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Numerator[expr]

gives the numerator of expr.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Modulus  
Trig  
Applications  
Properties & Relations  
See Also
Tech Notes
Related Guides
History
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Numerator

Numerator[expr]

gives the numerator of expr.

Details and Options

  • Numerator picks out terms which 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.
  • Numerator can be used on rational numbers.
  • Numerator takes the following options:
  • Modulus 0modulus to assume for integers
    Trig Falsewhether to do trigonometric as well as algebraic transformations

Examples

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Basic Examples  (3)

Extract the numerator of a rational number:

Wolfram Language code: Numerator[2 / 3]

Extract the numerator of a rational expression:

Wolfram Language code: Numerator[(x - 1)(x - 2) / (x - 3) ^ 2]

Extract the numerator of a symbolic expression:

Wolfram Language code: Numerator[Sin[x] ^ a(Sin[x] - 2) ^ -b]

Scope  (9)

Rational numbers:

Wolfram Language code: Numerator[3 / 7]

Gaussian rationals:

Wolfram Language code: Numerator[3 / 7 + I / 11]

Rational expressions:

Wolfram Language code: Numerator[(x - 1) ^ 2 / ((x - 2)(x - 3))]

Select terms without syntactically negative exponents:

Wolfram Language code: expr = a x ^ n y ^ -m Exp[a - b - 2c + 3d]
Wolfram Language code: Numerator[expr]

All exponents syntactically negative:

Wolfram Language code: Numerator[a ^ -b / x]

No syntactically negative exponents:

Wolfram Language code: Numerator[2x ^ y b ^ 2]

Numerator automatically threads over lists:

Wolfram Language code: Numerator[{1, 2, 3, 4, 5, 6} / 3]

Compute the numerator over the integers modulo 5:

Wolfram Language code: Numerator[24x ^ y (3b) ^ -3, Modulus -> 5]

Compute the numerator while incorporating common trigonometric identities:

Wolfram Language code: Numerator[Tan[x], Trig -> True]

Options  (2)

Modulus  (1)

Find numerators over integers modulo :

Wolfram Language code: Numerator[(1 / 3 x + 3 / 4 y) / (3 / 5x - 1 / 2y), Modulus -> 7]

Trig  (1)

Numerators of trigonometric functions:

Wolfram Language code: Numerator[{Sin[x], Cos[x], Tan[x], Csc[x], Sec[x], Cot[x]}, Trig -> True]

Applications  (2)

Explore patterns in reduced rational numbers:

Wolfram Language code: MatrixPlot@Table[Numerator[i / j], {i, 1, 100}, {j, 1, 100}]

View the occurrences of integers as the numerator in reduced rational numbers:

Wolfram Language code: Histogram[Flatten@Table[Numerator[i / j], {i, 1, 2000}, {j, 1, 2000}], 100]

Properties & Relations  (4)

Denominator gives the terms with negative exponents:

Wolfram Language code: Denominator[2 / 3(x - 1) / (x - 2)]

An expression is a quotient of its numerator and denominator:

Wolfram Language code: expr = 5 / 7(x - 1) ^ 2 / (x - 2) ^ 3a ^ b c ^ -d;
Wolfram Language code: num = Numerator[expr]
Wolfram Language code: den = Denominator[expr]
Wolfram Language code: expr === num / den

Use Cancel to cancel common factors between the numerator and the denominator:

Wolfram Language code: Cancel[(x - 1)(x - 2) / (x ^ 2 - 1)]

Together writes an expression as a fraction and cancels common terms:

Wolfram Language code: Together[x(x - 2) / (x ^ 2 - 1) + x / (x ^ 2 - 1) - 2 / (x ^ 2 - 1)]
Wolfram Research (1988), Numerator, Wolfram Language function, https://reference.wolfram.com/language/ref/Numerator.html.

Text

Wolfram Research (1988), Numerator, Wolfram Language function, https://reference.wolfram.com/language/ref/Numerator.html.

CMS

Wolfram Language. 1988. "Numerator." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Numerator.html.

APA

Wolfram Language. (1988). Numerator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Numerator.html

BibTeX

@misc{reference.wolfram_2026_numerator, author="Wolfram Research", title="{Numerator}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Numerator.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_numerator, organization={Wolfram Research}, title={Numerator}, year={1988}, url={https://reference.wolfram.com/language/ref/Numerator.html}, note=[Accessed: 12-June-2026]}