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The relationship between rational numbers and whole numbers can be described as a subset relationship.
Not all rational numbers are whole numbers. Whole numbers consist of the natural numbers (positive integers) and zero (0). In contrast, rational numbers are numbers that can be expressed as the quotient or fraction of two integers, with the denominator not equal to zero. Since whole numbers do not have a fractional component, they cannot be expressed as a quotient of two integers, therefore, not all rational numbers are whole numbers.
For example, consider the rational number 3/1. This can be expressed as the fraction of the integer 3 divided by the integer 1. However, it is not a whole number as it has a fractional component.
On the other hand, all whole numbers are rational numbers. As previously mentioned, rational numbers can be expressed as the quotient of two integers, and whole numbers are a subset of the set of rational numbers. Whole numbers can be expressed with a denominator of 1, making them a valid rational number.
For example, the whole number 7 can be written as 7/1. This fraction is a valid rational number since it can be expressed as the quotient of the integer 7 divided by the integer 1.
In summary, all whole numbers are rational numbers, but not all rational numbers are whole numbers.