Question

State whether the statement given in the question is true or False:

The sum of two rational numbers is always a rational number.

• A. True
• B. False

Answer 1

The correct option is A True

Given the statement, “The sum of two rational numbers is always a rational number."

Since rational numbers are closed under addition and multiplication, adding two rationals is equivalent to adding two such fractions, resulting in another fraction with the same form. Hence, the sum of two rational numbers is always a rational number.

Let us consider the two rational numbers $\frac{1}{2}$ and $\frac{3}{4}$ and calculate their sum:

$$\begin{gathered} \frac{1}{2}+\frac{3}{4}=\frac{2+3}{4} \\ \Rightarrow =\frac{5}{4} \end{gathered}$$

hence, $\frac{5}{4}$ is a rational number.

Hence, the given statement is “True”.