in a fraction with a denominator of 15, which values could the numerator be to produce a repeating decimal
The numerator could be any value that is not divisible by 3 or 5. For example, 1/15 = 0.0666... (repeating 6s), 2/15 = 0.1333... (repeating 3s), 4/15 = 0.2666... (repeating 6s), 7/15 = 0.4666... (repeating 6s), 8/15 = 0.5333... (repeating 3s), 11/15 = 0.7333... (repeating 3s), 13/15 = 0.8666... (repeating 6s), etc.
To determine the values for the numerator in a fraction with a denominator of 15 that would produce a repeating decimal, we need to find the prime factorization of 15. The prime factorization of 15 is 3 * 5.
In order for the fraction to produce a repeating decimal, the denominator needs to be divisible only by prime factors of 10 (2 and 5). Since the prime factorization of 15 contains a 3, the numerator would need to have a factor of 3 to produce a repeating decimal.
Therefore, any numerator value that is divisible by 3, such as 3, 6, 9, 12, and so on, could produce a repeating decimal when divided by 15.