Add, subtract, multiply or divide two fractions. Get a simplified fraction, decimal result and calculation steps, including negative fractions.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
Enter a numerator and a nonzero denominator for each fraction, then choose addition, subtraction, multiplication or division. The result is reduced to lowest terms, with a decimal approximation and calculation steps. Negative numerators and denominators are supported; each input must be an integer between -1,000,000 and 1,000,000. To divide, the second fraction must not be zero. Also see the mixed-number result, the common denominator for addition or subtraction, and the reciprocal when the answer is nonzero.
Recomputed from this page's implementation at build time · checked 2026-10-22
Fraction arithmetic has a single correct answer per operation, but at least three accepted ways to write it down. This page fixes which one you get, shows the same sum as another tool writes it, and marks the exact inputs that are refused rather than silently rounded.
| 2 | 3 | 4 | 6 | 8 | 12 | |
|---|---|---|---|---|---|---|
| add | 0.67 | 0.5 | 0.42 | 0.33 | 0.29 | 0.25 |
| sub | -0.33 | -0.17 | -0.08 | 0 | 0.04 | 0.08 |
| mul | 0.08 | 0.06 | 0.04 | 0.03 | 0.02 | 0.01 |
| div | 0.33 | 0.5 | 0.67 | 1 | 1.33 | 2 |
Addition never shrinks the value and multiplication never grows it, at any denominator. The row order is fixed by the operation, not by the numbers, which is why the middle two rows can never cross.
One improper fraction, already at its lowest terms. The decimal is rounded for display and is not the answer — it is a reading aid for people who think in money.
Two pages, one value. Because both reduce to the same improper fraction before printing, they cannot disagree about the arithmetic — only about presentation.
Simplification runs before display, so an equivalent-but-unreduced fraction never reaches the screen. That is a deliberate choice: showing two forms of one answer invites readers to think they got two answers.
A denominator of −2 is accepted as input, then normalised away: the sign moves into the numerator and the printed denominator is always positive.
Every field is capped at ±1,000,000, yet the numerator printed here is above that cap. The limit constrains what you may type, not what arithmetic may produce.
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A denominator of zero
Division by zero has no value, so the page reports that no answer exists. It does not substitute infinity, and it does not quietly drop the term.
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Dividing by a fraction equal to zero
The check runs on the value of the second fraction, not on its numerator alone. A zero hidden inside a valid-looking fraction is still a zero divisor.
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A field one step past the ceiling
The input is refused outright rather than clamped to the nearest legal value. Clamping would return a plausible number for a question the user did not ask.
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A decimal typed into a numerator
Fraction fields accept integers only. Typing 1.5 is treated as an unsupported input, not as 3/2 — guessing the intent here would hide a misunderstanding instead of surfacing it.
calculator.netchecked 2026-10-22
Why they built it that wayThe default output is a mixed number rather than an improper fraction. That is a school convention: answers are marked in mixed form, so the page optimises for what gets written on paper instead of what is easiest to keep calculating with.
A reader who wants 1 7/12 will find this page incomplete. The honest fix is the link below, which computes the mixed form from the same inputs, rather than a second result field here that would double the surface area for both pages.
Set the fields to 3/4 and 5/6 with Add selected: the result reads 19/12 and the decimal reads 1.583333. Then enter 1000001 in any numerator field and confirm the result is replaced by an unavailable message rather than a rounded number.
Hand-reduced 3/4 + 5/6 to 19/12 and confirmed the denominator sign rule with a negative input · impl 77d59fe7
Cross-multiply numerators for addition/subtraction; multiply directly or by the reciprocal for multiplication/division. Normalize denominator sign and divide both parts by their greatest common divisor. P1 consolidation retains the core model and adds input modes or derived outputs. The migration report records the input/output union and known-answer checks.
Integer inputs are limited to ±1,000,000. Zero denominators, division by a zero numerator and unsupported operations are rejected. Decimal output is rounded. Added display totals and migration adapters are implementation behavior, not independently validated claims.
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
+/-: n/d = (n1 x d2 +/- n2 x d1)/(d1 x d2); x: n = n1 x n2, d = d1 x d2; /: n = n1 x d2, d = d1 x n2; -> (n/g)/(d/g), g = gcd(|n|,|d|)
All four numerator and denominator inputs must be integers. The result is reduced with the Euclidean GCD; a zero denominator or division by a zero fraction is invalid.
For addition and subtraction, both fractions need the same denominator so their numerators count equal-sized parts. For example, convert halves and thirds to sixths before combining them. Multiplication and division use different rules and do not need a common denominator. A zero denominator is invalid; division by a fraction whose numerator is zero is also invalid.
Either order works. Simplifying before multiplication can keep intermediate numerators and denominators smaller, which may make hand calculations easier. The calculator reduces the final fraction automatically, so you do not need to simplify the inputs first.
No. All four inputs must be integers between -1,000,000 and 1,000,000. Negative values are allowed. Denominators cannot be zero, and you cannot divide by a fraction whose numerator is zero. The result is reduced exactly within this input range; its displayed decimal value is rounded.
Enter each numerator and nonzero denominator, then select addition. The tool uses a common denominator and reduces the result: 1/2 + 1/3 = 5/6. You can also select subtraction, multiplication or division; division by a zero fraction is invalid.