Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 15/2...7

possible digits: 0, 3, 6 or 9

Step-by-step explanation:

To make the fraction reducible, the number in the denominator needs to have a common prime factor with the number in the numerator.

The number in the numerator can be factored in 3 * 5, so the denominator needs to be multiple of 3 or 5.

To be multiple of 5, the last number needs to be 0 or 5, which is not the case.

To be multiple of 3, the sum of the digits needs to be a multiple of 3.

The sum of the digits is 2 + x + 7, with x being the missing digit.

To have a multiple of 3, we have that x + 9 needs to be multiple of 3, so we can have x=0, x=3, x=6 or x=9, which would give us the fractions:

x=0: 15/207 = 5/69

x=3: 15/237 = 5/79

x=6: 15/267 = 5/89

x=9: 15/297 = 5/99