The connection between rational numbers and whole numbers can be viewed as a subset relationship. While not all rational numbers qualify as whole numbers, whole numbers comprise the natural numbers (positive integers) along with zero (0). In contrast, rational numbers are defined as numbers that can be represented as the quotient or fraction of two integers, provided the denominator is not zero. Since whole numbers do not include a fractional part, they cannot be expressed as a quotient of two integers; thus, not all rational numbers are whole numbers.
For instance, take the rational number 3/1. This can be represented as the fraction of the integer 3 divided by the integer 1. However, it is not categorized as a whole number due to its fractional nature.
Conversely, every whole number is classified as a rational number. As mentioned earlier, rational numbers can be represented as the quotient of two integers, with whole numbers being a subset of the rational number set. Whole numbers can be expressed with a denominator of 1, which qualifies them as valid rational numbers.
For example, the whole number 7 can be expressed as 7/1. This fraction is a valid rational number because it represents the quotient of the integer 7 divided by the integer 1.
In conclusion, while all whole numbers are rational numbers, not all rational numbers are whole numbers.
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