Fraction Conversion Calculator

Convert between improper fractions, mixed numbers, and decimal forms:

\[ \text{Mixed Number} = \text{Whole Number} + \frac{\text{Numerator}}{\text{Denominator}} \] \[ \text{Improper Fraction} = \frac{(\text{Whole Number} \times \text{Denominator}) + \text{Numerator}}{\text{Denominator}} \] \[ \text{Decimal} = \text{Whole Number} + \frac{\text{Numerator}}{\text{Denominator}} \]

Input Type:

Whole Number:

Numerator:

Denominator:

Decimal:

Improper Fraction:

Mixed Number:

Decimal:

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1. What is Fraction Conversion?

Fraction conversion involves changing between different representations of numbers: improper fractions, mixed numbers, and decimals. An improper fraction has a numerator larger than its denominator, a mixed number combines a whole number with a proper fraction, and a decimal represents the value in base-10 notation.

2. How Does the Calculator Work?

The calculator performs conversions between these forms:

Conversion Process:

From improper fraction: Divide numerator by denominator to get decimal, extract whole number part
From mixed number: Multiply whole number by denominator and add numerator to get improper fraction
From decimal: Separate whole number part, convert fractional part to fraction using continued fractions algorithm

3. Importance of Fraction Conversion

Details: Different mathematical operations require different forms. Mixed numbers are easier to understand for measurements, improper fractions are better for calculations, and decimals are most precise for many applications.

4. Using the Calculator

Tips: Select your input type first, then enter the corresponding values. The calculator will automatically show all equivalent forms. For decimals, it will find the simplest fraction representation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between improper and mixed fractions?
A: An improper fraction has a numerator ≥ denominator (e.g., 5/4), while a mixed number combines a whole number with a proper fraction (e.g., 1 1/4).

Q2: How do you convert repeating decimals?
A: The calculator uses a continued fraction algorithm that can approximate repeating decimals, though exact representation may require special notation.

Q3: Why would I need to convert between these forms?
A: Different contexts require different forms - mixed numbers for measurements, improper fractions for calculations, decimals for precise values.

Q4: How accurate is the decimal to fraction conversion?
A: The algorithm is accurate to 6 decimal places, finding the simplest fraction within that tolerance.

Q5: Can I enter negative numbers?
A: The current version only handles positive numbers, but negative versions would follow the same conversion rules.