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The problem asks which list shows the numbers in order from greatest to least value. The numbers involved are:

1. \( \frac{19}{2} \)
2. \( \frac{3}{4} \)
3. \( -1.2 \)
4. \( \frac{38}{6} \)
5. \( 7 \)
6. \( -\frac{19}{2} \)
7. \( -\frac{3}{4} \)

### Step 1: Convert Fractions to Decimals

- \( \frac{19}{2} = 9.5 \)
- \( \frac{3}{4} = 0.75 \)
- \( \frac{38}{6} \approx 6.33 \)

### Step 2: Compare All Values

- \( 7 \) (exact value)
- \( \frac{19}{2} = 9.5 \)
- \( \frac{38}{6} \approx 6.33 \)
- \( 0.75 \) (already calculated)
- \( -1.2 \) (exact value)
- \( -\frac{3}{4} = -0.75 \)
- \( -\frac{19}{2} = -9.5 \)

### Step 3: Arrange in Order from Greatest to Least

The order of these numbers from greatest to least is:
\[
9.5, 7, 6.33, 0.75, -0.75, -1.2, -9.5
\]

### Step 4: Match to the Answer Choices

- The third answer choice, \( 7, \frac{38}{6}, \frac{19}{2}, \frac{3}{4}, -1.2, -\frac{3}{4}, -\frac{19}{2} \), matches the correct order.

Thus, the correct answer is the third option.

Would you like a further breakdown or additional examples?

Here are 5 questions that build on this:
1. What is the decimal equivalent of \( \frac{19}{4} \)?
2. How do you order fractions like \( \frac{7}{3} \) and \( \frac{5}{2} \) when compared to integers?
3. What happens if you multiply all the given numbers by \( -1 \)? How does the order change?
4. How would you handle comparing irrational numbers, like \( \sqrt{2} \), to fractions and decimals?
5. How do you convert repeating decimals into fractions?

**Tip:** When ordering numbers, always convert them to the same format (like decimals) for easy comparison.

Which list shows the numbers in order from greatest to least value?

Learn how to order a set of numbers including fractions, decimals, and integers from greatest to least value. This example includes converting fractions like 19/2 and 38/6 to decimals, and comparing the values step-by-step.

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