code.rb

class A
  def foo
    "a"
  end
end

class B < A
  def foo
    v = super
    "b#{v}"
  end
end

module M
  def foo
    v = super
    v.upcase
  end
end

b1 = B.new.extend(M)
p b1.singleton_class.ancestors
p b1.foo
b2 = B.new
b2.singleton_class.include(M)
p b2.singleton_class.ancestors
p b2.foo
b3 = B.new
b3.singleton_class.prepend(M)
p b3.singleton_class.ancestors
p b3.foo

run.out

ruby hoge.rb 
[#<Class:#<B:0x007f98b9962c70>>, M, B, A, Object, Kernel, BasicObject]
"BA"
[#<Class:#<B:0x007f98b99626a8>>, M, B, A, Object, Kernel, BasicObject]
"BA"
[M, #<Class:#<B:0x007f98b9962180>>, B, A, Object, Kernel, BasicObject]
"BA"