Question

Drako found an emerald in a cave at a depth between Negative one-half and Negative 1 and two-thirds meters. Which number could represent the depth at which the emerald is located?

A number line going from negative 3 to positive 3 in increments of 1.
Negative 2 and one-third meters
Negative three-fourths meters
Negative one-fourth meters
Negative 1 and StartFraction 5 Over 6 EndFraction meters

Answer 1

To find a number that represents the depth at which the emerald is located, we need to identify a number that falls within the range between \(-\frac{1}{2}\) and \(-\frac{5}{3}\) meters.

First, let's convert the fractions to have a common denominator for easier comparison:

1. \(-\frac{1}{2} = -\frac{3}{6}\)
2. \(-\frac{5}{3} = -\frac{10}{6}\)

So the range is between:
\[
-\frac{5}{3} \text{ meters} \quad \text{to} \quad -\frac{1}{2} \text{ meters}
\]
or:
\[
-\frac{10}{6} \text{ meters} \quad \text{to} \quad -\frac{3}{6} \text{ meters}
\]

Now, let's check each option to see if it lies within this range:

1. **Negative \(2 \frac{1}{3}\) meters** (which is \(-\frac{7}{3}\)):
\(-\frac{7}{3}\) is less than \(-\frac{10}{6}\) (it is more negative), so it does not fit in the range.

2. **Negative \(\frac{3}{4}\) meters**:
This is equivalent to \(-0.75\) or \(-\frac{9}{12}\), which is larger (less negative than) both \(-\frac{10}{6}\) and \(-\frac{3}{6}\), so it does not fit in the range.

3. **Negative \(\frac{1}{4}\) meters**:
This is equivalent to \(-0.25\) or \(-\frac{3}{12}\), which is larger than \(-\frac{3}{6}\), so it does not fit in the range.

4. **Negative \(1 \frac{5}{6}\) meters** (which is \(-\frac{11}{6}\)):
\(-\frac{11}{6}\) is also less than \(-\frac{10}{6}\), so it does not fit in the range.

Since we have checked all options and found none fall within \(-\frac{10}{6}\) and \(-\frac{3}{6}\), none of the provided numbers represents the depth at which the emerald is located.

Upon double-checking:
- The valid numbers must be in the range \(-\frac{10}{6} \leq \text{number} < -\frac{3}{6}\), equivalent to \(-1.6667\) to \(-0.5\).

None of the given numbers fit that criteria:
So:

**None of the provided options accurately represent the depth.**