Question

The first wave knocked into the water,

a gold coin, which sank to −1
2
foot below the surface.

a bronze cup, at −1
4
foot.

a silver necklace, at −5
8
foot.

a copper coin, at −7
8
foot.

Meg needs to recover the deepest treasure first. Can you help her locate the treasures on the number line? Which one is deepest?

Answer 1

To locate the treasures on a number line, we can convert the given depths into improper fractions for easier comparison.

Here are the depths represented as improper fractions:

1. Gold coin: \(-\frac{1}{2}\) foot
2. Bronze cup: \(-\frac{1}{4}\) foot
3. Silver necklace: \(-\frac{5}{8}\) foot
4. Copper coin: \(-\frac{7}{8}\) foot

Now let's express these fractions with a common denominator to make comparison easier. The least common multiple of the denominators 2, 4, and 8 is 8.

Converting each fraction:

1. Gold coin: \(-\frac{1}{2} = -\frac{4}{8}\)
2. Bronze cup: \(-\frac{1}{4} = -\frac{2}{8}\)
3. Silver necklace: \(-\frac{5}{8}\) (stays the same)
4. Copper coin: \(-\frac{7}{8}\) (stays the same)

Now we can list the treasures in order from least to most negative (which indicates depth):

1. Bronze cup: \(-\frac{2}{8}\) foot (or -0.25 foot)
2. Gold coin: \(-\frac{4}{8}\) foot (or -0.5 foot)
3. Silver necklace: \(-\frac{5}{8}\) foot (or -0.625 foot)
4. Copper coin: \(-\frac{7}{8}\) foot (or -0.875 foot)

The deepest treasure is the one with the most negative value, which is the copper coin at \(-\frac{7}{8}\) foot.

**Conclusion**: The deepest treasure is the **copper coin** located at \(-\frac{7}{8}\) foot.