What is the difference between fractions and rational numbers?
Rational numbers are formed using integers with non-zero denominator while fractions are formed using natural numbers
A fraction, as introduced in the primary curriculum, represents a part of a whole and is written as \(\frac{a}{b}\) where both the numerator and the denominator are natural numbers, with the denominator not equal to zero.
A rational number extends this idea and is any number that can be written as \(\frac{p}{q}\) where \(p\) and \(q\) are integers, so either can be negative, and \(q\neq0\), making every fraction a rational number but not every rational number a fraction in this strict sense.
This rules out there being no difference, and rational numbers are not restricted to being positive since integers include negative numbers, so it is fractions built from natural numbers, not rational numbers, that stay non-negative; both fractions and rational numbers are also infinite in number, so a finite-versus-infinite distinction does not hold either.
Hence, the real difference is that rational numbers are formed using integers with a non-zero denominator, while fractions are formed using natural numbers.
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