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 answer

Jolene is correct.

When you multiply two rational numbers, the product is always a rational number. Rational numbers are defined as numbers that can be expressed as the quotient of two integers (where the denominator is not zero). If you take two rational numbers, say \(a/b\) and \(c/d\) (where \(a, b, c,\) and \(d\) are integers and \(b, d \neq 0\)), their product can be computed as follows:

\[ \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d} \]

Since \(a \cdot c\) and \(b \cdot d\) are both integers (and \(b \cdot d \neq 0\)), the result \(\frac{a \cdot c}{b \cdot d}\) is also a rational number.

In conclusion, the statement that the product of two rational numbers will be irrational is incorrect; the product will always be rational.