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The question in the image asks:

"We know \( \frac{2}{5} \) and \( \frac{7}{3} \) are rational. Therefore, \( \frac{\frac{2}{5}}{\frac{7}{3}} \) is also rational. Is this conclusion correct? Why or why not?"

### Solution:
To determine whether the conclusion is correct, we need to evaluate the expression \( \frac{\frac{2}{5}}{\frac{7}{3}} \).

When dividing two fractions, we multiply by the reciprocal of the second fraction:

\[
\frac{\frac{2}{5}}{\frac{7}{3}} = \frac{2}{5} \times \frac{3}{7}
\]

Now, perform the multiplication:

\[
\frac{2 \times 3}{5 \times 7} = \frac{6}{35}
\]

Since \( \frac{6}{35} \) is a ratio of two integers, it is a rational number. 

### Conclusion:
Yes, the conclusion is correct. \( \frac{\frac{2}{5}}{\frac{7}{3}} = \frac{6}{35} \), and this result is a rational number because any number that can be expressed as a fraction of two integers is rational.

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### Related Questions:
1. What is the general rule for dividing two fractions?
2. Are all fractions with integers considered rational numbers?
3. How can you simplify the division of two fractions in different steps?
4. What is the reciprocal of a fraction, and how is it used in operations?
5. Can an irrational number ever result from dividing two rational numbers?

### Tip:
When dividing fractions, always remember to multiply by the reciprocal of the second fraction.

We know 2/5 and 7/3 are rational. Therefore, (2/5)/(7/3) is also rational. Is this conclusion correct? Why or why not?

Learn how to evaluate (2/5)/(7/3) and determine whether the result is a rational number. This problem covers key concepts such as fraction division and rational numbers. Suitable for Grades 7-9 students.

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