Add, Subtract, Multiply & Divide Fractions
Free fraction calculator. Learn how to add fractions, subtract fractions, multiply and divide fractions. Shows step-by-step solutions with simplified results.
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Dimensions: 100% width, 650px height, fully responsive.
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Styling: Clean minimal design with rounded border, optimized for embedding.
Understanding results
The calculator displays:
- Simplified Fraction: The result reduced to its lowest terms (e.g., 6/8 becomes 3/4)
- Decimal Equivalent: The fraction expressed as a decimal number
- Step-by-Step Breakdown: Shows exactly how the calculation was performed
These results help you verify your homework, understand the process, and convert between fraction and decimal forms.
Purpose
Quick Answer: To add fractions like 1/2 + 1/4, find a common denominator (4), convert (2/4 + 1/4), and add numerators = 3/4. To multiply fractions, multiply straight across. To divide, flip and multiply.
The fraction calculator helps you perform arithmetic operations with fractions quickly and accurately. Whether you need to add fractions, subtract fractions, multiply fractions, or divide fractions, this tool shows you the step-by-step solution and simplifies the result automatically.
Fractions are essential in everyday math, cooking, construction, and academics. This calculator handles both proper and improper fractions, giving you results in both fraction and decimal form.
How to use
Using the fraction calculator is simple:
- Enter the first fraction: Input the numerator (top number) and denominator (bottom number)
- Select the operation: Choose add (+), subtract (−), multiply (×), or divide (÷)
- Enter the second fraction: Input the numerator and denominator
- View results: See the step-by-step solution, simplified fraction, and decimal equivalent
Examples
Example 1: Adding Fractions
Problem: 1/2 + 1/4
- Find common denominator: (1×4 + 1×2) / (2×4) = 6/8
- Simplify: 6/8 = 3/4
Example 2: Multiplying Fractions
Problem: 2/3 × 2/3
- Multiply numerators: 2×2 = 4
- Multiply denominators: 3×3 = 9
- Result: 4/9
Example 3: Dividing Fractions
Problem: 2/3 ÷ 4 (same as 2/3 ÷ 4/1)
- Flip and multiply: 2/3 × 1/4 = 2/12
- Simplify: 2/12 = 1/6
How it works
Addition: a/b + c/d = (ad + bc) / bd
Subtraction: a/b − c/d = (ad − bc) / bd
Multiplication: a/b × c/d = (a×c) / (b×d)
Division: a/b ÷ c/d = (a×d) / (b×c)
After calculating, the result is simplified by dividing both numerator and denominator by their greatest common divisor (GCD).
FAQ
How do you add fractions?
Find a common denominator, adjust numerators, add the tops, keep the bottom. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do you subtract fractions?
Find a common denominator, subtract the numerators. Example: 3/4 − 1/2 = 3/4 − 2/4 = 1/4.
How do you multiply fractions?
Multiply the tops, multiply the bottoms. Example: 2/3 × 3/4 = 6/12 = 1/2. No common denominator needed.
How do you divide fractions?
Flip the second fraction and multiply. Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3. Remember: Keep, Change, Flip.
What is 1/2 plus 1/4?
1/2 + 1/4 = 2/4 + 1/4 = 3/4 (or 0.75 as a decimal).
What is 2/3 times 2/3?
2/3 × 2/3 = 4/9 (multiply tops: 2×2=4, multiply bottoms: 3×3=9).
What is 2/3 divided by 4?
2/3 ÷ 4 = 2/3 × 1/4 = 1/6. Write 4 as 4/1, flip to 1/4, then multiply.
How do you add fractions with different denominators?
Find the LCD (least common denominator), convert each fraction, then add. Example: 1/3 + 1/4 → LCD is 12 → 4/12 + 3/12 = 7/12.
What is 1/2 times 1/2?
1/2 × 1/2 = 1/4 (multiply tops: 1×1=1, multiply bottoms: 2×2=4).
What is the easiest way to add fractions?
Cross-multiply and add: a/b + c/d = (ad + bc) / bd. Then simplify. Example: 1/2 + 1/3 = (3+2)/6 = 5/6.
Can you add fractions with different denominators?
Yes. Convert to a common denominator first, then add the numerators. This calculator does it automatically.
Methodology
How This Calculator Works
The fraction calculator uses standard mathematical operations for fraction arithmetic:
Addition & Subtraction: Uses the cross-multiplication method to find a common denominator, then combines numerators.
Multiplication: Directly multiplies numerators together and denominators together.
Division: Inverts the second fraction (reciprocal) and multiplies.
Simplification: After every operation, the result is reduced to lowest terms by dividing both numerator and denominator by their Greatest Common Divisor (GCD) using the Euclidean algorithm.
Validation & Accuracy
Tested: Verified against Wolfram Alpha, scientific calculators, and educational math resources with 50+ test cases.
Accuracy: Results are mathematically exact. Decimal equivalents are shown to 6 decimal places for precision.
Sources
The methodology is based on standard mathematical principles for fraction arithmetic taught in US Common Core curriculum and internationally recognized math education standards.