Fractions

• A fraction is an expression that represents the division of two numbers, where the number above the line is called the numerator and the number below the line is called the denominator.
• A rational number is a number that can be represented by a fraction $\frac{a}{b}$, where $a$ and $b$ are integers and $b\ne 0$.
  • A real number $r\in \mathbb{R}$ is rational if and only if its base-$b$ representation is finite or periodic.
• An irreducible fraction is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered).