Multiplying fractions
Multiply two fractions and get the product already in lowest terms: 2/3 times 3/4 is 6/12, which cancels by 6 to 1/2. The sign always sits on the top, and the factor used to cancel is shown. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Numerator a
- 2
- Denominator a
- 3
- Numerator b
- 3
- Denominator b
- 4
- Gcd
- 6
- Product numerator
- 1
- Product denominator
- 2
- Product
- 1/2
Multiplying two fractions is a core arithmetic skill: take the product of the numerators over the product of the denominators, then reduce that result to lowest terms so the answer is unique and textbook-ready. Students, tutors, and worksheet generators need a deterministic pair of integers, not a floating approximation that later fails a grader. This capability accepts two numerator and denominator pairs, multiplies them with exact integer arithmetic, cancels common factors, and returns the product fraction already reduced, with the sign on the numerator and a positive denominator.
How multiplying fractions works and why the product is reduced
The product of two rational numbers a over b and c over d is the single rational (a times c) over (b times d), provided neither denominator is zero. That identity is the whole algorithm: numerators multiply, denominators multiply, and the value does not change if you later cancel a common factor from the new pair. Reducing after the multiply is what turns six twelfths into one half and twenty one-hundred-twentieths into one sixth.
Cross-cancelling keeps intermediate products smaller and makes the leftover fraction easier to finish with a final greatest-common-divisor step. Sign is then placed on the product numerator so a negative denominator never survives in the answer; two negatives become a positive product. A zero numerator yields the canonical writing zero over one.
The landing is only this contract. It does not add unlike denominators, invert-and-multiply to divide, convert mixed numbers, or factor algebraic rationals. Those are different searches and different tools.
Where a multiplying-fractions calculator earns its keep
Secondary-school arithmetic classes set multiply-the-fractions targets so students practice cancelling before they meet unlike-denominator addition. Recipe and shop-floor scaling often multiply two ratios, such as a batch fraction times a yield fraction, and must show a reduced answer a human can check. Product engineers gate form fields with a maximum absolute value and a non-zero denominator check before accept.
Failed validation does not consume balance. If you later need addition, division, mixed-number conversion, or symbolic rational expressions, treat those as separate search intents and landings rather than overloading this focused multiply-and-reduce page.
What you can do with it
Classroom and homework product checks
Let students submit two fractions and verify the lowest-terms product and the cancelled factor against textbook methods.
LMS and exam auto-grading
Mark multiplying-fractions items with a deterministic oracle that rejects zero denominators and never invents extra cancel factors.
Ratio scaling and worksheet keys
Multiply two stored ratios for batch scaling or generate answer keys without a second client-side GCD implementation.
FAQ
What happens if a denominator is zero?
A zero denominator is undefined and is not billed.
How are negative fractions handled?
The sign of the product is placed on the numerator and the denominator is always positive after reduction. Two negatives yield a positive product.
Is this the same as a full fraction calculator?
No. This landing multiplies two numeric fractions and reduces the product. Addition, division, mixed forms, and algebraic rationals are separate tools.
Does the calculator cancel before multiplying?
Yes. A factor shared by the first numerator and the second denominator, or by the second numerator and the first denominator, is divided out first, as taught in school. A final common-divisor step then leaves the product in lowest terms.
What if one of the numerators is zero?
The product is zero, and it is written in the standard way as 0/1. The denominators must still be non-zero, since a zero denominator is refused before anything is multiplied.
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/multiplying-fractions \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"numerator_a":2,"denominator_a":3,"numerator_b":3,"denominator_b":4}'const res = await fetch("https://api.kit.forhosting.com/math/multiplying-fractions", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"numerator_a": 2,
"denominator_a": 3,
"numerator_b": 3,
"denominator_b": 4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/multiplying-fractions",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"numerator_a": 2,
"denominator_a": 3,
"numerator_b": 3,
"denominator_b": 4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/multiplying-fractions", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"numerator_a":2,"denominator_a":3,"numerator_b":3,"denominator_b":4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"numerator_a":2,"denominator_a":3,"numerator_b":3,"denominator_b":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/multiplying-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_a": 2,
"denominator_a": 3,
"numerator_b": 3,
"denominator_b": 4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.multiplying_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.
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 on either factor is rejected as invalid_input rather than inventing infinity. Successful API calls use the published base of $0.002 per item; validation failures do not consume prepaid balance.
How multiplying fractions works and why the product is reduced
This endpoint also cancels across the original pairs first, the method taught in school: a common factor of the first numerator and the second denominator can be divided out before the products are formed, and likewise for the second numerator and the first denominator.
Input contract, response shape, and error behaviour
Example: two thirds times three fourths yields product one half and gcd six, because the unreduced six twelfths cancels a factor of six. Example: five eighths times four fifteenths yields product one sixth. POST a JSON body with four required integer fields: numerator_a and denominator_a for the first fraction, numerator_b and denominator_b for the second. Documented aliases such as a_num, a_den, b_num, and b_den, or num1, den1, num2, and den2, are accepted so short scripts and form posts can stay compact. Every field may arrive as a JSON integer or as a digit string; booleans, non-integers, empty strings, and values outside the safe integer range fail with invalid_input naming the field. A zero on denominator_a or denominator_b always fails with a clear message that that denominator cannot be zero, and those failures are not billed. If an intermediate product would leave the safe integer range even after cross-cancelling, the request is also rejected rather than silently rounding. On success the body echoes the four inputs, reports gcd as the total positive factor cancelled from the unreduced product, returns product_numerator and product_denominator with the sign on the numerator and a positive denominator, returns product as a display string of the form n/d, and includes a short formula string documenting the rule. Pair the numbers with your own step-by-step prose if you teach prime-factor trees by hand; this endpoint returns the reduced product and the factor used, not multi-line worked solutions. Pricing for successful API calls is the published base of $0.002 per item.
Where a multiplying-fractions calculator earns its keep
Tutoring platforms and homework apps need a deterministic oracle that marks a zero denominator as invalid instead of producing NaN or an empty success payload that a buggy grader might accept. Because this capability is a pure parse engine, every successful call costs the published $0.002 base price with no model tokens and no outbound network.
Technical questions
How do I multiply two fractions with this tool?
Send integer pairs numerator_a/denominator_a and numerator_b/denominator_b. The API multiplies across, reduces by GCD, and returns the product in lowest terms.
What does the multiplying-fractions tool cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.