Between two distinct rational numbers $a$ and $b$, there exists another rational number which is

### Concept & Logic Rational numbers are dense, meaning between any two rational numbers, there are infinitely many others. The most standard method to find a rational number between two others is calculating their arithmetic mean. ### Step-by-Step Solution * **Given:** Two distinct rational numbers $a$ and $b$. * **Deduction:** The midpoint of two points on a number line is always halfway between them. The formula for the midpoint (average) is: $$\text{Midpoint} = \frac{a + b}{2}$$ * This value is guaranteed to be rational if both $a$ and $b$ are rational. ### Exam Strategy & Shortcut If you are unsure, test with simple fractions. Let $a = 0$ and $b = 1$. The midpoint is $\frac{0 + 1}{2} = 0.5$, which is a rational number between $0$ and $1$. Other options like $ab/2$ would yield $0$, which is not *between* $a$ and $b$ (it is one of them). ### Common Pitfall Assuming that $ab/2$ (the geometric mean) always lies between the numbers. This fails if one of the numbers is negative or zero. The arithmetic mean formula is universally valid for finding a value in the interval. ### Final Answer Therefore, the correct answer is **$\\frac{a + b}{2}$**.