To determine where the treasure is located between \(-13\frac{4}{5}\) feet and \(-21\frac{2}{5}\) feet, we first convert these mixed numbers into improper fractions for easier comparison.
-
Convert \(-13\frac{4}{5}\):
\[ -13\frac{4}{5} = -\left(13 \times 5 + 4\right)/5 = -\frac{65 + 4}{5} = -\frac{69}{5} \]
-
Convert \(-21\frac{2}{5}\):
\[ -21\frac{2}{5} = -\left(21 \times 5 + 2\right)/5 = -\frac{105 + 2}{5} = -\frac{107}{5} \]
Now we have:
- Upper limit: \(-\frac{69}{5}\)
- Lower limit: \(-\frac{107}{5}\)
Next, we identify which of the provided options falls between these two values.
-
Negative 1 and one-half:
\[ -1\frac{1}{2} = -\frac{3}{2} = -\frac{7.5}{5} \]
-
Negative 2 and three-fourths:
\[ -2\frac{3}{4} = -\frac{11}{4} = -\frac{13.75}{5} \]
-
Negative 1 and one-fourth:
\[ -1\frac{1}{4} = -\frac{5}{4} = -\frac{6.25}{5} \]
-
Negative 2 and one-fourth:
\[ -2\frac{1}{4} = -\frac{9}{4} = -\frac{11.25}{5} \]
Now let's compare all the values:
- The converted bounds are:
- Upper limit: \(-\frac{69}{5} \approx -13.8\)
- Lower limit: \(-\frac{107}{5} \approx -21.4\)
Now, we will convert each candidate:
- Negative 1 and one-half: \(-\frac{7.5}{5}\) (which is greater than \(-\frac{69}{5}\) and not in bounds)
- Negative 2 and three-fourths: \(-\frac{13.75}{5}\) (which is also greater than \(-\frac{69}{5}\) and not in bounds)
- Negative 1 and one-fourth: \(-\frac{6.25}{5}\) (which is also greater than \(-\frac{69}{5}\) and not in bounds)
- Negative 2 and one-fourth: \(-\frac{11.25}{5}\)
From the values above, we can see that:
- \(-\frac{11.25}{5}\) = -2.25 falls between -21.4 and -13.8.
Thus the correct answer is: Negative 2 and one-fourth.
3 answers