Fraction Calculator
Calculate fraction addition, subtraction, multiplication, and division with step-by-step working.
Fraction Arithmetic
Calculated Answer
⚖️ Decision Verdict: Proper Fraction Form
The result (11/15) is a proper fraction (numerator < denominator) and is already fully reduced to lowest terms since 11 and 15 share no common divisors other than 1.
Step-by-Step Mathematical Solution
About this tool
How to use it
- Enter Fraction 1: specify optional whole number (for mixed fractions), numerator, and denominator.
- Select the arithmetic operator: `+` (Add), `−` (Subtract), `×` (Multiply), or `÷` (Divide).
- Enter Fraction 2 with its whole number, numerator, and denominator.
- Click 'Calculate & Simplify' to compute the result.
- Inspect the simplified fraction, mixed number, decimal equivalent, and full step-by-step mathematical working.
Why it matters
Fraction arithmetic requires distinct mathematical techniques depending on the operation. Adding and subtracting fractions with unlike denominators requires finding the Least Common Denominator (LCD), while fraction division uses the 'Keep, Change, Flip' reciprocal method. Displaying the explicit step-by-step working helps students verify their homework, teachers demonstrate concepts, and builders make precise material cuts.
When to use it
Use this calculator for middle and high school math homework, recipe scaling in cooking and baking, carpentry and woodwork measurements, or converting architectural blueprints.
Good to know
Simplification: Results are automatically simplified to lowest terms by dividing the numerator and denominator by their Greatest Common Divisor (GCD).
Common questions
How do you add fractions with different denominators?
To add fractions with unlike denominators, first find their Least Common Denominator (LCD). Multiply the top and bottom of each fraction by the necessary factor so both share the same denominator, then add the numerators together and simplify.
What is the rule for dividing fractions?
Follow the 'Keep, Change, Flip' rule: Keep the first fraction unchanged, change the division sign to multiplication, and flip the second fraction into its reciprocal (invert numerator and denominator). Then multiply straight across.
What is the difference between an improper fraction and a mixed number?
An improper fraction has a numerator greater than or equal to its denominator (e.g. 9/4). A mixed number expresses that same value as a whole number combined with a proper fraction (e.g. 2 1/4).
Can this calculator handle whole numbers?
Yes! Enter whole numbers in the 'Whole' input box next to either fraction, or leave the numerator and denominator blank with denominator = 1.
What happens if a denominator is zero?
Division by zero is undefined in mathematics. The calculator automatically guards against zero denominators and resets them to 1.