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Fraction Calculator

Calculate Fractions

Enter fractions as numerators and denominators, choose an operation, then press Calculate.

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Results & Actions

Calculate and view your fraction results

Simplified Fraction
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Decimal Value
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Mixed Number
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Step-by-Step Solution

Enter fractions and click "Calculate" to see step-by-step solution.

How It Works

Enter fractions as numerators and denominators, choose an operation, and get instant results with step-by-step explanations. Learn as you calculate.

Common Uses

Perfect for students doing homework, teachers creating examples, cooks adjusting recipes, and DIYers calculating measurements.

Always Accessible

Works completely in your browser - no data sent to servers. Use it anytime, anywhere with full privacy protection.

How the Fraction Calculator Works

  1. Input Recognition: The calculator accepts your fractions as numerators and denominators. It can also handle whole numbers if you enter them as a fraction (e.g., 3 as 3/1).
  2. Common Denominator (for +/-): For addition and subtraction, it finds the Least Common Denominator (LCD) by identifying the smallest number both denominators divide into evenly.
  3. Operation Execution: Based on your selection:
    • Add/Subtract: Converts fractions to equivalent forms with the LCD, then adds/subtracts numerators.
    • Multiply: Multiplies numerators together and denominators together.
    • Divide: Multiplies the first fraction by the reciprocal (flipped version) of the second fraction.
  4. Simplification: The result is simplified by dividing both the numerator and denominator by their Greatest Common Divisor (GCD).
  5. Conversion: The simplified fraction is also converted to a decimal and, if improper (numerator ≥ denominator), expressed as a mixed number.
  6. Output: All formats (simplified fraction, decimal, mixed number) and the solution steps are displayed clearly.

Fraction Calculation Rules

Addition/Subtraction

a/b ± c/d = (ad ± bc) / bd
a, c = numerators; b, d = denominators. First find a common denominator, then combine numerators.

Multiplication

(a/b) × (c/d) = (a × c) / (b × d)
a, c = numerators; b, d = denominators. Multiply straight across.

Division

(a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c)
a, c = numerators; b, d = denominators. Multiply by the reciprocal of the second fraction.

Simplification

Divide numerator and denominator by their Greatest Common Divisor (GCD)
Example: GCD of 8 and 12 is 4, so 8/12 = (8÷4)/(12÷4) = 2/3

Step-by-Step Examples

Example 1: Adding Fractions

Problem: 1/2 + 1/4 Steps: 1. Find LCD: Denominators are 2 and 4. LCD is 4. 2. Convert: 1/2 = (1×2)/(2×2) = 2/4. 3. Add: 2/4 + 1/4 = 3/4. 4. Simplify: 3/4 is already simplified.
Final Result: 3/4 or 0.75

Example 2: Multiplying Mixed Numbers

Problem: 2 1/3 × 3/4 Steps: 1. Convert mixed number: 2 1/3 = 7/3. 2. Multiply: (7/3) × (3/4) = 21/12. 3. Simplify: GCD of 21 and 12 is 3. 4. Result: 21/12 = 7/4. 5. Convert to mixed: 7/4 = 1 3/4.
Final Result: 7/4, 1 3/4, or 1.75

Practical Use Cases

Where Fraction Calculations Matter

Fraction calculations are essential in many everyday situations and professional fields. Understanding fractions helps with accurate measurements, fair distributions, and precise calculations.

Common Applications

  • Homework Help: Students can check their work on fraction problems and learn the steps behind the answer.
  • Recipe Scaling: Easily double, triple, or halve recipe ingredients that use fractional cups or teaspoons.
  • Construction & DIY: Accurately add and subtract fractional measurements for wood, piping, or fabric.
  • Financial Splits: Divide bills or expenses proportionally when amounts aren't whole numbers.
  • Teaching Aid: Teachers can generate examples and demonstrate solution processes visually.

Practical Example: Baking Cookies

Imagine a cookie recipe calls for 3/4 cup of sugar, but you want to make only 2/3 of the recipe.

Calculator Input:
  • Fraction: 3/4
  • Operation: Multiply
  • Multiplier: 2/3
Calculation:
3/4 × 2/3 = 6/12 = 1/2
Result:

You need 1/2 cup of sugar for 2/3 of the recipe.

How to Read the Results

The calculator provides three forms of the answer to suit different needs:

Simplified Fraction

This is the most reduced form of the answer (e.g., 3/4). It's the mathematically "pure" result and is best for further calculations or academic work. The numerator and denominator have no common factors other than 1.

Decimal Value

The fraction converted to a base-10 number (e.g., 0.75). Useful for quick comparisons, measurements on standard tools, or when working with calculators that don't handle fractions. The decimal is rounded to 3 places for clarity.

Mixed Number

For improper fractions (where the numerator is larger than the denominator), this shows the whole number part plus the remaining fraction (e.g., 1 3/4). This is the most intuitive form for everyday use, like in cooking or measuring with standard tools.

When to use each format: Use the simplified fraction for academic work, the decimal for quick reference and comparisons, and the mixed number for practical applications like recipes or measurements.

Frequently Asked Questions

What is the easiest way to add fractions?
Find a common denominator, convert both fractions, add the numerators, and keep the denominator. Our calculator shows these steps, helping you learn the process.
Why do I need to simplify fractions?
Simplification gives the most reduced, standard form of the answer, making it easier to understand, compare, and use in subsequent calculations.
How do I divide fractions with whole numbers?
First, convert the whole number to a fraction by putting it over 1 (e.g., 3 becomes 3/1). Then, follow the division rule: multiply by the reciprocal of the second fraction.
Can I input mixed numbers directly?
Currently, enter mixed numbers as improper fractions. For example, enter 2 1/2 as 5/2 (since 2*2+1=5). We show this conversion step in the solution.
What if my denominator is zero?
The calculator will show an error. Division by zero is mathematically undefined, both for fractions and general math. Always use a positive integer denominator.
How do I find the Least Common Denominator (LCD)?
Find the smallest number that both denominators divide into evenly. For example, the LCD of 4 and 6 is 12. The calculator does this automatically in the step-by-step solution.

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