Final answer:
The correct answer is option A. The fraction representing the blue tiles in Judy's mosaic is 8/12, which simplifies to 2/3 after dividing both numerator and denominator by their greatest common divisor, 4.
Step-by-step explanation:
Judy uses 12 tiles to make a mosaic. Eight of these tiles are blue. To find the fraction representing the blue tiles, you divide the number of blue tiles by the total number of tiles. Therefore, you have 8 blue tiles out of 12 tiles in total. This fraction is 8/12.
To simplify this fraction, you need to reduce it to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 8 and 12 is 4. Dividing the numerator (8) by 4 gives 2, and dividing the denominator (12) by 4 gives 3. Thus, the fraction 8/12 simplifies to 2/3.
Therefore, the fraction representing the blue tiles in its simplest form is 2/3, making option A the correct answer.