Is the product of two rational numbers always rational?
Understand the Problem
The question is asking whether the multiplication of two rational numbers results in another rational number. To answer this, we need to remember that a rational number is defined as any number that can be expressed as the quotient of two integers (where the denominator is not zero). When multiplying two such numbers, the product can also be expressed as a quotient of integers, thus remaining rational.
Answer
rational number
The final answer is rational number
Answer for screen readers
The final answer is rational number
More Information
When multiplying two rational numbers, both of which can be expressed as a ratio of two integers, the resulting product remains a ratio of two integers, which by definition is rational.
Tips
A common mistake is to confuse the multiplication of rational numbers with irrational numbers, where the product can result in either rational or irrational numbers.
