Final answer:
By following the order of operations (PEMDAS), we find that (3/4) * ((27/8) + (11/6)) / (17/8) - (9/2) simplifies to roughly -2.49.
Step-by-step explanation:
To solve the given problem, (3/4) * ((27/8) + (11/6)) / (17/8) - (9/2), you must remember the order of operations, which is parantheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). This is commonly known by the acronym PEMDAS.
First, simplify the terms inside the parantheses: (27/8) + (11/6) equals approximately 5.38.
Next, multiply this sum by 3/4, which gives approximately 4.04.
Then, divide this product by 17/8, which equals approximately 2.01.
Finally, subtract 9/2 (or 4.5) from this quotient. This gives a main answer of approximately -2.49.
So, the original expression simplifies to roughly -2.49 when you follow the order of operations.
In conclusion, it is crucial to apply the rules of mathematics consistently and correctly to arrive at the correct solution.
Learn more about Order of Operations