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Fraction Calculator

Comprehensive fraction calculator: operations, mixed numbers, simplify, decimal-to-fraction, and fraction-to-decimal conversions with step-by-step solutions.

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Calculator Modes

This comprehensive calculator offers 5 modes for all your fraction needs:

  • Operations: Add, subtract, multiply, and divide fractions
  • Mixed Numbers: Convert between mixed numbers and improper fractions
  • Simplify: Reduce fractions to lowest terms
  • Decimal→Fraction: Convert decimals to fractions
  • Fraction→Decimal: Convert fractions to decimals with repeating pattern detection

Fraction Operations

Perform basic arithmetic operations on fractions with step-by-step solutions.

Adding Fractions

Formula: a/b + c/d = (ad + bc) / bd

Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6

Subtracting Fractions

Formula: a/b - c/d = (ad - bc) / bd

Example: 3/4 - 1/2 = (3×2 - 1×4) / (4×2) = 2/8 = 1/4

Multiplying Fractions

Formula: a/b × c/d = ac / bd

Example: 2/3 × 3/4 = 6/12 = 1/2

Dividing Fractions

Formula: a/b ÷ c/d = a/b × d/c = ad / bc

Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2

Understanding Fractions

Parts of a Fraction

  • Numerator: The top number (how many parts you have)
  • Denominator: The bottom number (total equal parts)

Types of Fractions

  • Proper: Numerator < denominator (e.g., 3/4)
  • Improper: Numerator ≥ denominator (e.g., 5/3)
  • Mixed: Whole number + fraction (e.g., 1⅔)

Simplifying Fractions

To simplify, find the greatest common divisor (GCD) and divide both parts by it.

Example: 12/18 → GCD is 6 → 12÷6 / 18÷6 = 2/3

Mixed Number Conversions

Mixed to Improper

Formula: Whole × Denominator + Numerator / Denominator

Example: 2 3/4 = (2×4 + 3)/4 = 11/4

Improper to Mixed

Divide numerator by denominator. Quotient becomes whole number, remainder becomes new numerator.

Example: 7/3 = 2 1/3 (7÷3 = 2 remainder 1)

Decimal Conversions

Decimal to Fraction

Uses continued fractions algorithm for accurate conversion. Handles both terminating and repeating decimals.

Examples:

  • 0.75 → 3/4
  • 0.333... → 1/3
  • 0.125 → 1/8

Fraction to Decimal

Divides numerator by denominator and detects repeating patterns.

Examples:

  • 1/4 = 0.25 (terminating)
  • 1/3 = 0.333... (repeating)
  • 1/7 = 0.142857... (repeating pattern: 142857)

Common Fraction-Decimal-Percent Equivalents

  • 1/8 = 0.125 = 12.5%
  • 1/4 = 0.25 = 25%
  • 1/3 = 0.333... = 33.3%
  • 1/2 = 0.5 = 50%
  • 2/3 = 0.666... = 66.7%
  • 3/4 = 0.75 = 75%
  • 7/8 = 0.875 = 87.5%

Fractions in Real Life

  • Cooking: Recipes use fractions constantly — 1/2 cup flour, 3/4 tsp salt, 1/3 cup milk. Scaling a recipe requires multiplying fractions
  • Construction: Tape measures are marked in 1/16-inch increments. Lumber dimensions use fractions (a 2×4 is actually 1 1/2 × 3 1/2 inches)
  • Music: Note durations are fractions — whole, half, quarter, eighth, sixteenth notes. Time signatures like 3/4 and 6/8 are fractions
  • Finance: Stock prices historically used fractions (1/8 increments) before switching to decimals in 2001

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Calculate mean, median, mode, range, and standard deviation. Complete statistics for any data set.

Ratio Calculator

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Exponent Calculator

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Calculate square roots, cube roots, and nth roots. Simplify radicals and identify perfect squares.

Frequently Asked Questions

How do I add fractions?

Find a common denominator, add the numerators, then simplify. Formula: a/b + c/d = (ad + bc) / bd

How do I subtract fractions?

Find a common denominator, subtract the numerators, then simplify. Formula: a/b - c/d = (ad - bc) / bd

How do I multiply fractions?

Multiply numerators together and denominators together, then simplify. Formula: a/b × c/d = ac / bd

How do I divide fractions?

Multiply by the reciprocal (flip the second fraction). Formula: a/b ÷ c/d = a/b × d/c = ad / bc

What is simplifying a fraction?

Dividing both numerator and denominator by their greatest common divisor (GCD). Example: 6/8 simplifies to 3/4.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, add the numerator, then place over the original denominator. Example: 2 3/4 = (2×4 + 3)/4 = 11/4

How do I convert a decimal to a fraction?

The calculator uses continued fractions algorithm to find the best fractional representation. Example: 0.75 = 3/4, 0.333... = 1/3

What is a repeating decimal?

A decimal with digits that repeat infinitely. Example: 1/3 = 0.333..., 1/7 = 0.142857... (the pattern 142857 repeats)