What is a proper fraction versus an improper fraction?
A proper fraction is any fraction where the numerator is smaller than the denominator (e.g., 3/4 or 5/8), representing a quantity strictly less than 1. An improper fraction is a fraction where the numerator is equal to or greater than the denominator (e.g., 7/4 or 9/2), representing a quantity equal to or greater than 1.
How do you find the Least Common Denominator (LCD)?
To find the Least Common Denominator of two fractions, list the multiples of both denominators until you locate the smallest number shared by both lists. Alternatively, divide the product of the two denominators by their Greatest Common Divisor (GCD): LCD(a, b) = (a × b) / GCD(a, b).
Why can a denominator never be zero?
In mathematics, division by zero is undefined. A fraction (a/b) signifies splitting a quantity "a" into "b" equal parts. Dividing something into zero equal parts is logically impossible and violates basic algebraic axioms.
How does the calculator reduce fractions to lowest terms?
The calculator computes the Greatest Common Divisor (GCD) of the resulting numerator and denominator using the Euclidean algorithm. Both numbers are then divided by this GCD to ensure the fraction is in its simplest irreducible state.
Can I perform operations with negative fractions?
Yes, our calculator fully supports negative numerators. If you enter a negative number in the numerator field, the calculation will accurately apply standard integer sign rules for addition, subtraction, multiplication, and division.
What is the difference between a fraction and a ratio?
A fraction represents a part-to-whole relationship (such as 3 parts out of 4 total parts). A ratio represents a comparison between two separate quantities, which can be part-to-part (3 red balls to 1 blue ball) or part-to-whole.
How accurate is the result?
Results use JavaScript's 64-bit floating point — accurate to 15+ significant digits for most calculations.
Can I enter decimal numbers?
Yes, decimals are fully supported.
Is it free?
Yes, completely free.
Does it show the formula?
Yes, the formula is displayed on the page.
Can I use it on mobile?
Yes, the calculator is fully responsive.
Does it save my inputs?
No data is stored — all calculations are done locally in your browser.
What if I get an error?
Check for invalid inputs such as division by zero or negative square roots.