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From the image you uploaded, the task is to select all expressions that result in a product that is a rational number. Let's examine each expression:

1. \( \frac{4}{3} \times \frac{12}{3} \) - This is a product of two rational numbers and therefore is rational.
2. \( \frac{32}{4} \times \frac{15}{4} \) - Similar to the first, this is also a product of rational numbers and is rational.
3. \( \sqrt{3} \times \frac{22}{2} \) - Here, \(\sqrt{3}\) is irrational, but multiplying it by a rational number \( \frac{22}{2} \) still results in an irrational number because multiplying an irrational number by a non-zero rational number results in an irrational number.
4. \( \frac{11}{2} \times \frac{2}{3} \) - Again, this is a product of two rational numbers, hence it is rational.

The expressions that result in a rational product are:
- \( \frac{4}{3} \times \frac{12}{3} \)
- \( \frac{32}{4} \times \frac{15}{4} \)
- \( \frac{11}{2} \times \frac{2}{3} \)

Would you like more details on how these conclusions were reached or have any other questions?

1. How do you simplify rational numbers?
2. Why is the square root of a non-perfect square an irrational number?
3. What are some examples of irrational numbers besides square roots?
4. What is the definition of a rational number?
5. Can an irrational number ever become rational through mathematical operations?

Tip: Remember, a number is rational if it can be expressed as a fraction \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \).

Select all the expressions that result in a product that is a rational number.

Learn how to identify which expressions result in rational numbers by multiplying fractions. This problem covers multiplication of rational and irrational numbers, including key algebraic concepts and rules. Suitable for students in Grades 8-10.

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