class Rational(object):
  def __init__(self,a,b=1):
    if(b ==0 ):#對於分母為0的情況直接舉異常
      raise Exception("Denominator must not be 0!")
    else:
      g = self.gcd(abs(a), abs(b))#求分子分母的最大公約數然後進行約分
      self.a = a/g
      self.b = b/g

  def gcd(self,a,b):#求最大公約數
    if(b==0):return a
    else:return self.gcd(b,a%b)
#以下為運算子過載
 

  def __add__(self, another):
    try:
      return Rational(self.a*another.b +another.a*self.b,self.b*another.b)
    except TypeError:
      return NotImplemented

  def __mul__(self, another):
    try:
      return Rational(self.a*another.a,self.b*another.b)
    except TypeError:
      return NotImplemented
 


  def __sub__(self, another):
    try:
      return Rational(self.a * another.b - self.b * another.a, self.b * another.b)
    except TypeError:
      return NotImplemented

  def __div__(self, another):
    try:
      return Rational(self.a * another.b, self.b * another.a)
    except TypeError:
      return
 
 NotImplemented

  def __str__(self):
    return '%s/%s' % (self.a, self.b) if self.b != 1 else str(self.a)

# Below are tests:

a = Rational(3,6)
b = Rational(4,5)

print a,b

print a+b
print a*b
print b-a
print b/a

a = Rational(3,7)
b = Rational(4)
print a,b

print a+b
print a*b
print b-a
print b/a

a = Rational(3)
b = Rational(4,7)
print a,b

print a+b
print a*b
print b-a
print b/a

注意

在運算子過載的時候Python2和Python3有細微的不同，如果沒有實際經驗會報以下錯誤

TypeError: unsupported operand type(s) for /: ‘Rational’ and ‘Rational’

問題主要出在過載除法運算子的時候2和3有以下差異：

Python3 uses special division names: __truediv__ and __floordiv__ for the / and // operators, respectively.
python2 uses __div__