To compare the two values, we can convert them to improper fractions:
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For \(-8 \frac{1}{5}\):
- Convert to an improper fraction: \(-8 \frac{1}{5} = -\frac{41}{5}\) (since \(-8 \times 5 = -40\) and \(-40 + 1 = -41\))
-
For \(-8 \frac{3}{4}\):
- Convert to an improper fraction: \(-8 \frac{3}{4} = -\frac{35}{4}\) (since \(-8 \times 4 = -32\) and \(-32 + 3 = -35\))
Now, we can compare \(-\frac{41}{5}\) and \(-\frac{35}{4}\). To do this, we can find a common denominator. The least common multiple of 5 and 4 is 20.
Convert both fractions:
- \(-\frac{41}{5} = -\frac{41 \times 4}{5 \times 4} = -\frac{164}{20}\)
- \(-\frac{35}{4} = -\frac{35 \times 5}{4 \times 5} = -\frac{175}{20}\)
Now we can compare: \[ -\frac{164}{20} > -\frac{175}{20} \]
So, \(-8 \frac{1}{5} > -8 \frac{3}{4}\).
The correct sign to make the statement true is: