Can you think of other way(s) to find a rational number between any two rational numbers?
Yes, another way to find a rational number between any two rational numbers is by taking their average. For two rational numbers and , the average is calculated as . This value is always a rational number that lies strictly between and .
For example, a rational number between 1 and is found by taking their average: . Another effective method is to express the two rational numbers as equivalent fractions with a common, larger denominator, which allows us to easily identify multiple rational numbers lying between them.
Explanation
The textbook context explicitly introduces taking the average of two rational numbers as a method to find a number between them, citing the formula (a+b)/2. It also implicitly supports the method of using equivalent fractions with larger denominators through the exercises (e.g., finding 6 rational numbers between 3 and 4, or 5 between 2/5 and 3/5), which requires converting to equivalent fractions to find intermediate values.