"""练习 21 进阶版：用 map 一次转换分数行和实数行。"""
from fractions import Fraction

n = int(input())
rational_a, rational_b = map(Fraction, input().split())
real_a, real_b = map(float, input().split())

print("integer:", n)
print("is natural (including 0):", n >= 0)
print("integer is also rational and real:", True)
print("rational type:", type(rational_a).__name__)
print("real approximation type:", type(real_a).__name__)
print("rational + - *:", rational_a + rational_b, rational_a - rational_b, rational_a * rational_b)
print("rational /:", rational_a / rational_b if rational_b else "undefined when divisor is 0")
print("real + - *:", real_a + real_b, real_a - real_b, real_a * real_b)
print("real /:", real_a / real_b if real_b else "undefined when divisor is 0")