Fraction Calculators
Free online fraction calculators to simplify, compare, order, and perform arithmetic on proper, improper, and mixed numbers with step-by-step solutions.
Available Fractions Solvers
Select a calculator to view formula and step-by-step solution
Basic Operations
5 calculators
Fraction Calculator (All-in-One)
Add, subtract, multiply, and divide proper and improper fractions with step-by-step solutions.
Adding Fractions Calculator
Add two or more fractions with like or unlike denominators using the LCD method.
Subtracting Fractions Calculator
Subtract fractions with like and unlike denominators with complete step-by-step reduction.
Multiplying Fractions Calculator
Multiply fractions step-by-step with cross-cancellation and lowest terms simplification.
Dividing Fractions Calculator
Divide fractions using the reciprocal keep-change-flip (KCF) rule with full working.
Simplification & Mixed Numbers
4 calculators
Simplify Fractions Calculator
Reduce proper and improper fractions to their simplest lowest terms using the GCD.
Mixed Numbers Calculator
Add, subtract, multiply, and divide mixed numbers and whole integers with step-by-step steps.
Improper Fraction to Mixed Number
Convert improper fractions into whole mixed numbers with quotient and remainder.
Mixed Number to Improper Fraction
Convert mixed numbers into simplified improper fractions with step-by-step multiplication.
Comparing & Ordering
3 calculators
Comparing Fractions Calculator (<, >, =)
Compare two fractions to determine which is greater, smaller, or equal with cross-multiplication.
Ordering Fractions (Least to Greatest)
Order multiple fractions from least to greatest or greatest to least using common denominators.
Equivalent Fractions Calculator
Find equivalent fractions and missing numerators/denominators with visual multipliers.
Conversions & Helpers
3 calculators
Fraction to Decimal Calculator
Convert proper, improper, and mixed fractions into exact or repeating decimal numbers.
Decimal to Fraction Calculator
Convert terminating and repeating decimals into fully reduced simplified fractions.
Least Common Denominator (LCD) Calculator
Find the Least Common Denominator (LCD) of two or multiple fractions using the LCM.
Understanding Fractions: Parts of a Whole
The word fraction originates from the Latin "fractio", meaning "to break into pieces". Mathematically, a fraction represents a numerical value that is not an integer but a proportion of an integer—written as a ratio $\frac{a}{b}$. The upper number is the numerator (how many parts you have), and the lower number is the denominator (how many equal parts form the complete whole, where $b \neq 0$). Fractions form the foundation of ratios, algebra, scaling recipes, construction measurements, and higher-order calculus.
Explore Fraction Tools by Mathematical Focus
Fraction Arithmetic & Mixed Numbers
Add, subtract, multiply, and divide proper, improper, and mixed fractions with Least Common Denominator (LCD) balancing and cross-cancellation.
Simplification & Equivalent Chains
Reduce fractions to lowest terms using Greatest Common Factor (GCF/GCD) division, find equivalent ratios, and solve for missing variables.
Comparing & Ordering Fractions
Compare two or more fractions using cross-multiplication (butterfly method) or sort multiple fractions from least to greatest with LCD normalization.
Fraction Conversions
Convert improper fractions to mixed numbers, turn decimals into simplified fractions, and expand fractions into terminating or repeating decimals.
Master Fraction Rules Quick Reference
Below is a summary of the fundamental formulas and operational steps utilized across our fraction tools:
| Operation / Task | Standard Mathematical Rule | Example Expression |
|---|---|---|
| Addition (Unlike Denominators) | (a·d + b·c) / (b·d) | 1/3 + 1/4 = (4 + 3)/12 = 7/12 |
| Subtraction (Unlike Denominators) | (a·d - b·c) / (b·d) | 5/6 - 1/4 = (10 - 3)/12 = 7/12 |
| Multiplication | (a × c) / (b × d) | 2/3 × 3/5 = 6/15 = 2/5 |
| Division (Keep, Change, Flip) | (a / b) × (d / c) = (a·d) / (b·c) | 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 |
| Simplifying / Reducing | (a ÷ GCF) / (b ÷ GCF) | 18/24 ÷ 6/6 = 3/4 |
| Improper to Mixed Number | Quotient + (Remainder / Denominator) | 17/5 = 3 with rem 2 → 3 2/5 |
Core Rules & Mental Math Shortcuts for Fractions
- The Cross-Multiplication Butterfly Test: To quickly compare two fractions like $\frac{3}{7}$ and $\frac{4}{9}$, multiply diagonally: $3 \times 9 = 27$ and $4 \times 7 = 28$. Since $27 < 28$, $\frac{3}{7} < \frac{4}{9}$.
- Cross-Cancel Before Multiplying: Never multiply large numerators and denominators directly. Cancel out common factors between any top and any bottom number beforehand to keep figures in lowest terms automatically.
- The "Keep, Change, Flip" (KCF) Rule for Division: Never divide fractions straight across. Keep the first fraction, change division to multiplication, and flip the second fraction into its reciprocal.