Fraction Calculator
Add, subtract, multiply, divide, simplify, and convert fractions with our free Fraction Calculator. Get step-by-step solutions, mixed number support, and decimal conversions.
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What Is a Fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts. A common, vulgar, or simple fraction consists of a numerator displayed above a line and a non-zero denominator displayed below that line.
The numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole.
How Does the Fraction Calculator Work?
The Fraction Calculator is a versatile online tool that performs various operations on fractions, including addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Users can input fractions with whole numbers or mixed numbers and receive instant results with step-by-step explanations.
The calculator uses standard mathematical formulas for each operation. For example, when adding two fractions a/b and c/d, it uses the formula (a×d + c×b) / (b×d) to find a common denominator and then adds the numerators. Similarly, for subtraction, multiplication, and division, it applies the respective mathematical rules. For mixed numbers, it first converts them to improper fractions, performs the calculation, and then converts the result back to a mixed number if needed.
Adding Fractions: a/b + c/d = (a×d + c×b) / (b×d)
Subtracting Fractions: a/b − c/d = (a×d − c×b) / (b×d)
Multiplying Fractions: a/b × c/d = (a×c) / (b×d)
Dividing Fractions: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Simplifying: Divide numerator and denominator by their GCD
Mixed Number: Improper fraction → whole number + proper fraction
Mixed Numbers
A mixed number is a whole number and a proper fraction combined. For example, 2⅓ represents 2 + 1/3. To convert a mixed number to an improper fraction: a b/c = (a×c + b) / c.
Simplifying Fractions
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example, 8/12 = (8÷4)/(12÷4) = 2/3.
Why Use This Fraction Calculator?
- All Operations: Add, subtract, multiply, divide, simplify, convert to mixed numbers and decimals.
- Step-by-Step Solutions: Learn how the result is calculated with detailed steps.
- Visual Chart: See fractions represented visually for better understanding.
- Free & Private: No registration, no data storage — your calculations stay on your device.
- Mobile-Friendly: Works on any device, from desktop to smartphone.
Understanding Fraction Terminology
- Numerator: The top number in a fraction, representing how many parts we have.
- Denominator: The bottom number in a fraction, representing how many parts make a whole.
- Proper Fraction: Numerator is smaller than denominator (e.g., 3/4).
- Improper Fraction: Numerator is equal to or larger than denominator (e.g., 5/4).
- Mixed Number: A whole number plus a proper fraction (e.g., 1 1/4).
- Equivalent Fractions: Different fractions that represent the same value (e.g., 1/2 = 2/4).
❓ Fraction Calculator FAQ
What is a fraction?
A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). The denominator tells you how many equal parts make up the whole, and the numerator tells you how many of those parts you have.
How do I add fractions with different denominators?
To add fractions with different denominators, find a common denominator (usually the least common multiple of the denominators), convert both fractions to equivalent fractions with that denominator, then add the numerators.
What is the difference between a proper and improper fraction?
A proper fraction has a numerator smaller than the denominator (e.g., 3/4). An improper fraction has a numerator greater than or equal to the denominator (e.g., 5/4). Improper fractions can be converted to mixed numbers.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 2⅓. It represents the sum of the whole number and the fraction (2 + 1/3).
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator and add the numerator. Write this result over the original denominator. For example, 2⅓ = (2×3 + 1)/3 = 7/3.
How do I simplify a fraction?
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example, 8/12 simplifies to 2/3 because the GCD of 8 and 12 is 4.
What is the reciprocal of a fraction?
The reciprocal of a fraction is created by swapping the numerator and denominator. For example, the reciprocal of 3/4 is 4/3. Reciprocals are used when dividing fractions.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. The calculator shows the decimal equivalent of your result.
How do I convert a decimal to a fraction?
Write the decimal as a fraction with a denominator of 10, 100, 1000, etc. (based on the number of decimal places), then simplify. For example, 0.75 = 75/100 = 3/4.
What are equivalent fractions?
Equivalent fractions are different fractions that represent the same value. For example, 1/2, 2/4, and 3/6 are all equivalent because they represent the same proportion.
How do I multiply fractions?
Multiply the numerators together and multiply the denominators together. Then simplify the result if possible. For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2.
How do I divide fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. For example, 2/3 ÷ 3/4 = 2/3 × 4/3 = (2×4)/(3×3) = 8/9.
What is the least common denominator (LCD)?
The LCD is the smallest number that both denominators can divide into evenly. It's used when adding or subtracting fractions with different denominators.
Can I enter negative fractions?
Yes! Enter a negative number in the numerator field. For example, to enter -3/4, put -3 in the numerator and 4 in the denominator.
What is the difference between simplifying and reducing a fraction?
They mean the same thing: dividing the numerator and denominator by their GCD to get the simplest form of the fraction.
Can I use this calculator for fractions with large numbers?
Yes! The "Big Numbers" tab supports very large numerators and denominators, making it suitable for advanced mathematical work.
Is this fraction calculator free to use?
Yes, this fraction calculator is completely free to use. No registration or payment is required. Your privacy is protected — no data is stored or shared.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. For example, 3/4 = 0.75 × 100 = 75%. You can use our Percentage Calculator for quick conversions.