The first wave knocked into the water,

Question

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.