Question

are rational numbers always integers?

Answer 1

No, rational numbers are not always integers. A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. In mathematical terms, a rational number can be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

While all integers are indeed rational numbers (since any integer \( n \) can be expressed as \( \frac{n}{1} \)), not all rational numbers are integers. For example, \( \frac{1}{2}, \frac{-3}{4}, \) and \( \frac{7}{3} \) are all rational numbers, but none of them are integers.