To determine which sign makes the statement true for the expression \(-3 \frac{13}{16} \) and \(-7 \frac{1}{2} \), we need to compare the two numbers.
First, let's convert both mixed numbers into improper fractions or decimal forms for easier comparison.
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Convert \(-3 \frac{13}{16}\) to an improper fraction: \[ -3 \frac{13}{16} = -\left(3 \times 16 + 13\right) / 16 = -\left(48 + 13\right) / 16 = -61 / 16 \]
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Convert \(-7 \frac{1}{2}\) to an improper fraction: \[ -7 \frac{1}{2} = -\left(7 \times 2 + 1\right) / 2 = -\left(14 + 1\right) / 2 = -15 / 2 \]
Next, we will convert \(-15/2\) into a fraction with a denominator of 16 for easier comparison: \[ -15 / 2 = -15 \times \frac{8}{8} = -120 / 16 \]
Now, we compare \(-61 / 16\) and \(-120 / 16\):
- Since \(-120 / 16 < -61 / 16\), we have: \[ -3 \frac{13}{16} > -7 \frac{1}{2} \]
The comparison can be made using these signs:
\[ -3 \frac{13}{16} > -7 \frac{1}{2} \]
Thus, the statement is true with the "greater than" sign.
The final conclusion is: \(-3 \frac{13}{16} > -7 \frac{1}{2}\)