The Correct Answer and Explanation is:
Based on a mathematical evaluation of the provided options, none of them are equivalent to the fraction -9/16. A fraction is considered equal to another if they represent the same numerical value. We can analyze each choice to demonstrate why it is not the correct answer.
The question asks for a fraction that equals -9/16. This is a specific negative value. The correct answer must have the exact same value, even if it looks different, for instance, if it were an unsimplified fraction like -18/32.
Let’s examine the choices:
Option A is -3/4. To properly compare -3/4 with -9/16, we can find a common denominator, which is 16. To convert the denominator of 4 to 16, we multiply it by 4. We must do the same to the numerator to keep the fraction’s value the same. This gives us (-3 × 4) / (4 × 4), which equals -12/16. Since -12/16 is not equal to -9/16, option A is incorrect, even though it is circled in the image.
Options B and C are both 9/16. The most important difference here is the sign. The target fraction, -9/16, is negative, while 9/16 is positive. A positive number can never be equal to a negative number. Therefore, both options B and C are incorrect.
Option D is 3/4. Similar to options B and C, this is a positive fraction. It cannot be equal to the negative fraction -9/16. So, option D is also incorrect.
In conclusion, there appears to be an error in the question or the provided options, as none of the choices are mathematically equivalent to -9/16. The only fraction that truly equals -9/16 is -9/16 itself or another fraction that simplifies to it, none of which are listed.
