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The image contains a problem that asks about comparing rational numbers and understanding their relationships. Here's the interpretation:

### Problem Statement:
You are given three rational numbers, \(\frac{p}{q}\), \(\frac{r}{s}\), and \(\frac{t}{u}\). The conditions provided are:
1. \(\frac{p}{q} > \frac{r}{s}\)
2. \(\frac{r}{s} > \frac{t}{u}\)

You are asked to **compare \(\frac{p}{q}\) and \(\frac{t}{u}\)** and explain the reasoning.

### Step-by-Step Reasoning:
1. From the first inequality, \(\frac{p}{q} > \frac{r}{s}\), we know that \(\frac{p}{q}\) is greater than \(\frac{r}{s}\).
2. From the second inequality, \(\frac{r}{s} > \frac{t}{u}\), we know that \(\frac{r}{s}\) is greater than \(\frac{t}{u}\).
3. Using the transitive property of inequalities (if \(a > b\) and \(b > c\), then \(a > c\)), we can conclude:
   \[
   \frac{p}{q} > \frac{t}{u}
   \]
   
   Therefore, \(\frac{p}{q}\) is greater than \(\frac{t}{u}\).

### Explanation:
The relationship between \(\frac{p}{q}\) and \(\frac{t}{u}\) follows from the fact that \(\frac{p}{q}\) is greater than \(\frac{r}{s}\), which in turn is greater than \(\frac{t}{u}\). This means that \(\frac{p}{q}\) is the largest of the three rational numbers.

Would you like further clarification or details on any step?

Here are some related questions:
1. How do you compare two rational numbers?
2. Can the transitive property be applied to other inequalities?
3. What happens if one of the rational numbers is negative?
4. How would this change if \(\frac{p}{q}\) and \(\frac{t}{u}\) were fractions with equal denominators?
5. How do mixed numbers relate to this comparison?

**Tip:** When comparing fractions, it's often helpful to rewrite them with a common denominator to make direct comparisons easier!

Suppose \(\frac{p}{q}\), \(\frac{r}{s}\), and \(\frac{t}{u}\) represent three rational numbers. If \(\frac{p}{q}\) is greater than \(\frac{r}{s}\) and \(\frac{r}{s}\) is greater than \(\frac{t}{u}\), compare \(\frac{p}{q}\) and \(\frac{t}{u}\). Explain your reasoning.

Explore how to compare rational numbers using the transitive property. This problem involves inequalities between fractions \(\frac{p}{q}\), \(\frac{r}{s}\), and \(\frac{t}{u}\). The solution uses basic concepts of rational numbers and inequalities suitable for Grades 6-8.

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