Fractions Calculator - Add, Subtract, Multiply, Divide Fractions Online

Fractions Calculator - Add, Subtract, Multiply, Divide Fractions

Our free online fractions calculator makes it easy to perform mathematical operations on fractions. Whether you need to add, subtract, multiply, or divide fractions, this tool provides instant results with step-by-step calculations. Perfect for students, teachers, and anyone working with fractions in their daily calculations.

How to Use the Fractions Calculator

Select Operation: Choose from addition (+), subtraction (-), multiplication (×), or division (÷)
Enter Fractions: Input the numerator and denominator for both fractions
View Results: Get instant results with simplified fractions and mixed number options
See Steps: Review the detailed calculation steps to understand the process

Fraction Operations Explained

Adding Fractions

To add fractions with different denominators:

Find the Least Common Multiple (LCM) of the denominators
Convert each fraction to have the LCM as the denominator
Add the numerators and keep the common denominator
Simplify the result if possible

Example: 1/2 + 1/3 = (1×3 + 1×2)/(2×3) = 5/6

Subtracting Fractions

Subtraction follows the same process as addition:

Find the LCM of the denominators
Convert fractions to have common denominators
Subtract the numerators
Simplify the result

Example: 1/2 - 1/3 = (1×3 - 1×2)/(2×3) = 1/6

Multiplying Fractions

Multiplication is straightforward:

Multiply the numerators together
Multiply the denominators together
Simplify the result

Example: 1/2 × 1/3 = (1×1)/(2×3) = 1/6

Dividing Fractions

Division involves multiplying by the reciprocal:

Keep the first fraction as is
Change the division sign to multiplication
Flip the second fraction (find its reciprocal)
Multiply the fractions
Simplify the result

Example: 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2 = 1 1/2

Understanding Mixed Numbers

Mixed numbers combine whole numbers with fractions. For example, 1 1/2 means 1 whole plus 1/2. Our calculator can display results as mixed numbers when the option is enabled.

Simplifying Fractions

Fractions are simplified by dividing both the numerator and denominator by their Greatest Common Divisor (GCD). This gives you the fraction in its lowest terms.

Common Fraction Conversions

1/2 = 0.5 = 50%
1/3 ≈ 0.333 = 33.3%
1/4 = 0.25 = 25%
1/5 = 0.2 = 20%
1/8 = 0.125 = 12.5%

Tips for Working with Fractions

Always ensure denominators are not zero
Simplify fractions to their lowest terms for clarity
Use mixed numbers when the result is greater than 1
Double-check calculations by converting to decimals
Practice with simple fractions before tackling complex ones

Frequently Asked Questions

How do I add fractions with different denominators?

To add fractions with different denominators, first find the Least Common Multiple (LCM) of the denominators. Then convert each fraction to have the LCM as the denominator by multiplying both numerator and denominator by the appropriate factor. Finally, add the numerators and keep the common denominator.

What is the difference between proper and improper fractions?

A proper fraction has a numerator smaller than the denominator (e.g., 3/4), while an improper fraction has a numerator equal to or larger than the denominator (e.g., 5/4). Improper fractions can be converted to mixed numbers.

How do I simplify fractions?

To simplify a fraction, find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by this number. For example, 8/12 can be simplified to 2/3 by dividing both 8 and 12 by 4.

Can I use this calculator for negative fractions?

Yes, our fractions calculator supports negative numbers. Simply enter a negative value for the numerator or denominator, and the calculator will handle the operations correctly, including proper sign handling in the results.

What is a mixed number and how is it different from an improper fraction?

A mixed number combines a whole number with a proper fraction (e.g., 2 1/3). An improper fraction has a numerator larger than or equal to the denominator (e.g., 7/3). The mixed number 2 1/3 is equivalent to the improper fraction 7/3.

How accurate are the calculation steps shown?

The calculation steps are mathematically accurate and show the exact process used to arrive at the result. This includes finding LCM for addition/subtraction, showing the multiplication process, and displaying the final simplification steps.