Mixed number converter
Rewrite an improper fraction as a whole number plus a leftover: 11/4 becomes 2 3/4, and the leftover is reduced, so 10/4 gives 2 1/2. Handy for recipes, tape measures and worksheets. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Numerator
- 11
- Denominator
- 4
- Whole
- 2
- Remainder numerator
- 3
- Remainder denominator
- 4
- Mixed
- 2 3/4
An improper fraction has a numerator whose absolute value is at least as large as the denominator, so the value is one or more wholes plus a leftover piece. People search for a mixed number converter when they need to rewrite 11/4 as 2 3/4 for a recipe, a tape measure, a worksheet, or a grading script. This tool accepts a numerator and a denominator, divides with truncation toward zero, and returns the whole part together with the remaining proper fraction already reduced by the greatest common divisor.
What a mixed number is and how the conversion works
A mixed number writes a rational as a whole integer plus a proper fraction whose remainder is strictly smaller than the denominator. The conversion from an improper fraction a over b is ordinary integer division: the whole part q is the truncation of a divided by b toward zero, and the leftover remainder r is the absolute value of a modulo the absolute value of b. Then r over b is reduced by dividing both parts by their greatest common divisor.
For eleven over four, q is two and r is three, so the mixed number is two and three fourths. For ten over four the unreduced remainder is two fourths, which simplifies to one half, so the mixed number is two and one half. For eight over two the remainder is zero and the result is the integer four.
Proper inputs such as three fourths return a whole part of zero and the fraction itself. The sign lives on the whole part when the value is negative: negative eleven over four becomes negative two and three fourths, matching the school convention that writes the leftover remainder as a positive proper fraction. This is not the same search as a general fraction calculator that adds or multiplies; it answers only the rewrite from improper form to mixed form.
Where a mixed-number converter earns its keep
Classrooms and tutoring platforms use a mixed number converter so learners can check the rewrite of an improper fraction without mixing up the remainder and the whole part. Exam-prep generators need a deterministic oracle that marks a zero denominator as invalid instead of inventing a leftover. Recipe and workshop tools convert cup measures and stock lengths written as improper fractions into mixed form that a cook or a carpenter can actually portion.
Construction take-offs and shop drawings often arrive as 11/4 inches; displaying 2 3/4 inches next to the cut list prevents a missed whole. Failed validation does not consume balance. Keep requests inside the published integer bound, pin whole plus the reduced remainder in tests, and you get reproducible mixed numbers for homework, LMS plugins, recipes, and edge workers without standing up a computer-algebra stack of your own.
What you can do with it
Classroom and homework checks
Let students submit a numerator and a denominator and verify the whole part plus the reduced leftover against the textbook method for improper fractions.
Recipes and workshop measures
Rewrite a cup measure or a stock length given as an improper fraction into mixed form a cook or carpenter can portion without extra arithmetic.
Exam keys and LMS auto-grading
Mark mixed-number items with a deterministic oracle that rejects a zero denominator and never invents a leftover remainder.
FAQ
How do I convert an improper fraction to a mixed number?
Send integers numerator and denominator (denominator must be non-zero).
Does the leftover fraction get simplified?
Yes. After the integer division the remainder over the (positive) denominator is reduced by their greatest common divisor, so 10/4 becomes 2 1/2 rather than 2 2/4.
How are negative improper fractions written?
The sign lives on the whole part and the leftover remainder stays a positive proper fraction. Negative 11/4 is returned as −2 3/4. A negative denominator is accepted and normalized the same way.
What happens when the fraction divides exactly?
You get a whole number with no leftover fraction. For 8/2 the remainder is zero, so the result is simply 4 rather than 4 and zero halves.
Can the denominator be negative?
Yes. The minus sign is moved to the top of the fraction before dividing, so the leftover always has a positive denominator, which is how worksheets expect a mixed number to look.
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-number \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"numerator":11,"denominator":4}'const res = await fetch("https://api.kit.forhosting.com/math/mixed-number", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"numerator": 11,
"denominator": 4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/mixed-number",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"numerator": 11,
"denominator": 4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/mixed-number", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"numerator":11,"denominator":4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"numerator":11,"denominator":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/mixed-number", 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": 11,
"denominator": 4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.mixed_number",
"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.
Limits
max_abs | 1000000000000000 |
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 and is not billed.
Input contract, response shape, and error behaviour
Denominator may also be sent as den, d, or b. A denominator of zero is rejected with a clear division-by-zero message — that is the product contract for this capability, and those failures do not consume balance. A negative denominator is accepted: the sign is moved onto the numerator so the leftover remainder always uses a positive denominator, which is what worksheets expect. Example: numerator 11 and denominator 4 yields whole 2, remainder 3 over 4, and mixed 2 3/4. Example: numerator 10 and denominator 4 yields mixed 2 1/2 after reducing two fourths. POST a JSON body with two required integers: numerator, the top of the fraction, and denominator, the non-zero bottom. Numerator may arrive as a JSON integer or as a signed digit string; aliases num, n, and a are accepted when numerator is omitted. Missing fields, empty strings, non-integer text, NaN, and Infinity fail with invalid_input naming the field and are not billed. Magnitudes above one quadrillion are rejected so every returned integer stays inside the safe JSON number range. On success the body echoes the parsed numerator and denominator; returns whole as the integer part; lists remainder_numerator and remainder_denominator as the reduced leftover; sets mixed to a display string such as 2 3/4; repeats the original pair as improper; flags is_integer when the remainder is zero; and includes a short formula string plus a one-line message. Pair the payload with your own labels; this endpoint does not emit plots or multi-step classroom prose beyond the message and formula fields.
Technical questions
What happens if the denominator is zero?
The task fails with invalid_input. Division by zero is undefined, so a zero denominator is rejected and the request is not billed.
What does the mixed number converter cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.