A rational number is said to be in the standard form, if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.

Standard Form of Rational Number:
The standard form of a rational number is the form in which the numerator and the denominator are both integers, and the denominator is positive. It is the simplest and most concise representation of a rational number.

Understanding Natural Numbers, Whole Numbers, and Integers:
In order to understand the standard form of a rational number, it is important to have a clear understanding of natural numbers, whole numbers, and integers.

Natural Numbers: Natural numbers are the counting numbers starting from 1 and going up to infinity. They do not include zero or any negative numbers. Examples of natural numbers are 1, 2, 3, 4, 5, ...

Whole Numbers: Whole numbers are the set of numbers that includes all natural numbers along with zero. They do not include any negative numbers. Examples of whole numbers are 0, 1, 2, 3, 4, 5, ...

Integers: Integers are the set of numbers that includes all whole numbers along with their negative counterparts. They can be positive, negative, or zero. Examples of integers are -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...

The Standard Form of a Rational Number:
A rational number is a number that can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero. The standard form of a rational number is when the fraction is written in its simplest form, where the numerator and denominator are coprime (have no common factors other than 1).

To write a rational number in standard form, follow these steps:
1. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
2. Ensure that the denominator is positive. If it is negative, multiply both the numerator and denominator by -1.

Examples:
1. The rational number 6/9 can be simplified by dividing both the numerator and denominator by their GCD, which is 3. So, the standard form of 6/9 is 2/3.
2. The rational number -8/-12 can be simplified by dividing both the numerator and denominator by their GCD, which is 4. However, the denominator is negative, so we need to multiply both the numerator and denominator by -1. The standard form of -8/-12 is 2/3.

Summary:
The standard form of a rational number is the simplest form in which the numerator and denominator are both integers, and the denominator is positive. It is obtained by simplifying the fraction and ensuring that the denominator is positive. Understanding natural numbers, whole numbers, and integers is essential in order to grasp the concept of the standard form of a rational number.