Numerator and Denominator in Fractions

Numerator

• The number on the top of a fraction; counts parts being considered.

Denominator

• The number on the bottom; total number of equal parts in the whole.
• Must be nonzero: $b \neq 0$.

Notation and Value

• Fraction form: $\frac{a}{b}$ where $a, b \in \mathbb{Z}$ and $b \neq 0$.
• Value of the fraction: $\frac{a}{b}$.

Key Relationships

• If $a = 0$, value is $0$.
• If $a = b$, value is $1$.
• If a > b, fraction is improper; value > 1.
• If 0 < a < b, fraction is proper; value < 1.
• If $b = 1$, value equals $a$.

Quick reference

• Denominator must be nonzero; numerator can be zero.
• Fractions can be simplified by common divisors of $a$ and $b$.

Examples

• $\frac{3}{4}$ has numerator $3$ and denominator $4$.
• $\frac{7}{7} = 1$.
• $\frac{0}{5} = 0$.