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)
Responses
Malanna
Malanna
Jolene
Jolene
Both options are possible depending on the numbers.
Both options are possible depending on the numbers.
Neither of them, it depends on the number.
Jolene
Neither of them, it depends on the numbers. The product of two rational numbers can be rational or irrational, depending on the specific numbers being multiplied.
Both options are possible depending on the numbers.
To determine who is correct, we need to understand the properties of rational and irrational numbers and how they behave when multiplied.
Rational numbers are numbers that can be expressed as a fraction of two integers. They can be written in the form a/b, where a and b are integers and b is not equal to 0. Examples of rational numbers include 1/2, -3/4, and 5.
Irrational numbers, on the other hand, cannot be expressed as a fraction of two integers. They are non-repeating and non-terminating decimals. Examples of irrational numbers include pi (3.14159...), the square root of 2 (√2), and the golden ratio (φ).
When multiplying two rational numbers, the product will always be a rational number. This is because when we multiply two fractions, the numerator and denominator are both integers, and we can simplify the fraction if necessary to obtain a fully reduced rational number.
However, there are cases where the product of two rational numbers can be irrational. This happens when one or both of the rational numbers have an irrational component. For example, if we multiply the rational number 2/3 with the irrational number √3, the product will be 2√3/3, which is an irrational number.
Based on this explanation, both options are possible depending on the numbers being multiplied. If both rational numbers are such that their product does not involve any irrational components, then the product will be rational. But if one or both of the rational numbers have an irrational component, then the product will be irrational. Therefore, we cannot definitively say who is correct without knowing the specific rational numbers being multiplied.