Fraction Calculator
How to Add Fractions
Formula: (a/b) + (c/d) = (ad + bc)/(bd)
Master Fraction Calculations with Our Free Online Tool
Working with fractions doesn't have to be complicated. Our fraction calculator handles all four basic operations—addition, subtraction, multiplication, and division—giving you instant results whether you're solving homework problems, checking your work, or tackling real-world math challenges.
What makes this tool stand out? It automatically simplifies your answers to their lowest terms and shows results in both improper fraction and mixed number formats. This means you get the exact answer you need, presented in the way that makes the most sense for your situation.
Students love using this calculator because it helps them understand fraction operations through clear examples. Teachers appreciate how it saves time during lesson planning and grading. Professionals find it useful for quick calculations in fields like engineering, construction, and finance where precise fractional measurements matter.
The calculator works with any combination of positive and negative fractions, handles whole numbers, and even works with mixed numbers. Simply enter your numerators and denominators, choose your operation, and click calculate. You'll see your result in seconds, ready to use.
Step-by-Step Examples
Example 1: Adding Fractions with Different Denominators
When adding fractions, you need a common denominator. Here's how to add 1/2 and 1/3.
Input: 1/2 + 1/3
Output: 5/6 (or 0 5/6 as a mixed number)
To add 1/2 and 1/3, find a common denominator (6). Convert: 1/2 = 3/6 and 1/3 = 2/6. Then add: 3/6 + 2/6 = 5/6. The result is already in simplest form.
Example 2: Subtracting Fractions
Subtracting fractions follows the same process as addition—find a common denominator first.
Input: 3/4 - 1/6
Output: 7/12 (or 0 7/12 as a mixed number)
Common denominator is 12. Convert: 3/4 = 9/12 and 1/6 = 2/12. Subtract: 9/12 - 2/12 = 7/12. This fraction cannot be simplified further.
Example 3: Multiplying Fractions
Multiplying fractions is straightforward—multiply numerators together and denominators together, then simplify.
Input: 2/3 × 3/4
Output: 1/2 (or 0 1/2 as a mixed number)
Multiply numerators: 2 × 3 = 6. Multiply denominators: 3 × 4 = 12. Result: 6/12. Simplify by dividing both by 6: 6/12 = 1/2.
Example 4: Dividing Fractions
To divide fractions, multiply by the reciprocal of the second fraction, then simplify the result.
Input: 5/8 ÷ 2/3
Output: 15/16 (or 0 15/16 as a mixed number)
Dividing by 2/3 is the same as multiplying by 3/2. So: 5/8 × 3/2 = (5×3)/(8×2) = 15/16. This is already in simplest form.
Example 5: Adding Fractions That Result in Mixed Numbers
Sometimes adding fractions gives you a result greater than 1, which we express as a mixed number.
Input: 3/4 + 2/3
Output: 17/12 (or 1 5/12 as a mixed number)
Common denominator is 12. Convert: 3/4 = 9/12 and 2/3 = 8/12. Add: 9/12 + 8/12 = 17/12. As a mixed number: 17 ÷ 12 = 1 remainder 5, so 1 5/12.
Frequently Asked Questions
How do I add fractions with different denominators?
To add fractions with different denominators, first find a common denominator. The easiest method is to multiply the two denominators together. Then, convert each fraction to an equivalent fraction with that common denominator by multiplying both the numerator and denominator by the same number. Finally, add the numerators and keep the common denominator. Don't forget to simplify your answer if possible.
What's the difference between an improper fraction and a mixed number?
An improper fraction has a numerator that's equal to or larger than the denominator (like 7/4 or 5/5). A mixed number combines a whole number with a proper fraction (like 1 3/4). Both represent the same value—our calculator shows you both formats so you can use whichever is more appropriate for your needs.
Can I use this calculator for negative fractions?
Yes, our fraction calculator handles negative fractions. Simply enter a negative number for the numerator or denominator. The calculator will correctly perform all operations with negative values, following standard mathematical rules.
How do I simplify fractions?
To simplify a fraction, find the greatest common factor (GCF) of the numerator and denominator, then divide both by that number. For example, 8/12 can be simplified because both 8 and 12 are divisible by 4: 8÷4 = 2 and 12÷4 = 3, giving you 2/3. Our calculator automatically simplifies all results to their lowest terms.
Why do I need to find a common denominator when adding or subtracting?
Fractions represent parts of a whole, but they need to represent parts of the same-sized whole to be added or subtracted. A common denominator ensures both fractions are divided into the same number of equal parts. Think of it like trying to add 3 apples and 2 oranges—you need to convert them to the same unit first.
What happens if I divide by zero?
Division by zero is undefined in mathematics. If you try to divide a fraction by 0/1 (or any fraction equivalent to zero), our calculator will show an error message. Always ensure your second fraction's numerator is not zero when performing division.
Can I use this calculator for homework?
Absolutely! This calculator is perfect for checking your homework answers or understanding how fraction operations work. However, make sure your teacher allows calculator use for assignments. It's also a great tool for learning—try working out problems by hand first, then use the calculator to verify your answers.
How accurate are the results?
Our fraction calculator provides exact results, not decimal approximations. This means you get precise answers in fraction form, which is often more useful than decimal equivalents. The calculator handles all operations with complete mathematical accuracy.
What if my fraction has large numbers?
Our calculator can handle fractions with large numerators and denominators. However, very large numbers might take a moment longer to process as the calculator simplifies the result. The tool is designed to work efficiently with numbers of any reasonable size.
Do I need to simplify fractions before using the calculator?
No, you don't need to simplify your input fractions. Enter them exactly as they are, and the calculator will automatically simplify the final result. This saves you time and reduces the chance of making errors during manual simplification.