Question

How to find rational numbers between two rational numbers

Answer 1

A rational number is a number which can be written in the form of p/q (ratio) where the denominator(q) is not equal to zero. This implies that it can be represented in the form of a fraction. Thus, every rational number has a numerator and a denominator, that is, one integer divided by another integer (excluding zero).

Let us first go through some of the examples and then learn how to find rational numbers between two other rational numbers.

Finding Rational Numbers between Two Rational Number

• The simplest method to find a rational number between 2 rational numbers x and y is to divide their sum by 2.

Example: 31 and 41. The rational number between them is (3 + 4)/2 = 3+42=72

Example: For numbers with common denominator like 320 and 920 , the rational number between them can be 420, 520, 620, 720, 820, etc.

• For a negative and a positive number like 3−3 and 320 , we have −220, −120, 020, 120, 220, etc.
• We can write 320 as 30200 and 920 as 90200 . Thus, rational number between 320 and 920 can also be 31200, 32200, 33200, 34200,…….. 89200 and so on .
• For finding rational numbers between two rational numbers with different denominators, we first find their equivalent fraction with the same denominator and then find the rational number between them. For example, for finding numbers between −13 and 59. , we convert −13 to −1×33×3=−39. Now, we have −29, −19, 09, 19, 29, 39, 49 between them.