Question

Which sign makes the statement true? -3 13/16 -7 1/2

Answer 1

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.

1. Convert \(-3 \frac{13}{16}\) to an improper fraction:
\[
-3 \frac{13}{16} = -\left(3 \times 16 + 13\right) / 16 = -\left(48 + 13\right) / 16 = -61 / 16
\]

2. 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:
\(-3 \frac{13}{16} > -7 \frac{1}{2}\)