This option is correct because simplifying a ratio involves dividing both terms by their greatest common divisor. The greatest common divisor of 8 and 12 is 4. Dividing both by 4 gives 8:12 = 2:3. Therefore, the simplest form of the ratio is 2:3.
Option A:
The ratio 3:2 reverses the order of the terms and does not preserve the original relationship. It corresponds to 12:8 after scaling, which is not equal to 8:12. Thus, this option is incorrect.
Option B:
The ratio 4:6 is equivalent to 8:12 but not in simplest form. Both terms still have a common factor of 2. Since we can reduce further to 2:3, 4:6 is not fully simplified.
Option C:
The ratio 2:3 is obtained by dividing both 8 and 12 by 4. It has no further common factor greater than 1, so it is in simplest form. This matches the standard requirement for simplified ratios.
Option D:
The ratio 1:3 would correspond to 4:12 when scaled up, which is different from 8:12. Therefore, 1:3 does not represent the same relationship and is not correct.
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