Fraction Calculator
Work with fractions accurately
This Fraction Calculator helps you add, subtract, multiply, and divide fractions with clean, step-by-step working. It accepts standard fractions like 7/8, whole numbers like 5, and mixed numbers like 2 1/3 (including negatives). You can simplify to lowest terms, convert to a mixed number, and optionally show a rounded decimal and percentage.
If you’re comparing sizes, adjusting recipes, or checking homework, you’ll usually want a simplified final fraction plus a quick decimal check. For related tools, you may also find the mixed fraction calculator and the Algebra Calculator helpful. You can also browse the full directory on our all calculators page.
Input examples: -3 5/8, 10/3, 0. Decimals are intentionally rejected to keep results exact.
Calculator Tool
Tip: press Enter in either input to calculate.
Results
How It Works
Internally, each input is parsed into a normalized fraction n/d where n is an integer numerator and d > 0 is an integer denominator. Mixed numbers like w a/b are converted to improper fractions using n = sign × (|w|×b + a), d = b. Then the calculator applies the operation exactly and simplifies using the greatest common divisor (GCD).
For addition and subtraction, we use a common denominator (LCD). If A is a/b and B is c/d, then: g = gcd(b, d), LCD = (b/g)×d. Convert numerators: a' = a×(LCD/b), c' = c×(LCD/d), then combine: (a' ± c')/LCD. For multiplication and division: (a/b)×(c/d) = (a×c)/(b×d) and (a/b)÷(c/d) = (a/b)×(d/c).
Finally, simplification divides numerator and denominator by gcd(n, d). If you’re practicing fraction skills, you can compare results with the partial fraction calculator when working with algebraic expressions, or check related probability work using the binomial distribution calculator.
Decimals and percentages are derived from the exact fraction and then rounded at the selected precision.
Use Cases
- Scale a recipe up or down when ingredients are listed as fractions (for example, 3/4 cup × 2).
- Combine measurements in woodworking or DIY plans, such as adding 1 3/8 inches and 5/16 inches.
- Check homework steps for fraction addition/subtraction with a clear common-denominator breakdown.
- Divide portions fairly, like splitting 7/8 of a pizza among 1/2-slice servings.
- Convert an improper fraction into a mixed number for easier interpretation (e.g., 17/6 → 2 5/6).
- Sanity-check a fraction by viewing a rounded decimal and percent without losing the exact fraction result.
Examples
3/4 and 2/33/4 = 9/12, 2/3 = 8/12. Add numerators: 9 + 8 = 17.17/12 (mixed: 1 5/12, decimal ≈ 1.4167 at 4 dp).1 1/2 and 5/81 1/2 = 3/2. LCD of 2 and 8 is 8. Convert: 3/2 = 12/8. Subtract: 12 − 5 = 7.7/8 (already simplified; decimal ≈ 0.8750 at 4 dp).-3/5 and 6/7(-3/5) ÷ (6/7) = (-3/5) × (7/6). Multiply: -21/30. Simplify with GCD 3.-7/10 (decimal ≈ -0.7000 at 4 dp; percent ≈ -70.0000%).Common Mistakes
- Adding denominators directly (for example, 1/2 + 1/3 is not 2/5).
- Forgetting to convert mixed numbers to improper fractions before doing multiplication or division.
- Dropping the negative sign or applying it to the wrong part of a mixed number.
- Dividing by a fraction without using the reciprocal step.
- Not simplifying at the end, leaving results like 6/8 instead of 3/4.
- Using a denominator of 0 (which is undefined) or trying to divide by 0.
Quick Tips
- For add/subtract, find an LCD first; it often saves time and avoids mistakes.
- Keep denominators positive; move any negative sign to the numerator for consistency.
- After multiplying, simplify by GCD to keep numbers small and readable.
- When dividing, flip the second fraction (reciprocal) and multiply.
- Use the decimal view as a quick check, but rely on the simplified fraction for exactness.
- If a mixed number’s remainder is 0, it’s simply a whole number.
FAQ
1) What fraction formats can I enter?
Enter a proper or improper fraction like 7/8 or -10/3, a whole number like 5 or -2, or a mixed number with a single space like 2 1/3 or -3 5/8. The calculator trims extra whitespace and normalizes the sign so the denominator stays positive. If you enter something with letters, multiple slashes, or an empty numerator/denominator, it will show a friendly inline message and keep the results area stable.
2) How does the calculator simplify fractions?
Simplification divides the numerator and denominator by their greatest common divisor (GCD). For example, 21/30 has gcd(21, 30) = 3, so it becomes 7/10 by dividing both parts by 3. This keeps the value identical while making the fraction easier to read and compare. Even when you turn off the simplify toggle, the calculator still computes and stores the reduced form safely so it can show the GCD and avoid messy displays.
3) Why do addition and subtraction use a common denominator?
You can only add or subtract fractions after expressing them with the same denominator. The calculator finds a least common denominator (LCD) using gcd(b, d) so it doesn’t inflate numbers unnecessarily. It converts each fraction to that common denominator, combines numerators, and then simplifies. Seeing the LCD step helps you verify that 3/4 becomes 9/12 and 2/3 becomes 8/12 before adding to reach 17/12. This is the standard, reliable method.
4) How does division of fractions work?
Dividing by a fraction means multiplying by its reciprocal. So (a/b) ÷ (c/d) becomes (a/b) × (d/c). The calculator always shows this reciprocal step in the breakdown when steps are enabled, because it’s the most common place mistakes happen. If the second fraction evaluates to zero, division is undefined, so the calculator blocks the operation and prompts you to correct Fraction B rather than showing confusing output.
5) When will I see a mixed number?
If “Show as mixed number (when applicable)” is on and the absolute numerator is at least the denominator, the result is shown as a whole part plus a proper remainder. For example, 17/12 becomes 1 5/12, and -7/3 becomes -2 1/3. The calculator keeps the remainder positive and attaches the sign to the whole part for a clean, standard display. If the remainder is zero, the mixed form is just a whole number.
6) Why are decimals shown as approximations?
Many fractions produce repeating decimals (like 1/3 = 0.333…). This tool calculates the fraction exactly first, then converts it to a decimal rounded to 2, 4, 6, or 8 places using a consistent half-up rounding policy. That makes the decimal useful for quick comparisons without pretending it’s exact. The percentage is derived from the same exact fraction and rounded to the same precision so the decimal and percent stay consistent.
7) What happens with negative fractions?
Negatives are supported in all accepted input styles. You can write -3/5, -2 1/3, or even put the negative sign in the numerator like -10/3. Internally, the calculator normalizes the fraction so the denominator is always positive and the sign is carried by the numerator. This avoids sign confusion and makes steps clearer. For mixed results, the sign is shown on the whole part, with a positive remainder fraction.
8) Is my data private and are results exact?
Your inputs are processed locally in your browser, so the calculator does not send the fractions to a server. Fraction arithmetic is performed exactly using integer math, then simplified by GCD for readability. Only the optional decimal and percent views involve rounding, and they follow the precision setting you choose. If you copy results, the clipboard text is plain and clean so it’s easy to paste into notes, homework, or documentation.
Accuracy, Precision, and Privacy
Sources & References
Fraction arithmetic rules (add/subtract with a common denominator; multiply numerators and denominators; divide by multiplying the reciprocal), and simplification using GCD/LCD concepts.