The statement in question is:

"The sum of a rational number and a rational number is a rational number."

Solution:

A rational number is defined as a number that can be expressed as the quotient of two integers $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$. The sum of two rational numbers is also a rational number because:

1. Let $x = \frac{a}{b}$ and $y = \frac{c}{d}$, where $a, b, c,$ and $d$ are integers and $b, d \neq 0$.
2. The sum of $x$ and $y$ is: $x + y = \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$
3. Since $ad + bc$ and $bd$ are integers, $\frac{ad + bc}{bd}$ is also a rational number.

Therefore, the sum of two rational numbers is always a rational number.

Conclusion:

The correct answer is "always true".

Would you like further details, or do you have any questions?

Here are 5 related questions to deepen understanding:

1. What is the difference between rational and irrational numbers?
2. Can the product of two rational numbers be irrational?
3. Is the sum of a rational number and an irrational number always irrational?
4. How can you prove that the product of two rational numbers is rational?
5. What is an example of a rational number that is also an integer?

Tip: When working with rational numbers, remember they can always be expressed as fractions with integer numerators and denominators.