Add, subtract, multiply and divide fractions with steps shown. Enter your fractions and get the simplified answer, mixed number and decimal.
Fraction Calculator
Add, subtract, multiply, and divide proper, improper, or mixed fractions with automatic Least Common Denominator (LCD) and Greatest Common Divisor (GCD) reduction.
Enter your fractions
Whole number fields are optional — leave blank for simple fractions.
Your result will appear here
Enter your values above, then press Calculate Fractions — or press Enter in any field.TinyExe · Fraction Result
Exact reduced fraction, mixed number & decimal equivalent
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All fractions are simplified to lowest terms using Euclid's Greatest Common Divisor (GCD) algorithm.
Fraction operation rules at a glance
Each arithmetic operation follows a distinct algebraic rule before simplifying the final fraction by its Greatest Common Divisor (GCD).
| Operation | Symbolic Rule | Key Requirement |
|---|---|---|
| Addition (+) | (a·d + b·c) / (b·d) | Requires a common denominator (LCD of b and d). |
| Subtraction (−) | (a·d − b·c) / (b·d) | Requires a common denominator (LCD of b and d). |
| Multiplication (×) | (a · c) / (b · d) | Multiply numerators directly and denominators directly. |
| Division (÷) | (a · d) / (b · c) | Multiply the first fraction by the reciprocal of the second. |
The formula
Mixed numbers are first converted to improper fractions so every operation is exact.
Add & Subtract via LCD
Where L = LCM(b, d) is the Least Common Denominator. Once combined over L, divide top and bottom by GCD(numerator, L).
Multiply & Divide
Multiplication requires no common denominator. Division flips the second fraction (reciprocal d/c) and multiplies.
Worked examples
Three common fraction problems worked out step by step.
Example 1 · Addition
2/5 + 1/3
Adding two proper fractions with different denominators.
| Calculation | Steps |
|---|---|
| LCD(5, 3) = 15 | Scale 2/5 to 6/15 and 1/3 to 5/15. |
| 6/15 + 5/15 = 11/15 | GCD(11, 15) = 1 (already in lowest terms, ≈ 0.7333). |
11/15 (0.7333)
Example 2 · Multiplication
3/4 × 2/9
Multiplying and reducing by GCD.
| Calculation | Steps |
|---|---|
| (3 × 2) / (4 × 9) = 6/36 | Multiply numerators and denominators. |
| 6/36 ÷ 6 = 1/6 | Divide both by GCD(6, 36) = 6. |
1/6 (0.1667)
Example 3 · Mixed Division
1 1/2 ÷ 3/4
Dividing a mixed number by a proper fraction.
| Calculation | Steps |
|---|---|
| 1 1/2 = 3/2 | Convert mixed number to improper fraction. |
| 3/2 × 4/3 = 12/6 = 2 | Multiply by reciprocal 4/3 and simplify. |
2 (Exact Whole)
How to use this calculator
Enter the first fraction
Type the numerator and denominator for Fraction 1 (and an optional whole number if working with mixed numbers).
Choose the arithmetic operation
Select Add (+), Subtract (−), Multiply (×), or Divide (÷).
Enter the second fraction
Type the numerator and denominator for Fraction 2.
Press Calculate Fractions
View the reduced fraction, mixed number form, decimal equivalent, percentage, and LCD/GCD steps.
Save or compare on the tape
Download a branded PDF/PNG certificate or compare multiple fraction problems in the session tape.
Frequently asked questions
How do you multiply fractions?
Multiply the two numerators together to get the new numerator, multiply the two denominators together to get the new denominator, and then divide both by their Greatest Common Divisor (GCD).
How do I convert a fraction to a decimal?
Divide the top number (numerator) by the bottom number (denominator). For example, 2/5 = 2 ÷ 5 = 0.4, and 1/3 = 1 ÷ 3 ≈ 0.333333.
How does mixed number calculation work?
A mixed number like 2 3/4 is converted to the improper fraction ((2 × 4) + 3)/4 = 11/4 before performing the operation, then converted back to mixed form at the end.
Why can't the denominator be zero?
Division by zero is undefined in mathematics. Both denominators (and the second fraction itself when dividing) must be non-zero.