Equivalent fractions calculator
Scaling 3/4 by 2 gives 6/8, and scaling it by 5 gives 15/20: the same value written with a bigger denominator. Enter a fraction and a whole-number multiplier to get the equivalent fraction exactly, ready for adding or comparing. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Numerator
- 3
- Denominator
- 4
- Multiplier
- 2
- Equivalent numerator
- 6
- Equivalent denominator
- 8
- Fraction
- 3/4
- Equivalent
- 6/8
Equivalent fractions describe exactly the same value: 3/4 and 6/8 occupy the same point on the number line. This capability automates the operation in a single call, validates that every input is an integer, and rejects a zero denominator or a zero multiplier with a clear error instead of returning a meaningless result.
What an equivalent fraction actually is
Two fractions are equivalent when they represent the same rational number, even though they are written with different numerators and denominators. The standard way to build one is to multiply the numerator and the denominator by the same non-zero integer: 3/4 scaled by 2 becomes 6/8, scaled by 5 becomes 15/20, and so on. Because you multiply the top and the bottom by the same factor, the ratio between them never changes, so the value of the fraction is preserved exactly.
The equivalent fractions calculator implements this definition directly: it multiplies both terms by the multiplier you supply and returns the resulting pair of integers. There is no rounding, no floating-point approximation and no simplification step, so the output fraction is always exactly the input fraction scaled by your multiplier. This matters in teaching contexts, where the whole point is to show that the same quantity can be written in infinitely many ways, and in software contexts, where a scaled denominator is needed before fractions can be compared or added.
Validation rules and error handling
Every input must be an integer. Fractions with a decimal multiplier such as 1.5 are rejected, because the equivalent-fraction definition is stated over integers and silently rounding a float would hide a modelling error in the calling code. The denominator must not be zero, since division by zero is undefined; the multiplier must not be zero either, because scaling by zero collapses every fraction to 0/0, which is meaningless.
Negative numerators, denominators and multipliers are all legal: the arithmetic is exact integer multiplication, so -3/4 scaled by 2 correctly yields -6/8, and scaling by -2 yields -6/-8, which is still the same value.
What you can do with it
Build a common denominator
Rewrite 3/4 with denominator 8 by scaling it by 2, so it can be added to another eighth-based fraction.
Scale fractional measurements
Convert a fractional measurement to a denominator that matches the tools at hand, such as eighths or sixteenths.
FAQ
What inputs are accepted?
Three integers: a numerator, a non-zero denominator and a non-zero multiplier. Integer strings like "7" or "-3" are also accepted.
Why is a zero multiplier rejected?
Because multiplying by zero produces 0/0, which is not a valid fraction and carries no information about the original value.
Can I use negative numbers?
Yes. Negative numerators, denominators and multipliers are all valid; only zero is rejected for the denominator and the multiplier.
Does it simplify the result?
No. The result is exactly the input fraction scaled by your multiplier, so 3/4 with multiplier 2 returns 6/8, not a reduced form.
Is the arithmetic exact?
Yes. The computation is pure integer multiplication with no floating-point rounding, within the published value limit.
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/equivalent-fractions \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"numerator":3,"denominator":4,"multiplier":2}'const res = await fetch("https://api.kit.forhosting.com/math/equivalent-fractions", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"numerator": 3,
"denominator": 4,
"multiplier": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/equivalent-fractions",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"numerator": 3,
"denominator": 4,
"multiplier": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/equivalent-fractions", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"numerator":3,"denominator":4,"multiplier":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"numerator":3,"denominator":4,"multiplier":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/equivalent-fractions", 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": 3,
"denominator": 4,
"multiplier": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.equivalent_fractions",
"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_value | 1000000000000 |
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
The equivalent fractions API takes a numerator, a denominator and an integer multiplier, and returns the equivalent fraction produced by multiplying the numerator and the denominator by that multiplier.
Validation rules and error handling
When any of these rules is violated, the API responds with an invalid_input error whose message names the offending field, so a pipeline can log the problem and stop instead of propagating a bad value. Valid integer strings such as "7" or "-3" are accepted and parsed, which makes the endpoint friendly to form data where numbers arrive as text. Inputs are bounded by a published limit so responses stay fast and payloads stay small.
Where it fits in real workflows
The most common use is generating common denominators: before two fractions can be added or compared, they must be rewritten with the same denominator, and that rewriting is precisely an equivalent-fraction operation. Recipe-scaling and construction tools use it when measurements expressed as fractions need a finer or coarser denominator, for example turning 3/4 of a cup into 6/8 to match an eighth-cup measuring set. Educational platforms use the endpoint to generate exercise sets and worked examples, showing a fraction and its scaled forms side by side. The capability runs on our global edge with nothing stored, and the same deterministic code that powers the API runs free in your browser on this page: you can check a single conversion by typing it in, and only pay $0.002 per request when you automate the call from your own systems. Because the algorithm is pure integer arithmetic, the result you see in the browser is byte-for-byte the result the API returns, which makes integration testing trivial.
Integration use cases
Generate teaching exercises
Produce equivalent-fraction pairs like 2/5 and 8/20 for worksheets and quizzes from one API call.
Technical questions
What does it cost?
$0.002 per request. It is also free to run in your browser on this page.