Fraction Calculator (2026)
Working with fractions by hand means finding common denominators, cross-multiplying, and remembering to simplify — easy to get wrong under time pressure. This calculator adds, subtracts, multiplies, or divides any two fractions or mixed numbers instantly, automatically reduces the answer to lowest terms, and shows the equivalent decimal, so you always get a clean, verified result.
Multiply: multiply the numerators together and the denominators together.
Divide: multiply the first fraction by the reciprocal (flip) of the second.
Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 (≈ 0.4167)
Always simplify the final answer by dividing numerator and denominator by their greatest common factor (GCF).
What Is a Fraction?
A fraction represents a part of a whole and is written as one number (the numerator) over another (the denominator), separated by a line — for example, 3/4 means "3 parts out of 4 equal parts." The denominator tells you how many equal pieces the whole is divided into, and the numerator tells you how many of those pieces you have.
- Proper fraction: numerator smaller than denominator, e.g. 3/4 (value less than 1)
- Improper fraction: numerator equal to or greater than denominator, e.g. 7/4 (value ≥ 1)
- Mixed number: a whole number plus a proper fraction, e.g. 1 3/4
- Like fractions share the same denominator; unlike fractions do not
- Every fraction can be converted to an equivalent decimal by dividing numerator ÷ denominator
- A fraction is in "lowest terms" once its numerator and denominator share no common factor besides 1
Adding & Subtracting Fractions
Fractions can only be added or subtracted once they share the same denominator, because you can only combine parts that are the same size. If the denominators already match, simply add or subtract the numerators and keep the denominator. If they don't match, first rewrite both fractions using their least common multiple (LCM) as a shared denominator.
Step 2: Scale each numerator by the same factor used to reach that denominator
Step 3: Add or subtract the numerators; keep the common denominator
Step 4: Simplify the result to lowest terms
Example: 1/4 + 1/6 → LCM(4,6) = 12 → 3/12 + 2/12 = 5/12 (already simplest form)
Multiplying & Dividing Fractions
Multiplying fractions is more direct than adding them — there is no need for a common denominator. Simply multiply the two numerators together and the two denominators together, then simplify.
Example: 2/3 × 3/5 = 6/15 = 2/5 (simplified)
Dividing fractions uses the "keep, change, flip" method: keep the first fraction as-is, change the division sign to multiplication, and flip (take the reciprocal of) the second fraction — then multiply as usual.
Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3 (simplified)
Simplifying Fractions (GCF/GCD)
Simplifying (or reducing) a fraction means dividing both the numerator and denominator by their greatest common factor (GCF), also called the greatest common divisor (GCD), until no common factor remains besides 1. A fast, reliable way to find the GCD of two numbers is the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller number, until the remainder is 0 — the last non-zero remainder is the GCD.
| Unsimplified Fraction | GCF of Numerator & Denominator | Simplified Fraction |
|---|---|---|
| 4/8 | 4 | 1/2 |
| 6/9 | 3 | 2/3 |
| 8/12 | 4 | 2/3 |
| 10/15 | 5 | 2/3 |
| 18/24 | 6 | 3/4 |
| 21/28 | 7 | 3/4 |
Fraction to Decimal Conversion Table
To convert any fraction to a decimal, divide the numerator by the denominator. Some fractions convert to a terminating decimal, while others (like thirds and sevenths) produce a repeating decimal.
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/8 | 0.125 |
| 1/3 | 0.333... | 3/8 | 0.375 |
| 2/3 | 0.667... | 5/8 | 0.625 |
| 1/4 | 0.25 | 7/8 | 0.875 |
| 3/4 | 0.75 | 1/10 | 0.1 |
| 1/5 | 0.2 | 1/16 | 0.0625 |
| 1/6 | 0.1667 | 1/9 | 0.111... |
| 1/7 | 0.142857... | 5/6 | 0.8333... |
Working With Mixed Numbers
A mixed number combines a whole number and a proper fraction, such as 2 3/4. To do arithmetic with mixed numbers, it's usually easiest to first convert them into improper fractions: multiply the whole number by the denominator, add the numerator, and place the total over the same denominator.
