Fraction Calculator
Comprehensive fraction calculator that performs addition, subtraction, multiplication, and division of fractions with automatic simplification to lowest terms. Enter two fractions and select an operation to see results in improper fraction, mixed number, and decimal forms. The calculator shows step-by-step calculations using the greatest common divisor (GCD) method for simplification. Perfect for students, teachers, or anyone working with fractions in mathematics, cooking, or measurements. All calculations happen instantly in your browser with complete privacy—no data is stored or transmitted.
Fraction Calculator
First Fraction
Second Fraction
How it works: This calculator performs operations on fractions and automatically simplifies the results. Enter two fractions and select an operation to see the result in improper fraction, mixed number, and decimal forms. The calculator shows step-by-step calculations and uses the greatest common divisor (GCD) to simplify fractions to their lowest terms.
What Is a Fraction Calculator?
A fraction calculator performs arithmetic operations — addition, subtraction, multiplication, and division — on fractions and mixed numbers, and automatically simplifies the result to its lowest terms. Unlike decimal calculations, fraction arithmetic requires finding common denominators for addition and subtraction, and involves numerator-denominator manipulation for multiplication and division.
Fractions appear everywhere: cooking recipes (2/3 cup), construction measurements (3/4 inch), probability (1 in 6 chance = 1/6), investment returns (3/8 percentage point), and school math. This calculator handles proper fractions, improper fractions (numerator > denominator), and mixed numbers (e.g., 2 3/4), giving results in both fraction and decimal form.
How to Use This Fraction Calculator
- Enter the numerator and denominator for each fraction. For mixed numbers, enter the whole number separately.
- Select the operation: + (add), − (subtract), × (multiply), or ÷ (divide).
- The calculator shows the result as a simplified fraction, mixed number, and decimal equivalent.
- To enter a whole number as a fraction, put it over 1 (e.g., 5 = 5/1).
Worked Examples: All Four Operations
Addition: 3/4 + 2/3
LCM(4,3) = 12 → 9/12 + 8/12 = 17/12 = 1 5/12 ≈ 1.417
Subtraction: 5/6 − 1/4
LCM(6,4) = 12 → 10/12 − 3/12 = 7/12 ≈ 0.583
Multiplication: 2/3 × 3/5
Multiply straight across: (2×3)/(3×5) = 6/15 = 2/5 = 0.4
Division: 3/4 ÷ 2/3
Multiply by reciprocal: 3/4 × 3/2 = 9/8 = 1 1/8 = 1.125
Mixed number example: 2 3/4 + 1 1/2 → convert to improper: 11/4 + 3/2 → 11/4 + 6/4 = 17/4 = 4 1/4
Fraction to Decimal Reference Table
| Fraction | Decimal | Percentage | Common Use |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half of anything; splitting evenly |
| 1/3 | 0.3333… | 33.3% | One third; repeating decimal |
| 2/3 | 0.6667… | 66.7% | Two thirds; recipe scaling |
| 1/4 | 0.25 | 25% | Quarter; discounts, tips |
| 3/4 | 0.75 | 75% | Three quarters; measurements |
| 1/5 | 0.2 | 20% | One fifth; tax rates, tips |
| 1/6 | 0.1667… | 16.7% | One sixth; dice probability |
| 1/8 | 0.125 | 12.5% | One eighth; imperial measurements |
| 3/8 | 0.375 | 37.5% | Three eighths; woodworking |
| 5/8 | 0.625 | 62.5% | Five eighths; engineering |
| 7/8 | 0.875 | 87.5% | Seven eighths; near whole |
| 1/10 | 0.1 | 10% | One tenth; simple percentages |
Key Concepts: GCF, LCM, and Simplification
Greatest Common Factor (GCF) is the largest number that divides evenly into both numerator and denominator. To simplify a fraction, divide both by their GCF. Example: 12/18 — GCF(12,18) = 6 → 12÷6 / 18÷6 = 2/3. A fraction is in lowest terms when GCF = 1.
