Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step solutions. Get results as proper fractions, mixed numbers, and decimals instantly.
Calculate Fractions
What is a Fraction?
A fraction represents a part of a whole or a ratio between two numbers. It consists of a numerator (the top number) and a denominator (the bottom number), written as numerator/denominator. The numerator indicates how many parts you have, while the denominator shows how many equal parts make up the whole.
For example, in the fraction 3/4 (three-quarters), the numerator is 3 and the denominator is 4, meaning you have 3 parts out of 4 equal parts that make up the whole. Fractions are fundamental in mathematics and are used extensively in everyday calculations, from cooking measurements to financial calculations and engineering specifications.
Understanding fractions is essential for performing operations like addition, subtraction, multiplication, and division with non-whole numbers. Our calculator handles all these operations automatically, providing simplified results and step-by-step explanations to help you understand the process.
How to Use the Fraction Calculator
Our fraction calculator makes it easy to perform calculations with fractions. Follow these simple steps:
Step 1: Enter the First Fraction
Input the numerator (top number) and denominator (bottom number) of your first fraction in the respective fields. You can use whole numbers, decimals, or even negative numbers.
Step 2: Select the Operation
Choose the mathematical operation you want to perform: addition (+), subtraction (-), multiplication (×), or division (÷). Click the corresponding button to select it.
Step 3: Enter the Second Fraction
Input the numerator and denominator of your second fraction. The calculator will automatically compute the result as you type.
Step 4: Review the Results
The calculator displays your result in multiple formats: simplified fraction, mixed number (if applicable), and decimal. You can also view detailed step-by-step solutions showing how the answer was calculated.
How to Calculate Fractions
Adding & Subtracting
- Find the Least Common Denominator (LCD)
- Convert each fraction to equivalent with LCD
- Add or subtract the numerators
- Keep the common denominator
- Simplify if possible
Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12
Multiplying
- Multiply the numerators together
- Multiply the denominators together
- Simplify the result
Tip: Cross-cancel before multiplying for easier math!
Example: 2/3 × 3/4 = 6/12 = 1/2
Dividing (Keep, Change, Flip)
- Keep the first fraction as is
- Change the division sign to multiplication
- Flip the second fraction (reciprocal)
- Multiply and simplify
Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
Frequently Asked Questions
How do I add fractions with different denominators?
First find the least common denominator (LCD) of both fractions. Convert each fraction to an equivalent fraction with the LCD as the denominator. Then add the numerators while keeping the denominator the same. Finally, simplify if possible.
Why do we flip and multiply when dividing fractions?
Dividing by a fraction is the same as multiplying by its reciprocal. When you divide by a/b, you're asking 'how many a/b's fit into the first number?' This is equivalent to multiplying by b/a.
How do I multiply mixed numbers?
First convert each mixed number to an improper fraction. Then multiply the numerators together and the denominators together. Finally, simplify and convert back to a mixed number if desired.
What is the easiest way to simplify fractions?
Find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by the GCF. For example, to simplify 12/18, the GCF is 6, so 12÷6/18÷6 = 2/3.
Can I add fractions without finding the LCD?
Yes! You can use any common denominator, not just the LCD. Simply multiply each fraction by the other's denominator. However, using the LCD keeps numbers smaller and requires less simplifying at the end.
How do I subtract a larger fraction from a smaller one?
The process is the same - find the common denominator and subtract. You'll get a negative result. For example, 1/4 - 3/4 = -2/4 = -1/2.