Which of the following expressions are equivalent to $-\left(\frac{8}{3}\right)$? Choose all answers that apply:
A. $\frac{8}{-3}$
B. $-\frac{8}{-3}$
C. None of the above
Answer (2)
The expression equivalent to − ( 3 8 ) is only − 3 8 . Therefore, the correct choice is (A).
;
We are given the expression − 3 8 .
Option A: − 3 8 is equivalent to − 3 8 .
Option B: − − 3 8 simplifies to 3 8 , which is not equivalent.
Therefore, the answer is A .
Explanation
Understanding the Problem We are given the expression − 3 8 and asked to identify equivalent expressions from a list of options.
Listing the Options The options are: (A) − 3 8 (B) − − 3 8 (C) None of the above
Objective We need to determine which of the given expressions are equivalent to − 3 8 .
Evaluating the Options Let's evaluate each option and compare it to the given expression − 3 8 .
Option (A): − 3 8 = − 3 8 . This is equivalent to the given expression. Option (B): − − 3 8 = − ( − 3 8 ) = 3 8 . This is not equivalent to the given expression.
Identifying Correct Options Based on the evaluation, we can identify all correct options.
Final Answer The expression equivalent to − 3 8 is − 3 8 . Therefore, the correct answer is (A).
Examples
Understanding equivalent expressions is crucial in various real-life scenarios. For instance, when dealing with financial transactions, knowing that $-\frac{ 10}{2} is the same as $\frac{ 10}{-2} helps in interpreting debts or credits accurately. Similarly, in physics, if you're calculating the rate of change of velocity (acceleration) and you find it to be − 2 5 m / s 2 , it's the same as saying the acceleration is − 2 5 m / s 2 , indicating deceleration or slowing down. Recognizing these equivalencies simplifies problem-solving and ensures clear communication.
