FinanceCalcs
Fraction Calculator
Add, subtract, multiply, or divide any two fractions — including mixed numbers — with step-by-step working shown. Results are automatically simplified to lowest terms. Also converts to decimal and mixed number form.
Fraction Calculator
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Step-by-Step Working
Equivalent Fractions
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"Fractions were used by ancient Egyptians, but they only allowed unit fractions (numerator = 1). 3/4 would be written as 1/2 + 1/4. The concept of any numerator took centuries to develop."
— History of Mathematics
How fraction arithmetic works
Adding and subtracting fractions requires a common denominator. Find the least common multiple (LCM) of the denominators, convert both fractions, then add or subtract the numerators. Multiplying is simpler: multiply numerators together and denominators together. Dividing: multiply by the reciprocal (flip the second fraction, then multiply).
To simplify a fraction, divide both the numerator and denominator by their greatest common factor (GCF). The result is the fraction in lowest terms. A fraction is fully simplified when the GCF of numerator and denominator is 1.
Fraction FAQs
What is the difference between a proper and improper fraction?
A proper fraction has a numerator smaller than the denominator (e.g. 3/4 — value less than 1). An improper fraction has a numerator equal to or greater than the denominator (e.g. 7/4 — value 1 or more). Improper fractions can be converted to mixed numbers: 7/4 = 1 and 3/4.
What is the LCM and why does it matter for fractions?
The Least Common Multiple is the smallest number that both denominators divide into evenly. When adding 1/4 + 1/6, the LCM of 4 and 6 is 12. Convert both fractions to 12ths: 3/12 + 2/12 = 5/12. Without a common denominator, fraction addition is not defined.
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About FinanceCalcs.net — FinanceCalcs.net is a free financial calculator directory built and maintained by Ted Grajeda. The site exists to give everyone access to fast, accurate financial math — no subscriptions, no paywalls, no signup required. Every calculator runs entirely in your browser using standard financial formulas.