Mathematics · Algebra

Fraction Simplifier

Reduce a fraction to lowest terms using the greatest common divisor.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
Simplified numerator3
Simplified denominator4
Greatest common divisor6

Calculation steps

  1. GCD(18, 24) = 6.
  2. Divide both terms by 6.
  3. The simplified fraction is 3/4.

Understand Fraction simplifier

One idea, three depths

Choose how deeply to explain Fraction simplifier

Fraction simplifier: Reduce a fraction to lowest terms using the greatest common divisor.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Fraction simplifier to answer this question: reduce a fraction to lowest terms using the greatest common divisor? Enter Numerator and Denominator; the calculator shows Simplified numerator. For example: 18/24 has GCD 6, so it simplifies to 3/4. The answer tells you Simplified numerator.

Age 15Explain it to a 15-year-oldConnect it to the formula

Dividing the numerator and denominator by their greatest common divisor preserves the fraction's value. The rule is Simplified fraction = (numerator ÷ GCD) / (denominator ÷ GCD). Its input values are Numerator, Denominator, and the main result is Simplified numerator. For example: 18/24 has GCD 6, so it simplifies to 3/4.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated fraction simplifier relation over the valid integer domain stated below. The implemented relation is Simplified fraction = (numerator ÷ GCD) / (denominator ÷ GCD), evaluated from Numerator, Denominator to produce Simplified numerator. Dividing the numerator and denominator by their greatest common divisor preserves the fraction's value. The denominator can never be zero.

Inputs and valid domain

  • Numerator must be an integer.
  • Denominator must be an integer.

Important boundary: The denominator can never be zero.

The formula

Simplified fraction = (numerator ÷ GCD) / (denominator ÷ GCD)

How the calculator works through it

It substitutes Numerator, Denominator into the formula and exposes every numerical step above. The main output is Simplified numerator, accompanied by Simplified denominator, Greatest common divisor.

Read the result correctly

The Simplified numerator is the direct answer to “reduce a fraction to lowest terms using the greatest common divisor.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

18/24 has GCD 6, so it simplifies to 3/4.

Where this model stops being reliable

The denominator can never be zero.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Fraction simplifier works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Fraction simplifier uses Simplified fraction = (numerator ÷ GCD) / (denominator ÷ GCD). You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

Optional enrichment

  • Powers and exponents

    Powers are not required for every Fraction simplifier calculation, but they make related algebraic forms and code easier to read.

    Review this foundation about 4 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Find gcd(|numerator|, |denominator|) with Euclid's algorithm.
  2. Divide both terms by the GCD.
  3. Move a negative sign to the numerator.
Python
            from math import gcd

def simplified_numerator(numerator: int, denominator: int) -> int:
    if denominator == 0:
        raise ValueError("denominator cannot be zero")
    divisor = gcd(numerator, denominator)
    return (numerator // divisor) * (-1 if denominator < 0 else 1)

assert simplified_numerator(18, 24) == 3
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <stdint.h>

int64_t gcd64(int64_t a, int64_t b) {
    if (a < 0) a = -a; if (b < 0) b = -b;
    while (b) { int64_t r = a % b; a = b; b = r; }
    return a;
}
int64_t simplified_numerator(int64_t n, int64_t d) {
    int64_t g = gcd64(n, d);
    return (n / g) * (d < 0 ? -1 : 1);
}
int main(void) { assert(simplified_numerator(18, 24) == 3); }
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cstdint>
#include <numeric>

std::int64_t simplified_numerator(std::int64_t n, std::int64_t d) {
    const auto g = std::gcd(n, d);
    return (n / g) * (d < 0 ? -1 : 1);
}
int main() { assert(simplified_numerator(18, 24) == 3); }
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · integer arguments in rdi, rsi and rdx

            ; int64_t simplified_numerator(int64_t numerator, int64_t denominator)
global simplified_numerator
section .text
gcd64:
    mov rax, rdi
    test rax, rax
    jns .a_ok
    neg rax
.a_ok:
    mov rcx, rsi
    test rcx, rcx
    jns .b_ok
    neg rcx
.b_ok:
    test rcx, rcx
    jz .done
.loop:
    xor rdx, rdx
    div rcx
    mov rax, rcx
    mov rcx, rdx
    test rcx, rcx
    jnz .loop
.done:
    ret

simplified_numerator:
    push rbx
    mov rbx, rdi
    mov r8, rsi
    call gcd64
    mov rcx, rax
    mov rax, rbx
    cqo
    idiv rcx
    test r8, r8
    jns .positive_denominator
    neg rax
.positive_denominator:
    pop rbx
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = simplified_numerator(numerator, denominator)
    if denominator == 0, error("denominator cannot be zero"); end
    divisor = gcd(round(numerator), round(denominator));
    result = (round(numerator) / divisor) * sign(denominator);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[numerator_Integer, denominator_Integer] /; denominator != 0 :=
    Numerator[Cancel[numerator/denominator]];
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Algebra and Trigonometry 2e

Read the related free OpenStax mathematics chapters
Cite this book
APA 7
Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
MLA 9
Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
Chicago author-date
Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Fraction Simplifier. MW SysArc Tools. https://math.mwsysarc.com/algebra/fraction-simplifier

MLA 9

MW SysArc. “Fraction Simplifier.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/algebra/fraction-simplifier. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Fraction Simplifier.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/algebra/fraction-simplifier.

Harvard

MW SysArc (2026) ‘Fraction Simplifier’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/algebra/fraction-simplifier (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_fraction_simplifier_2026,
  author = {{MW SysArc}},
  title = {Fraction Simplifier},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/algebra/fraction-simplifier},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Fraction Simplifier
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/algebra/fraction-simplifier
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Fraction simplifier do?

Reduce a fraction to lowest terms using the greatest common divisor.

How does the Fraction simplifier work?

The calculator applies Simplified fraction = (numerator ÷ GCD) / (denominator ÷ GCD). Dividing the numerator and denominator by their greatest common divisor preserves the fraction's value.

What can I learn from the Fraction simplifier?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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