Final answer:
To evaluate the expression (3 1/2 + 1/4 - 1/8) / 2 1/54, simplify the addition and subtraction inside the parentheses. Then, find a common denominator and combine the fractions. Finally, divide the result by the given mixed number.
Step-by-step explanation:
To evaluate the expression (3 1/2 + 1/4 - 1/8) / 2 1/54, we need to follow the order of operations. First, simplify the addition and subtraction inside the parentheses:
(3 1/2 + 1/4 - 1/8) = (7/2 + 1/4 - 1/8)
Next, find a common denominator for the fractions:
(7/2 + 1/4 - 1/8) = (28/8 + 2/8 - 1/8)
Combine the fractions: (28/8 + 2/8 - 1/8) = 29/8
Now, divide this result by 2 1/54. Convert the mixed number to an improper fraction:
2 1/54 = (108/54 + 1/54) = 109/54
Divide 29/8 by 109/54:
(29/8) / (109/54) = (29/8) * (54/109) = 783/872
So, the answer is 783/872.