https://file.aiquickdraw.com/mathbot/file/1726185687829l4i9sh12.jpg

The problem in the image states:

- A dolphin is at the surface of the water and then descends to a depth of \( -4 \frac{1}{2} \) feet. 
- Then the dolphin swims down another \( -2 \frac{3}{4} \) feet.

The task is to find the dolphin's new location relative to the surface of the water.

### Steps to solve:
1. The initial position of the dolphin is \( -4 \frac{1}{2} \) feet.
2. The dolphin swims down another \( -2 \frac{3}{4} \) feet.

To find the total depth, we add the two negative values:

\[
-4 \frac{1}{2} + -2 \frac{3}{4}
\]

### Converting to improper fractions:
\[
-4 \frac{1}{2} = -\frac{9}{2}
\]
\[
-2 \frac{3}{4} = -\frac{11}{4}
\]

Now, we need to add \( -\frac{9}{2} \) and \( -\frac{11}{4} \). First, find a common denominator:

\[
-\frac{9}{2} = -\frac{18}{4}
\]

Now, add the fractions:
\[
-\frac{18}{4} + -\frac{11}{4} = -\frac{29}{4}
\]

Convert \( -\frac{29}{4} \) back to a mixed number:

\[
-7 \frac{1}{4}
\]

### Conclusion:
The dolphin's location relative to the surface of the water is \( -7 \frac{1}{4} \) feet.

Would you like further details on this solution or have any additional questions?

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Here are 5 related questions to consider:
1. How do you add fractions with different denominators?
2. What is the process of converting mixed numbers to improper fractions?
3. How do you subtract a positive value from a negative value on a number line?
4. How do negative numbers affect calculations in real-world scenarios like this one?
5. How can we visualize adding or subtracting fractions on a number line?

### Tip:
When adding or subtracting mixed numbers, always convert them to improper fractions first to make the calculation easier.

A dolphin is at the surface of the water and then descends to a depth of -4 1/2 feet. Then the dolphin swims down another -2 3/4 feet. What is the location of the dolphin relative to the surface of the water?

Solve the dolphin depth problem by adding negative mixed numbers: -4 1/2 feet and -2 3/4 feet. Learn how to add fractions with common denominators and find the new depth relative to the surface. Suitable for students in Grades 6-7.

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