What fraction of all four digit natural numbers have a product of their digits that is even?

To find the fraction of four-digit natural numbers with an even product of their digits, we first note that a four-digit number ranges from 1000 to 9999, giving us a total of 9000 four-digit numbers. The product of the digits is even if at least one digit is even. The only case where the product is odd is if all four digits are odd. The odd digits are 1, 3, 5, 7, and 9, offering 5 choices for each digit. Thus, the total odd-digit combinations for four-digit numbers is (5^4 = 625). Therefore, the number of four-digit numbers with an even product is (9000 - 625 = 8375). The fraction is then ( \frac{8375}{9000} = \frac{335}{360} ), which simplifies to approximately ( \frac{67}{72} ).