{c}}, "
      end
    end
  end
end

cf. https://twitter.com/jmitani/status/901083528611323909
cf. https://twitter.com/hyuki/status/901095403415756800