Yes, fractions can indeed be a part of a system that includes whole numbers; however, they belong to a different number system known as the rational numbers. The rational number system includes all integers (whole numbers and their negatives), as well as fractions and decimals that can be expressed as a ratio of two integers.
In mathematical terms:
- Whole numbers: \(0, 1, 2, 3, \dots\)
- Integers: \(\dots, -3, -2, -1, 0, 1, 2, 3, \dots\)
- Rational numbers: Any number that can be expressed in the form \(\frac{a}{b}\), where \(a\) is an integer and \(b\) is a non-zero integer.
Fractions like \(\frac{1}{2}\), \(\frac{3}{4}\), and so on can be part of calculations that involve whole numbers, and they can represent parts of whole numbers when used in expressions or equations. However, fractions themselves are not whole numbers; they are used to represent quantities that are not whole.
In summary, fractions are part of the broader rational number system, which encompasses whole numbers, but they are distinct from whole numbers themselves.