Least Common Multiple (LCM) is the smallest number that both denominators divide into evenly — used for finding a common denominator when adding or subtracting fractions. LCM(4,6) = 12 because 12 ÷ 4 = 3 (whole) and 12 ÷ 6 = 2 (whole). Quick method: LCM(a,b) = (a × b) ÷ GCF(a,b).
Improper fractions vs. mixed numbers. An improper fraction has numerator ≥ denominator (e.g., 7/4). A mixed number separates the whole part (e.g., 1 3/4). To convert: divide numerator by denominator — quotient is the whole number, remainder is the new numerator. 7 ÷ 4 = 1 remainder 3 → 1 3/4.
Tips for Fraction Arithmetic
Always simplify before multiplying. When multiplying fractions, simplify any numerator with any denominator across the multiplication sign before computing — this is called “cross-cancellation.” Example: (4/9) × (3/8) — cancel 4 and 8 by 4, cancel 3 and 9 by 3: (1/3) × (1/2) = 1/6. Much easier than multiplying first and simplifying 12/72 after.
Division = multiply by the reciprocal. Never try to divide fractions directly. Flip the second fraction (swap numerator and denominator) and multiply. (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8 = 1 7/8. This rule — “keep, change, flip” — works for all fraction division problems.
Convert mixed numbers before computing. Convert mixed numbers to improper fractions before any operation. 2 3/4 = (2×4+3)/4 = 11/4. Then add, subtract, multiply, or divide the improper fractions. Convert back to mixed number format at the end if needed. Trying to operate on mixed numbers directly leads to errors.
Frequently Asked Questions
How do you add fractions with different denominators?
Find the Least Common Multiple (LCM) of the denominators to get a common denominator. Convert each fraction so it has that denominator, then add the numerators. Finally, simplify if possible. Example: 1/3 + 1/4 → LCM(3,4)=12 → 4/12 + 3/12 = 7/12.
How do you simplify a fraction?
Divide both the numerator and denominator by their Greatest Common Factor (GCF). Example: 18/24 — GCF(18,24)=6 → 18÷6 / 24÷6 = 3/4. If GCF=1, the fraction is already in simplest form. You can find GCF using prime factorization or Euclid's algorithm.
What is an improper fraction?
An improper fraction has a numerator larger than or equal to its denominator (e.g., 9/4, 7/7, 15/8). It represents a value ≥ 1. To convert to a mixed number: divide numerator ÷ denominator. Quotient = whole number, remainder/denominator = fractional part. 9÷4 = 2 remainder 1 → 2 1/4.
How do you multiply fractions?
Multiply numerators together and denominators together. Simplify the result. Example: (2/3) × (3/5) = (2×3)/(3×5) = 6/15 = 2/5. Tip: cross-cancel common factors before multiplying to keep numbers small. (4/9) × (3/8) → cancel 4&8 and 3&9 → (1/3) × (1/2) = 1/6.
How do you divide fractions?
Use the 'keep, change, flip' rule: keep the first fraction, change ÷ to ×, flip the second fraction (take its reciprocal). Example: (3/4) ÷ (2/3) = (3/4) × (3/2) = 9/8 = 1 1/8. This works because dividing by a number is the same as multiplying by its multiplicative inverse.
What is a mixed number?
A mixed number combines a whole number and a proper fraction (e.g., 3 1/2, 2 3/4). It is equivalent to an improper fraction: 3 1/2 = 7/2. Mixed numbers are easier to visualize but harder to compute with — always convert to improper fractions before doing arithmetic, then convert back afterward.
How do you convert a decimal to a fraction?
Count the decimal places and use that as your denominator's power of 10. Example: 0.75 = 75/100 = 3/4 (divide by GCF=25). For repeating decimals: let x = 0.333… → 10x = 3.333… → 10x − x = 3 → 9x = 3 → x = 3/9 = 1/3. Use the calculator to verify your conversion.
What is the difference between a proper and improper fraction?
A proper fraction has a numerator less than its denominator (value < 1): 3/4, 2/7, 5/9. An improper fraction has numerator ≥ denominator (value ≥ 1): 7/4, 9/9, 15/8. Both are valid — improper fractions are often more useful in calculations, while proper fractions are easier to compare in everyday contexts.