# NumeratorDenominator

NumeratorDenominator[expr]

gives the list {Numerator[expr],Denominator[expr]} of expr.

# Details and Options • Numerator picks out terms that do not have superficially negative exponents. Denominator picks out the remaining terms.
• An exponent is "superficially negative" if it has a negative number as a factor.
• The standard representation of rational expressions as products of powers means that you cannot simply use Part to extract numerators.
• NumeratorDenominator can be used on rational numbers.
• NumeratorDenominator automatically threads over lists.

# Examples

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## Basic Examples(2)

Extract the numerator and denominator of a rational number:

Extract the numerator and denominator of a rational expression:

## Scope(5)

Rational numbers:

Gaussian rationals:

Rational expressions:

Select terms with syntactically positive and negative exponents:

Reconstruct the original expression:

## Options(2)

### Modulus(1)

Find numerators and denominators over integers modulo :

### Trig(1)

Numerators and denominators of trigonometric functions:

## Properties & Relations(1)

An expression is a quotient of its numerator and denominator:

## Neat Examples(1)

Plot semitransparent blue squares at positions {i, j} for which i/j is an irreducible fraction:

Introduced in 2019
(12.0)