Fraction Calculator
Add, subtract, multiply, and divide fractions and mixed numbers with step-by-step simplification.
Fraction Calculator
Add, subtract, multiply, and divide fractions, mixed numbers, and decimals with step-by-step reduction, LCD calculation, and visual fraction diagrams.
Standard Fraction Calculator
Perform arithmetic on two fractions: (N₁ / D₁) op (N₂ / D₂)
Common Fractions to Decimals & Percentages Cheatsheet
| Fraction | Decimal | Percentage | Quick Action |
|---|---|---|---|
| 1/2 | 0.5 | 50% | |
| 1/3 | 0.3333... | 33.33% | |
| 2/3 | 0.6667... | 66.67% | |
| 1/4 | 0.25 | 25% | |
| 3/4 | 0.75 | 75% | |
| 1/5 | 0.2 | 20% | |
| 1/8 | 0.125 | 12.5% | |
| 3/8 | 0.375 | 37.5% | |
| 5/8 | 0.625 | 62.5% | |
| 7/8 | 0.875 | 87.5% |
Comprehensive Guide to Fractions & Arithmetic
Anatomy of a Fraction: Numerator & Denominator
A fraction represents a numerical quantity that is not a whole number. It consists of two essential parts separated by a horizontal fraction bar (vinculum):
- Numerator (Top): Indicates how many equal parts of the whole are being considered.
- Denominator (Bottom): Represents the total number of equal parts that make up the whole. The denominator can never be zero (D ≠ 0).
1. Adding & Subtracting Fractions
Fractions must have a common denominator before adding or subtracting. Find the Least Common Denominator (LCD), convert each fraction, then add or subtract the numerators:
2. Multiplying Fractions
Multiply straight across: multiply the numerators together, then multiply the denominators together, and reduce using the GCD:
3. Dividing Fractions (Keep, Change, Flip)
Invert the divisor fraction (reciprocal) and multiply:
4. Negative Mixed Fractions Rule
A negative sign applies to the entire mixed fraction, not just the whole number:
Frequently Asked Questions
Why can a denominator never be zero?
Dividing by zero is mathematically undefined. A fraction a/b answers "how many groups of b are in a?". If b = 0, no number of zeros can ever equal a non-zero numerator, making division impossible.
What is the difference between proper, improper, and mixed fractions?
A proper fraction has a numerator smaller than its denominator (e.g. 3/4 < 1). An improper fraction has a numerator equal to or greater than its denominator (e.g. 7/4 ≥ 1). A mixed number combines an integer and a proper fraction (e.g. 1 3/4).
How does the calculator simplify fractions to lowest terms?
It uses the Euclidean algorithm to calculate the Greatest Common Divisor (GCD) of the numerator and denominator, then divides both numbers by the GCD.
What is the Least Common Denominator (LCD)?
The LCD is the Least Common Multiple (LCM) of the denominators of two or more fractions. Converting fractions to the LCD allows them to be directly added or subtracted.
How does the Big Number calculator avoid precision loss?
Standard JavaScript numbers use 64-bit floating point (IEEE-754) with 53 bits of precision (~15-17 digits). The Big Number calculator uses native arbitrary-precision BigInt integers, allowing calculations on numbers with hundreds of digits without rounding error.
Understanding Fraction Calculator & Formula
The Fraction Calculator on CalculatorScale.com is engineered to deliver instant, mathematically verified calculations conforming strictly to standard institutional equations. Whether planning long-term investments, managing household budgets, tracking clinical fitness targets, analyzing academic genetics, calculating veterinary dosages, or converting dimensional units, every calculation updates dynamically in real time without lag.
Every formula used in this tool adheres to certified international standards, including World Health Organization biometric metrics, veterinary clinical guidelines, NIST physical conversion constants, and standard biological equations. Results are computed entirely client-side inside your browser with complete data privacy, ensuring your sensitive numbers and statistics never leave your device.
Our calculators are 100% free with no registration, subscriptions, or paywalls required. You can toggle between imperial and metric units, customize input parameters, export calculation summaries, or embed this calculator directly into your own website or blog.
How to Use the Fraction Calculator
- 1 Enter the numerator and denominator for Fraction 1 and Fraction 2.
- 2 Select the arithmetic operation: Addition (+), Subtraction (-), Multiplication (×), or Division (÷).
- 3 Click "Calculate ▶️" to view the simplified fraction, mixed number representation, decimal equivalent, and step-by-step common denominator working.
Fraction Calculator — Frequently Asked Questions
Q1 How do you add or subtract fractions with different denominators? ▾
To add or subtract fractions with unlike denominators, find the least common denominator (LCD), convert each fraction to an equivalent fraction with the LCD, add or subtract the numerators, and simplify the result.
Q2 How do you multiply and divide fractions? ▾
To multiply fractions, multiply the numerators together and the denominators together. To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction.
Q3 How do you convert an improper fraction to a mixed number? ▾
Divide the numerator by the denominator. The whole number quotient becomes the whole part, the remainder becomes the new numerator, and the denominator stays the same.
Q4 What does simplifying a fraction mean? ▾
Simplifying (or reducing) a fraction means dividing both the numerator and denominator by their greatest common factor (GCF) until no common divisor other than 1 remains.
More in Fractions calculators
Ratio Calculator
ProportionsSolve proportions (A:B = C:D) via cross-multiplication, find missing values, and scale ratios (shrink or enlarge) with GCD reduction.
Adding Fractions Calculator
FractionsAdd two proper, improper, or mixed fractions: a/b + c/d.
Comparing Fractions Calculator
FractionsCompare two fractions a/b and c/d using cross multiplication ad vs bc.
Decimal to Fraction Calculator
FractionsConvert terminating or repeating decimals into exact reduced rational fractions.
Dividing Fractions Calculator
FractionsDivide fractions by multiplying by the reciprocal: (a/b) ÷ (c/d) = (a×d) / (b×c).
Equivalent Fractions Calculator
FractionsGenerate family of equivalent fractions by scaling numerator and denominator by k.
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