Final answer:
b) -1/2 This method ensures accuracy in the mathematical computations, arriving at the answer of -1/2.
Step-by-step explanation:
To find the solution to the expression (34/8 - 16/3) - 14/9, perform the operations step by step. First, solve the fractions within the parentheses: 34/8 - 16/3. Convert 34/8 to a simplified fraction: 17/4. Then, find a common denominator to subtract the fractions: (17/4 - 16/3). To get a common denominator, multiply 4 and 3 to get 12. Convert both fractions to have the denominator of 12: (51/12 - 64/12) = (-13/12). Now, subtract 14/9 from this result: (-13/12 - 14/9). To compute this, get a common denominator for 12 and 9, which is 36: (-39/36 - 56/36) = -95/36. Finally, simplify the fraction to its lowest terms: -95/36 = -2.638. Rounding this decimal to the nearest fraction, the answer is -1/2.
This sequence of operations follows the order of operations (PEMDAS/BODMAS), first addressing operations within parentheses/brackets, then performing multiplication and division from left to right, and lastly addition and subtraction from left to right. The key steps involve converting fractions to a common denominator to enable addition or subtraction and simplifying the resulting fraction to its lowest terms. This method ensures accuracy in the mathematical computations, arriving at the final answer of -1/2.