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Fraction Calculator

Add, subtract, multiply, and divide fractions with automatic simplifying (GCD), mixed numbers, and decimal/percent conversion. Every result includes a step-by-step solution and exact repeating-decimal notation.

4 operations 2+ fractions Automatic simplifying (GCD) Step-by-step solution Updated: Jul 19, 2026
Examples: 3/4 (fraction) · 1 1/2 (mixed number) · 0.75 (decimal) · 75% (percent) · 0.(3) (repeating)
Quick answer A fraction calculator adds, subtracts, multiplies, and divides two or more fractions and automatically simplifies the result. Addition and subtraction find a common denominator using the LCM; multiplication multiplies numerators and denominators directly; division multiplies by the reciprocal of the second fraction. This tool also shows the step-by-step solution and the decimal/percent equivalent.
—Simplified
—Mixed number
—Decimal
—Percent
⚙️ How it works: All calculations run in your browser using exact integer arithmetic — there is no rounding error. Addition/subtraction equalizes denominators using the LCM; results are simplified to lowest terms using the GCD. When a division doesn't terminate, the repeating part of the decimal is shown in parentheses; for example 1/3 → 0.(3). No data is sent to a server.
🧮 Fraction Calculator — ToolPico ↗

What is a fraction, and how do you calculate with one?

A complete guide — with formulas and examples — to adding, subtracting, multiplying, and dividing fractions, finding a common denominator, simplifying, and converting to decimals and percents.

A fraction expresses one or more equal parts of a whole. The number above the line is the numerator; the number below the line is the denominator. Fraction calculation covers adding, subtracting, multiplying, and dividing two or more fractions, simplifying the result to lowest terms, and converting it to a decimal or percent. You can also convert between improper fractions and mixed numbers, and compare fractions to see which is larger. The calculator above handles all of these operations in separate tabs, instantly and with a step-by-step explanation.

How do you add and subtract fractions?

Quick answerIf the denominators are already equal, add or subtract the numerators directly. If not, first find a common denominator: take the LCM of the two denominators, expand each fraction to that denominator, then combine the numerators and simplify. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
  • Step 1: Find the least common multiple (LCM) of the denominators.
  • Step 2: Expand each fraction to the common denominator — multiply the numerator by (common denominator ÷ its own denominator).
  • Step 3: Add or subtract the numerators; the common denominator stays the same.
  • Step 4: Simplify by dividing by the GCD of the numerator and denominator.

How do you multiply and divide fractions?

Quick answerMultiplication needs no common denominator: multiply the numerators together and the denominators together (2/3 × 4/5 = 8/15). Division keeps the first fraction, flips the second fraction (its reciprocal), and multiplies (2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6). Simplify the result when possible.

How do you simplify a fraction? (GCD)

Quick answerFind the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For 8/12, GCD(8,12) = 4, so 8/12 = 2/3. A fraction is fully simplified once the numerator and denominator have no common factor left besides 1.

Converting a fraction to a decimal and percent

Quick answerTo convert a fraction to a decimal, divide the numerator by the denominator (3/4 = 0.75). For a percent, multiply the decimal by 100 (0.75 → 75%). If the division doesn't terminate, the decimal is repeating, and the repeating block is written in parentheses: 1/3 = 0.(3). The "Convert" tab shows the fraction, decimal, and percent forms together.

Improper fractions and mixed numbers

Quick answerA fraction whose numerator is larger than its denominator is an improper fraction (7/4). An improper fraction converts to a mixed number by dividing the numerator by the denominator: the quotient becomes the whole part, and the remainder becomes the new numerator (7/4 = 1 3/4). To reverse the process, multiply the whole part by the denominator and add the numerator (2 1/3 = 7/3).

Common fraction calculations (example table)

Common addition, subtraction, multiplication, and division results. For exact and decimal results with any fraction, use the calculator above.

