Question

Which fractions equal - 9/16 ? Select all that apply. A -3/4 B 9/-16 C 9/16 D 3 /4 E -9/16 F 3 /-4

Answer 1

To determine which fractions are equal to \(-\frac{9}{16}\), we can evaluate each option:

A. \(-\frac{3}{4}\)
To convert \(-\frac{3}{4}\) to a fraction with a denominator of 16, we multiply by \(\frac{4}{4}\):
\[
-\frac{3}{4} = -\frac{3 \times 4}{4 \times 4} = -\frac{12}{16} \quad (\text{not equal})
\]

B. \(\frac{9}{-16}\)
This can be rewritten as \(-\frac{9}{16}\) (since a negative sign in the denominator is equivalent to having it in the numerator):
\[
\frac{9}{-16} = -\frac{9}{16} \quad (\text{equal})
\]

C. \(\frac{9}{16}\)
This fraction is positive and is not equal to \(-\frac{9}{16}\):
\[
\frac{9}{16} \quad (\text{not equal})
\]

D. \(\frac{3}{4}\)
Following the same conversion as in option A:
\[
\frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16} \quad (\text{not equal})
\]

E. \(-\frac{9}{16}\)
This is exactly the same as the target fraction:
\[
-\frac{9}{16} \quad (\text{equal})
\]

F. \(\frac{3}{-4}\)
This can be rewritten as \(-\frac{3}{4}\), which we already evaluated in option A and found it does not equal \(-\frac{9}{16}\):
\[
\frac{3}{-4} = -\frac{3}{4} \quad (\text{not equal})
\]

In conclusion, the fractions that are equal to \(-\frac{9}{16}\) are:
- B. \( \frac{9}{-16} \)
- E. \( -\frac{9}{16} \)

So the correct answers are **B and E**.