Simplify mixed fraction
Reduce a mixed number or fraction to lowest terms and get both forms at once: 2 4/6 becomes 2 2/3, which is 8/3 as an improper fraction. The common factor used is shown too, so you can check the reduction by hand. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Whole
- 2
- Numerator
- 4
- Denominator
- 6
- Gcd
- 2
- Improper numerator
- 8
- Improper denominator
- 3
- Improper
- 8/3
Mixed numbers and improper fractions are two writings of the same rational value, and every arithmetic textbook eventually asks you to simplify a fraction to lowest terms and flip between those writings without changing the value. Students, tutors, worksheet generators, and automation scripts need a single deterministic contract: feed a whole part plus a numerator and denominator (or a bare fraction with whole zero), get back the reduced improper fraction, the canonical mixed form, the GCD used, and a short formula string. This mixed fraction simplify and convert tool does exactly that with pure integer arithmetic—no floating approximation until an optional display decimal—so homework checks, LMS plugins, and edge workers always agree on 15/6 becoming 5/2 or 2 1/2.
What simplifying and converting mixed fractions means
A fraction a over b is in lowest terms when the greatest common divisor of the absolute values of a and b is one and the denominator is positive. An improper fraction has an absolute numerator at least as large as its denominator; a mixed number writes the same value as a signed whole part plus a non-negative proper fractional part.
Converting mixed to improper multiplies the whole part by the denominator and combines it with the numerator, taking care that a negative mixed number such as negative two and one fourth means minus the sum of two and one fourth, not a half-positive hybrid. Converting improper to mixed divides the absolute numerator by the denominator, keeps the remainder as the new numerator, and reattaches the sign to the whole part when the absolute value is at least one.
When the reduced denominator is one the value is an integer and the mixed form collapses to that integer alone. When the absolute value is less than one the mixed whole is zero and the pretty string is the signed proper fraction.
What you can do with it
Classroom and homework checks
Let students submit a mixed number or improper fraction and verify the reduced lowest-terms improper and mixed forms against textbook methods.
Exam and LMS auto-grading
Mark simplify-and-convert items with a deterministic oracle that rejects zero denominators and never invents extra factors in the GCD reduction.
Recipes, measures, and display formatting
Store amounts as improper fractions for calculation and render them as mixed numbers for human-facing labels without a second client-side reducer.
FAQ
How do I simplify a mixed fraction with this tool?
Send whole (optional, default 0), numerator, and a non-zero denominator.
How is a negative mixed number interpreted?
Put the sign on whole and keep the fractional numerator non-negative. For example whole −2, numerator 1, denominator 4 means −2 1/4 = −9/4, not a conflicting sign on the numerator.
Does it convert both improper to mixed and mixed to improper?
Yes. Every successful response includes the reduced improper pair and the canonical mixed parts (or an integer when the remainder is zero).
How do I enter a plain fraction instead of a mixed number?
Leave the whole part at zero and type the numerator and denominator. For 15/6 the tool divides by 3 and returns 5/2, written as 2 1/2 in mixed form.
What happens if the denominator is zero?
The fraction is refused with a clear message that the denominator cannot be zero. You never get an infinite or made-up result, so a typing slip is caught before it reaches your worksheet.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/math/mixed-fraction-simplify \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"numerator":4,"denominator":6}'const res = await fetch("https://api.kit.forhosting.com/math/mixed-fraction-simplify", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"numerator": 4,
"denominator": 6
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/mixed-fraction-simplify",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"numerator": 4,
"denominator": 6
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/mixed-fraction-simplify", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"numerator":4,"denominator":6}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"numerator":4,"denominator":6}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/mixed-fraction-simplify", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"numerator": 4,
"denominator": 6
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.mixed_fraction_simplify",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
A zero denominator is rejected as invalid_input rather than silently inventing infinity. The free browser path and the prepaid API path share the same pure module, so classroom demos match production responses byte for byte on the same inputs.
What simplifying and converting mixed fractions means
This endpoint performs both directions after a single GCD reduction, so you never simplify twice or disagree with textbook answers that put the sign on the whole number.
Input contract, response shape, and error behaviour
Denominator zero always fails with a clear message that the denominator cannot be zero, and those failures are not billed. When whole is non-zero the fractional numerator must be non-negative so the sign lives on the whole part; a negative numerator with a non-zero whole is a sign conflict and is rejected. Example: whole two, numerator four, denominator six yields gcd two, improper five over two, and mixed two one half. POST a JSON body with required integers numerator and denominator, and optional integer whole defaulting to zero for a plain fraction. Every field may arrive as a JSON integer or as a digit string; booleans, non-integers, and values outside the safe integer range fail with invalid_input naming the field. On success the body echoes the input whole, numerator, and denominator; reports the gcd used in reduction; returns improper_numerator, improper_denominator, and an improper display string; returns mixed_whole, mixed_numerator, mixed_denominator, and a mixed display string; and flags is_integer and is_proper plus a twelve-decimal display decimal and a short formula. Pair the numbers with your own step-by-step prose if you teach long division of fractions; this endpoint returns the reduced results and forms, not multi-line worked solutions.
Where a mixed fraction simplify API earns its keep
Classrooms and tutoring platforms use a mixed fraction converter so learners can check both the reduced improper form and the mixed writing without GCD slips. Failed validation does not consume balance. Exam generators and LMS auto-graders need a deterministic oracle that marks zero denominators as invalid instead of producing NaN or empty success payloads that buggy graders might accept. Recipe and measurement apps often store quantities as improper fractions for math and display them as mixed numbers for cooks; calling a tiny parse API avoids shipping a second GCD implementation in every client.
Technical questions
What happens if the denominator is zero?
The task fails with invalid_input and a message that the denominator cannot be zero. Invalid input is not billed.
What does the mixed fraction simplify converter cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.