Calculate the value of: 12 3/4 multiplied by the quotient of 1 2/17 divided by 8 1/6, then divided by 5 4/3.

Explanation

First, convert mixed numbers to improper fractions: 12 3/4 = 51/4, 1 2/17 = 19/17, 8 1/6 = 49/6, and 5 4/3 = 19/3. Then, apply the operations step-by-step: (19/17) ÷ (49/6) = (19/17) × (6/49). Multiply 51/4 by this result and then divide by 19/3, which is equivalent to multiplying by 3/19. Simplifying yields 27/98.