Math & General

Fraction Calculator

Add, subtract, multiply and divide fractions in one click. Simplify, convert to mixed numbers or decimals, find LCM/GCD, and compare fractions — with full step-by-step working shown.

7 Calculation Types
Step-by-Step Working
Mixed Number Support
100% Free

Fraction Calculator — All Types

Select a calculation type, enter your fractions, and get the answer with complete step-by-step working

Add
a/b + c/d
Subtract
a/b − c/d
✖️
Multiply
a/b × c/d
Divide
a/b ÷ c/d
Simplify
Reduce a/b
🔄
Convert
Fraction ↔ Decimal
⚖️
Compare
Which is bigger?
➕ Addition: a/b + c/d = ?
Enter any fraction
and it will be reduced
to its simplest form.
→ decimal, %, mixed number
✨ RESULT
Formula applied
Result Summary
More Useful Results
Visual Breakdown
Step-by-Step Working
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    What Is a Fraction?

    The core concept behind fractions, types, and why they matter in everyday calculations

    A Part of a Whole

    A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator (the top number) and a denominator (the bottom number). The denominator tells you how many equal parts the whole is divided into; the numerator tells you how many of those parts you have.

    For example, the fraction 3/4 means the whole is divided into 4 equal parts, and you have 3 of them. Fractions appear everywhere — from cooking recipes (½ cup of flour) to finance (¾ of a portfolio) to construction measurements.

    Key insight: Every fraction a/b is simply a division problem: a ÷ b. This means 3/4 = 0.75 exactly. Understanding this relationship makes converting between fractions and decimals trivially easy.
    🔵
    Proper Fraction

    Numerator is less than denominator. Value is between 0 and 1. Examples: 1/2, 3/4, 7/8.

    🟠
    Improper Fraction

    Numerator is greater than or equal to denominator. Value ≥ 1. Examples: 5/3, 9/4, 7/7.

    🟢
    Mixed Number

    A whole number combined with a proper fraction. Examples: 1¾, 2½, 3⅔. Can always be converted to an improper fraction.

    🟣
    Equivalent Fractions

    Different fractions that represent the same value. 1/2 = 2/4 = 3/6 = 50/100. Multiplying or dividing both parts by the same number creates equivalents.

    Fraction Formulas — Complete Reference

    All fraction operation rules with worked examples

    OperationFormulaExampleResult
    Additiona/b + c/d = (ad + bc) / bd1/3 + 1/47/12
    Subtractiona/b − c/d = (ad − bc) / bd3/4 − 1/35/12
    Multiplicationa/b × c/d = (a×c) / (b×d)2/3 × 3/46/12 = 1/2
    Divisiona/b ÷ c/d = (a×d) / (b×c)2/3 ÷ 4/510/12 = 5/6
    Simplify (GCD)(a÷GCD) / (b÷GCD)12/18, GCD=62/3
    To Decimala ÷ b3/40.75
    To Mixed Number⌊a/b⌋ remainder (a mod b)/b7/32 1/3
    LCM Tip for addition/subtraction: Instead of multiplying denominators (which can get large), find the Least Common Multiple (LCM) of the denominators first. For 1/6 + 1/4: LCM(6,4) = 12, so convert to 2/12 + 3/12 = 5/12. Same answer as (1×4 + 1×6)/(6×4) = 10/24 = 5/12 — just simpler numbers.

    How to Use This Calculator

    Step-by-step guide to getting the most out of all 7 fraction tools

    For Add / Subtract / Multiply / Divide: Select the operation, enter the numerator and denominator for each fraction, and click Calculate. The result is automatically simplified using the GCD. You can also switch to Mixed Number mode to input numbers like 1 3/4 directly.

    For Simplify: Enter any fraction (e.g., 24/36) and the calculator finds the GCD and reduces it step by step.

    For Convert: Switch between Fraction → Decimal and Decimal → Fraction. Decimal-to-fraction conversion shows the exact fraction (e.g., 0.125 = 1/8) using the GCD method.

    For Compare: Enter two fractions to find which is greater, lesser, or if they are equal. Results show cross-multiplication working.

    Frequently Asked Questions

    Common questions about fractions and how to solve them

    How do you add fractions with different denominators?
    Find the LCM of the denominators, convert both fractions to equivalent fractions with that LCM as the denominator, then add the numerators. Example: 1/3 + 1/4. LCM(3,4) = 12. Convert: 4/12 + 3/12 = 7/12. Simplify if needed (already in simplest form).
    How do you divide fractions?
    To divide by a fraction, multiply by its reciprocal (flip the second fraction). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = (2×5)/(3×4) = 10/12 = 5/6. The acronym KCF helps: Keep the first fraction, Change division to multiplication, Flip the second fraction.
    How do I simplify a fraction to its lowest terms?
    Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. Example: 24/36 — GCD(24,36) = 12. 24÷12 = 2, 36÷12 = 3. So 24/36 = 2/3. A fraction is in lowest terms when GCD(numerator, denominator) = 1.
    How do I convert a mixed number to an improper fraction?
    Multiply the whole number by the denominator, then add the numerator. Keep the same denominator. Example: 2 3/4 = (2×4 + 3)/4 = (8+3)/4 = 11/4. To reverse: divide numerator by denominator: 11÷4 = 2 remainder 3, so 11/4 = 2 3/4.
    What is the difference between GCD and LCM?
    GCD (Greatest Common Divisor) is the largest number that divides both numbers. Used to simplify fractions. LCM (Least Common Multiple) is the smallest number that both numbers divide into. Used to find a common denominator for addition/subtraction. For 12 and 18: GCD = 6 (12/6=2, 18/6=3). LCM = 36 (36/12=3, 36/18=2). Note: GCD × LCM = product of the two numbers (12×18 = 216 = 6×36 ✓).
    How do you convert a repeating decimal to a fraction?
    For a decimal like 0.333...: let x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3. For 0.142857... (repeating 6 digits): multiply by 10⁶ to shift: 999999x = 142857, x = 142857/999999 = 1/7. This calculator handles terminating decimals (e.g., 0.75 = 3/4) by multiplying by the appropriate power of 10 and simplifying.
    Is this calculator private? Is any data stored?
    Yes, completely private. All calculations run entirely in your browser using JavaScript — no data is ever sent to a server. This page works fully offline once loaded. Your inputs disappear when you close or refresh the tab.