Question 28 of 58intermediate🔍 AnalyzeEssay2 marks

Can you think of other way(s) to find a rational number between any two rational numbers?

Correct Answer

Yes, another way to find a rational number between any two rational numbers is by taking their average. For two rational numbers aa and bb, the average is calculated as a+b2\frac{a+b}{2}. This value is always a rational number that lies strictly between aa and bb.

For example, a rational number between 1 and 32\frac{3}{2} is found by taking their average: 1+322=54\frac{1 + \frac{3}{2}}{2} = \frac{5}{4}. 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.

Exercise: Exercise Set 3.4 | Q: *6 | (Page 12)
For More Understanding

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.