Fraction operation examples with decimal equivalents
ExpressionResultDecimal
1/2 + 1/43/40.75
2/3 + 1/65/60.8(3)
3/4 − 1/35/120.41(6)
5/8 − 1/43/80.375
2/3 × 3/52/50.4
1/2 × 1/41/80.125
2/3 ÷ 1/644
3/4 ÷ 1/23/2 (1 1/2)1.5

Popular calculations

Related mini converters

Quick helper tools for converting a decimal to a fraction, a fraction to a decimal and percent, generating equivalent fractions, finding a fraction of a number, and finding the least common denominator.

🔢Decimal → Fraction
Convert a decimal or percent to its simplest fraction form. Use 0.(3) for repeating decimals.
📐Fraction → Decimal & Percent
Enter a numerator and denominator to get its decimal, percent, and mixed-number form.
🟰Equivalent Fraction Finder
Generates equivalent fractions by multiplying the numerator and denominator by the same number.
✖️Fraction of a Number
Find what a fraction of a given number is — e.g. 2/3 of 60 = 40.
🔗LCD Finder
Find the least common denominator of two or more denominators.

Fraction reference tables

Citable conversions: common fraction–decimal–percent equivalents, the four operation rules, and fraction types.

Common fraction, decimal, and percent equivalents
FractionDecimalPercent
1/20.550%
1/30.(3)33.(3)%
2/30.(6)66.(6)%
1/40.2525%
3/40.7575%
1/50.220%
2/50.440%
1/80.12512.5%
3/80.37537.5%
1/100.110%
1/1000.011%
Rules for the four fraction operations
OperationRuleExample
AdditionEqualize denominators, add numerators1/2 + 1/3 = 5/6
SubtractionEqualize denominators, subtract numerators3/4 − 1/2 = 1/4
MultiplicationNumerator × numerator, denominator × denominator2/3 × 4/5 = 8/15
DivisionFlip the 2nd fraction, then multiply2/3 ÷ 4/5 = 5/6
SimplifyingDivide numerator and denominator by GCD8/12 = 2/3
Types of fractions
TypeDefinitionExample
Proper fractionNumerator smaller than denominator, value < 13/4
Improper fractionNumerator equal to/greater than denominator, value ≥ 17/4
Mixed numberWhole number + proper fraction1 3/4
Equivalent fractionSame value, different form1/2 = 2/4
Unit fractionFraction with numerator 11/5

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Fraction terms glossary

Short definitions of the core terms used in fraction calculations.

NumeratorThe number above the fraction line; shows how many parts of the whole are taken.
DenominatorThe number below the fraction line; shows how many equal parts the whole is divided into.
SimplifyingReducing a fraction to its lowest terms by dividing the numerator and denominator by their GCD.
GCDGreatest Common Divisor — the largest number that divides both the numerator and denominator evenly; used to simplify a fraction.
LCMLeast Common Multiple — the smallest number that both denominators divide into evenly; used to find a common denominator.
Improper fractionA fraction whose numerator is equal to or greater than its denominator, with a value of 1 or more (e.g. 7/4).
Mixed numberA whole number written together with a proper fraction, such as 1 3/4.
Equivalent fractionA fraction with a different numerator and denominator but the same value, such as 1/2 and 2/4.
Repeating decimalA decimal in which one or more digits repeat forever; the repeating block is written in parentheses, e.g. 0.(3).
ReciprocalA fraction with its numerator and denominator swapped; used when dividing fractions (4/5 → 5/4).

In-depth guides

Step-by-step explanations of the most commonly confused fraction questions.

Finding a common denominator step by step (LCM method)

To add or subtract fractions with different denominators, first find a common denominator. The most practical common denominator is the least common multiple (LCM) of the denominators. For 1/4 and 1/6, LCM(4,6) = 12.

