Malanna says that when she multiplies two rational numbers, her product will be irrational. Jolene says that the product in this case will be rational. Who is correct?(1 point)

Question

Responses

Jolene
Jolene

Malanna
Malanna

Neither of them, it depends on the number.
Neither of them, it depends on the number.

Both options are possible depending on the numbers.

Answer 1

Jolene is correct. The product of two rational numbers is always a rational number.

To explain further:

• A rational number is defined as any number that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \neq 0 \).
• When you multiply two rational numbers, say \( \frac{a_1}{b_1} \) and \( \frac{a_2}{b_2} \), the product is \( \frac{a_1 \cdot a_2}{b_1 \cdot b_2} \), which is also a fraction (and thus rational) as long as \( b_1 \) and \( b_2 \) are not zero.

Therefore, the correct answer is Jolene.