Final answer:
The true statement about the sum of two rational numbers is that it can always be written as a fraction, as rational numbers are defined as fractions and their sum is also a rational number.
Step-by-step explanation:
The question is about the properties of the sum of two rational numbers. A rational number is any number that can be represented as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. This definition immediately answers our question - the sum of two rational numbers is always a rational number itself. Therefore, the correct statement about the sum of two rational numbers is that it can always be written as a fraction.
When adding two rational numbers, if they have different denominators, we find a common denominator and then add the numerators. The common denominator is found through the multiplication of the denominators, not by addition. This process ensures that the sum will also be a rational number, which can be written as a reduced fraction if there are common factors between the numerator and the denominator. This sum might sometimes be a repeating decimal or a terminating decimal, depending on the resulting fraction.
Let’s consider an example: If we add ½ and ⅓, we find a common denominator, which in this case is 6 (2*3=6), and then convert ½ to 3⁄6 and ⅓ to 2⁄6. Thus, the sum is ⅛⁄6, which simplifies to 5⁄6 and can be written as a fraction. This process works regardless of the values involved and always results in a fraction, confirming that the sum of two rational numbers can be represented as a fraction and does not always result in a repeating or terminating decimal, although it can be expressed in these forms as well.