Final answer:
To perform the indicated operation with fractions and decimals, subtract the fractions ((5/4) - (2/3)), then divide the result by the fraction (1/6). The final answer is 7/2.
Step-by-step explanation:
To perform the indicated operation, ((5/4) - (2/3)) ÷ (1/6), we will follow the order of operations, which is parentheses, multiplication and division (from left to right), and then addition and subtraction (from left to right).
First, evaluate the subtraction inside the parentheses: 5/4 - 2/3.
To subtract fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 12. Multiply the numerator and denominator of the first fraction (5/4) by 3, and the numerator and denominator of the second fraction (2/3) by 4.
Now, subtract the fractions: (15/12) - (8/12) = 7/12.
Next, divide the result by the fraction (1/6). Division of fractions is equivalent to multiplying by the reciprocal. The reciprocal of 1/6 is 6/1.
Therefore, (7/12) ÷ (1/6) = (7/12) * (6/1) = 42/12.
Simplify the result: 42/12 = 21/6 = 7/2.