Fraction Calculator — Add, Subtract, Multiply, Divide

Enter whole numbers, fractions (e.g., -7/4), or mixed numbers (e.g., 2 3/5). Private by design—everything runs locally in your browser.

Inputs & Options

Formats: 5, -7/4, 2 3/5
Supports negatives and mixed numbers

Privacy: Everything runs in your browser. Nothing is uploaded.

Result

Result (fraction):
Results will appear here.
Result (mixed):
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Result (decimal):
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Tip: Press Enter in an input field to calculate.

How the Fraction Calculator Works

This tool converts any inputs (whole numbers, simple fractions, mixed numbers) to improper fractions, performs the selected operation, and then reduces the result to lowest terms using the greatest common divisor (GCD). You’ll also see the mixed-number form and a decimal approximation.

Operations

  • Add/Subtract: Uses a common denominator (least common multiple of the two denominators) to combine numerators, then simplifies.
  • Multiply: Multiply numerators together and denominators together, then simplify.
  • Divide: Multiply by the reciprocal of the second fraction (i.e., flip it), then simplify.

Example

Compute \( 1 \tfrac{1}{2} + \tfrac{3}{8} \): Convert to improper forms: \( \tfrac{3}{2} + \tfrac{3}{8} \). LCM of 2 and 8 is 8, so \( \tfrac{12}{8} + \tfrac{3}{8} = \tfrac{15}{8} \). Mixed form is \( 1 \tfrac{7}{8} \).

Understanding Fractions

A fraction represents a part of a whole. It consists of two numbers:

  • Numerator: the top number, showing how many parts we have.
  • Denominator: the bottom number, showing into how many equal parts the whole is divided.

Types of Fractions

  • Proper fraction: numerator smaller than denominator (e.g., \( \tfrac{3}{4} \)).
  • Improper fraction: numerator larger than or equal to denominator (e.g., \( \tfrac{9}{5} \)).
  • Mixed number: whole number plus a proper fraction (e.g., \( 1 \tfrac{2}{3} \)).

Why Simplify Fractions?

Simplifying means dividing numerator and denominator by their greatest common divisor (GCD). For example:

\( \tfrac{12}{16} = \tfrac{12 \div 4}{16 \div 4} = \tfrac{3}{4} \)

This makes fractions easier to understand and compare.

Fractions in Daily Life

  • Cooking: Recipes often use halves, thirds, or quarters.
  • Construction: Measurements use eighths and sixteenths of an inch.
  • Probability: A fair coin has a probability of \( \tfrac{1}{2} \) for heads or tails.

Quick Conversion Tip

To convert a fraction to a decimal, divide numerator by denominator. For example, \( \tfrac{7}{8} = 0.875 \).

5 Fun Facts about Fractions

Decimal ≠ fraction? Not always

0.1 looks simple, but it’s \(1/10\). Meanwhile 0.1 in binary is repeating—fractions depend on the base you use.

Base-dependent

Egyptians loved unit fractions

Ancient scribes wrote every fraction as sums of distinct unit fractions (like \(1/2 + 1/6\)), never repeated.

History twist

Simplify with primes

Factoring numerator and denominator into primes makes reducing a fraction trivial—just cancel shared factors.

Prime power

Repeating decimals hide fractions

Any repeating decimal is rational. For example, 0.\(\overline{3}\) = 1/3, 0.\(\overline{142857}\) = 1/7.

Pattern clue

Mixed numbers are just improper

\(1\tfrac{3}{4} = \tfrac{7}{4}\). Switching forms is a single multiply-and-add—handy for calculations.

Form swap

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