Each fraction is expanded to the common denominator: since 12 ÷ 4 = 3, 1/4 = 3/12; since 12 ÷ 6 = 2, 1/6 = 2/12. Once the denominators match, the numerators are added: 3/12 + 2/12 = 5/12. Since the result is already in lowest terms, the process ends there. The "Operation" tab above shows every one of these steps automatically.

What does 0.(3) mean? Understanding repeating decimals

Converting a fraction to a decimal means dividing the numerator by the denominator. When the division doesn't terminate, some digits repeat forever — this is called a repeating (recurring) decimal. Instead of writing 1/3 = 0.3333..., we write the repeating block in parentheses: 0.(3).

Some fractions have a non-repeating part followed by a repeating part: 1/6 = 0.1(6). This tool automatically detects the repeating block when it computes a decimal equivalent and wraps it in parentheses, so you see the exact value with no rounding.

Converting improper fractions to mixed numbers (and back)

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole part, the remainder becomes the new numerator, and the denominator stays the same. For 11/4: 11 ÷ 4 = 2 remainder 3, so the result is 2 3/4.

Going the other way, to convert a mixed number to an improper fraction, multiply the whole part by the denominator and add the numerator: 2 3/4 = (2×4 + 3)/4 = 11/4. Enter a value in the "Convert" tab to see both forms at once.

Frequently asked questions

How do you add and subtract fractions?
If the denominators are already equal, add or subtract the numerators directly. If not, first find a common denominator: take the LCM of the two denominators, expand each fraction to that denominator, then combine the numerators and simplify. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do you simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For 8/12, GCD(8,12) = 4, so 8/12 = 2/3. A fraction is fully simplified once the numerator and denominator share no common factor other than 1.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. If the division doesn't terminate, the result is a repeating decimal; for example 1/3 = 0.333... = 0.(3). This tool shows the repeating block in parentheses for an exact result.
What is an improper fraction?
A fraction whose numerator is equal to or greater than its denominator (value ≥ 1), such as 7/4. An improper fraction converts to a mixed number by dividing the numerator by the denominator: the quotient is the whole part and the remainder is the new numerator. 7/4 = 1 3/4.
How do you divide fractions?
Keep the first fraction, flip (take the reciprocal of) the second fraction, and multiply. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. Simplify the result with the GCD when needed.
How do you find a common denominator?
Finding a common denominator means bringing fractions with different denominators to a shared one — typically the LCM of the denominators. Each fraction is expanded by multiplying its numerator and denominator by whatever makes the denominator equal to the LCM. For 1/4 and 1/6, LCM(4,6) = 12, so the fractions become 3/12 and 2/12.
How do you convert a fraction to a percent?
Convert the fraction to a decimal first, then multiply by 100 — or divide the numerator by the denominator and multiply by 100 directly. 3/4 = 0.75 → 75%; 1/8 = 0.125 → 12.5%. The "Convert" tab shows the fraction, decimal, and percent forms together.
Can you use negative fractions in this calculator?
Yes. Enter a minus sign (−) in the numerator or whole-number field to make a fraction negative. The tool carries the sign correctly through every operation — for example, −1/2 + 1/3 = −1/6, with the full step-by-step solution.
How do you find a fraction of a number?
Multiply the number by the fraction's numerator, then divide by its denominator. For example, 2/3 of 60 = 60 × 2 ÷ 3 = 40. The "Fraction of a Number" mini tool below performs this calculation instantly for any fraction and number.

Methodology & sources

ToolPico's Fraction Calculator is a free, browser-based tool. The calculation engine uses exact integer arithmetic: addition and subtraction equalize denominators using the LCM; simplifying divides the numerator and denominator by the GCD, found with the Euclidean algorithm; the decimal equivalent is produced by tracking remainders during long division so that any repeating block is detected and shown in parentheses. Results contain no rounding error, and no data is sent to a server.

Basis: Standard mathematics (fraction arithmetic). Last updated: July 19, 2026. Results are for informational purposes only; double-check schoolwork or exam calculations yourself.
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