Choose the option that is arranged in descending order:

To compare fractions that have different denominators, convert each fraction into an equivalent fraction with a common denominator equal to the LCM of the original denominators. Once every fraction shares the same denominator, the fraction with the larger numerator represents the larger value, so ordering the numerators directly orders the fractions.

1. The four fractions are 3/4, 2/3, 9/16, and 5/12, with denominators 4, 3, 16, and 12 respectively.

2. The LCM of 4, 3, 16, and 12 is 48.

3. Convert each fraction to an equivalent fraction with denominator 48: 3/4 = 36/48, 2/3 = 32/48, 9/16 = 27/48, and 5/12 = 20/48.

4. Compare the numerators over the common denominator 48: 36 > 32 > 27 > 20.

5. Since all four fractions now share the same denominator, a larger numerator means a larger fraction, so arranging the numerators from largest to smallest gives the fractions in descending order: 3/4, 2/3, 9/16, 5/12.

As an independent check, convert each fraction to a decimal: 3/4 = 0.75, 2/3 ≈ 0.667, 9/16 = 0.5625, and 5/12 ≈ 0.417. This decimal ordering (0.75 > 0.667 > 0.5625 > 0.417) confirms the same descending sequence found above.

The sequence 3/4, 2/3, 9/16, 5/12 is therefore the one arranged in descending order.