Fraction Calculator
Perform fraction addition, subtraction, multiplication, division and simplification
Enter fractions and select operation to calculate
Components
Numerator represents parts we have, denominator represents total equal parts.
Simplification
Dividing numerator and denominator by their greatest common divisor.
Operations
Different rules for adding, subtracting, multiplying and dividing fractions.
Mixed Numbers
Combination of a whole number and a proper fraction.
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All calculations run locally in your browser. We do not store or transmit your data.
What is a Fraction?
A fraction represents a part of a whole. It is written as two numbers separated by a line: the numerator (top) tells you how many parts you have, and the denominator (bottom) tells you how many equal parts the whole is divided into. So ¾ means “3 out of 4 equal parts.”
Fractions appear constantly in daily life — splitting a pizza (⅛ of a pizza), measuring ingredients (½ cup of flour), telling time (“a quarter past three”), and calculating discounts. They are also the foundation of decimals and percentages: ½ = 0.5 = 50%.
There are three main types. A proper fraction has a smaller numerator than denominator (¾). An improper fraction has a larger numerator (5/3), which equals a whole number plus a fraction (1 ⅔). A mixed number combines a whole number and a fraction (2 ½).
How to Calculate Fractions
Each operation has its own rule:
Add/Subtract: find a common denominator, then operate on numerators
Multiply: multiply numerators, multiply denominators
Divide: flip the second fraction, then multiply
Example — add ½ + ⅓:
Common denominator = 6 → ½ = 3/6, ⅓ = 2/6 → 3/6 + 2/6 = 5/6
Example — multiply ⅔ × ¾:
(2×3) / (3×4) = 6/12 = ½ (simplified)
Key tip: Always simplify the final result by dividing both numerator and denominator by their greatest common divisor (GCD). Our calculator does this automatically.
Common Use Cases
Cooking and baking — Recipes use fractions constantly: ¾ cup of sugar, ½ teaspoon of salt. Scaling a recipe up or down means multiplying fractions.
Carpentry and construction — Measurements in inches use fractions (3 ½ inches, ¼ inch). Adding and subtracting these is essential for accurate cuts.
Finance — Stock prices were historically quoted in fractions (eighths), and interest calculations involve fractional time periods.
Education — Fractions are a core math topic from elementary school onward, and the gateway to decimals, percentages, ratios, and algebra.
Frequently Asked Questions
How do I add two fractions with different denominators?
Find a common denominator (usually the least common multiple of the two), convert each fraction to an equivalent fraction with that denominator, then add the numerators. For ½ + ⅓, the common denominator is 6: ½ becomes 3/6 and ⅓ becomes 2/6, so 3/6 + 2/6 = 5/6. Our calculator handles the common-denominator step automatically.
How do I multiply fractions?
Multiply the numerators together and the denominators together: a/b × c/d = (a×c) / (b×d). For example, ⅔ × ¾ = (2×3) / (3×4) = 6/12, which simplifies to ½. Unlike addition and subtraction, multiplication does not require a common denominator — you multiply straight across.
How do I divide fractions?
To divide fractions, multiply the first fraction by the reciprocal (flip) of the second: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c). For example, ⅔ ÷ ¾ = ⅔ × 4/3 = 8/9. The common mistake is trying to divide straight across — you must flip the second fraction and multiply instead.
How do I simplify (reduce) a fraction?
Divide both the numerator and denominator by their greatest common divisor (GCD). For example, 8/12: the GCD of 8 and 12 is 4, so 8÷4 / 12÷4 = ⅔. A fraction is fully simplified when the numerator and denominator share no common factor other than 1. Our calculator simplifies results automatically.
How do I convert a fraction to a decimal or percentage?
To convert a fraction to a decimal, divide the numerator by the denominator: ¾ = 3 ÷ 4 = 0.75. To convert to a percentage, multiply the decimal by 100: 0.75 × 100 = 75%. For recurring decimals like ⅓ = 0.333…, the decimal repeats infinitely and is written as 0.3̄ or rounded.