A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. This means that for any rational number r, it can be represented in the form:
- r = a/b
Here, a is an integer (it can be positive, negative, or zero), and b is a non-zero integer. For example, the number 3/4 is a rational number because it is the result of dividing the integer 3 by the non-zero integer 4.
Rational numbers also include whole numbers and integers since they can be expressed as a fraction with a denominator of 1. For instance:
- The whole number 5 can be written as 5/1.
- The integer -2 can be written as -2/1.
In summary, every rational number can always be written in the form a/b, where a and b fit the criteria mentioned above, demonstrating the versatile nature of rational numbers within the realm of mathematics.