Improper → Mixed: 11/4 → 11 ÷ 4 = 2 remainder 3 → 2 3/4
This calculator accepts an optional whole-number field for each fraction, so you can enter mixed numbers directly — it converts them to improper fractions automatically before calculating.
Worked Examples
2/5 + 1/3 → common denominator 15 → 6/15 + 5/15 = 11/15 (≈ 0.7333)
3/4 − 1/6 → common denominator 12 → 9/12 − 2/12 = 7/12 (≈ 0.5833)
5/6 × 2/3 = 10/18 = 5/9 (≈ 0.5556)
1 1/2 ÷ 2/3 → improper: 3/2 ÷ 2/3 = 3/2 × 3/2 = 9/4 = 2 1/4 (= 2.25)
Common Mistakes to Avoid
- Adding denominators together. 1/3 + 1/3 is not 2/6 — the denominator stays the same when the fractions already match; only the numerators add.
- Forgetting to find a common denominator before adding/subtracting. You cannot combine numerators directly unless the denominators are equal.
- Forgetting to flip the second fraction when dividing. a/b ÷ c/d is not a/b × c/d — the second fraction must be inverted first.
- Leaving the answer unsimplified. 6/8 is mathematically correct but should be reduced to 3/4 for a complete answer.
- Mishandling mixed numbers. Convert to an improper fraction before multiplying or dividing — multiplying whole numbers and fraction parts separately gives the wrong answer.
Limitations of This Calculator
- Denominators cannot be zero. Division by zero is undefined, so a zero denominator will return an error instead of a result.
- Repeating decimals are rounded for display. Fractions like 1/3 are shown as a rounded decimal (0.3333) — the exact simplified fraction is always the precise value.
- This tool covers two-fraction arithmetic. For chained expressions with more than two fractions, calculate the result in pairs, using the output of one calculation as an input to the next.
Glossary
- Numerator
- The top number in a fraction, representing how many parts of the whole are being counted.
- Denominator
- The bottom number in a fraction, representing how many equal parts the whole is divided into.
- Least Common Multiple (LCM)
- The smallest number that both denominators divide into evenly; used as the common denominator when adding or subtracting fractions.
- Greatest Common Factor (GCF / GCD)
- The largest number that divides evenly into both the numerator and denominator; dividing by it simplifies a fraction to lowest terms.
- Improper Fraction
- A fraction whose numerator is equal to or greater than its denominator, representing a value of 1 or more (e.g. 7/4).
- Mixed Number
- A whole number combined with a proper fraction, such as 1 3/4, equivalent to an improper fraction.
- Reciprocal
- A fraction flipped upside down (numerator and denominator swapped); used to convert division into multiplication.
Frequently Asked Questions
Q: How do you add or subtract fractions?
A: Find a common denominator (the LCM of the two denominators), scale each numerator to match, then add or subtract the numerators and keep the shared denominator.
Q: How do you multiply fractions?
A: Multiply the numerators together and the denominators together, then simplify — no common denominator is needed.
Q: How do you divide fractions?
A: Multiply the first fraction by the reciprocal of the second fraction ("keep, change, flip"), then simplify.
Q: How do you simplify a fraction?
A: Divide the numerator and denominator by their greatest common factor (GCF) until no common factor remains besides 1.
Q: How do you convert a fraction to a decimal?
A: Divide the numerator by the denominator; some fractions terminate and others repeat.
Q: How do you convert a mixed number to an improper fraction?
A: Multiply the whole number by the denominator, add the numerator, and place the total over the same denominator.
Q: What is the difference between a proper fraction, an improper fraction, and a mixed number?
A: A proper fraction is less than 1 (numerator smaller than denominator), an improper fraction is 1 or more (numerator equal to or greater than denominator), and a mixed number expresses the same improper-fraction value as a whole number plus a proper fraction.
This calculator is provided for general educational purposes to help with fraction arithmetic. For homework or exam preparation, always double-check results and show your own step-by-step work as required by your instructor.