Fraction Calculator
What This Tool Does
This fraction calculator performs the four basic operations on fractions — addition, subtraction, multiplication, and division — along with simplifying fractions and converting between fractions and decimals.
You can also use this Margin Calculator.
How It’s Calculated
Addition/Subtraction (needs a common denominator): a/b + c/d = (ad + bc) ÷ bd
Multiplication (no common denominator needed): a/b × c/d = ac ÷ bd
Division (multiply by the reciprocal): a/b ÷ c/d = a/b × d/c = ad ÷ bc
Worked examples: Using 2/5 and 3/7.
- Addition: (2×7 + 3×5) ÷ (5×7) = (14+15) ÷ 35 = 29/35
- Multiplication: (2×3) ÷ (5×7) = 6/35
- Division: 2/5 × 7/3 = (2×7) ÷ (5×3) = 14/15
Edge Cases and Special Rules
- A denominator can never be zero: A fraction with a zero denominator is undefined, regardless of the numerator.
- Common denominators are only needed for addition and subtraction: Multiplication and division work directly on the numerators and denominators as given — this trips up many people who assume every fraction operation needs matching denominators first.
- Using the LCM gives a more efficient result than multiplying all denominators: Simply multiplying every denominator together always works, but can produce unnecessarily large numbers that then need simplifying — finding the least common multiple of the denominators first usually avoids that extra step.
- Mixed numbers need converting to improper fractions first: Before adding, subtracting, multiplying, or dividing a mixed number (like 2¾), convert it to an improper fraction (11/4) to apply the standard rules correctly.
Working with Two Fractions vs. Three or More
The same core rules extend to three or more fractions — multiplication and division still just chain across all the numerators and denominators involved. For addition and subtraction with three or more fractions, finding a common denominator (ideally the LCM of all the denominators involved) becomes a bit more involved, but the underlying method doesn’t change: convert each fraction to that common denominator, then add or subtract the numerators.
Who Uses This
- Students learning fraction arithmetic
- Cooking and baking enthusiasts adjusting recipe quantities
- Construction and DIY projects requiring precise measurement arithmetic
- Anyone converting between fraction, decimal, and percentage representations for a specific need
Common Denominator Method vs. LCM Method
These are two valid ways to add or subtract fractions, with a tradeoff between simplicity and efficiency. The common denominator method multiplies every denominator together — straightforward to understand, but the result often isn’t in simplified form and needs an extra step afterward. The LCM method finds the least common multiple of the denominators first, which usually produces a smaller, already-closer-to-simplified result, at the cost of one extra step upfront (finding the LCM itself).
FAQ
How do I add fractions with different denominators?
Find a common denominator (ideally the LCM), convert each fraction to that denominator, then add the numerators.
Do I need a common denominator to multiply fractions?
No, multiply the numerators together and the denominators together directly, with no common denominator required.
How do I convert a fraction to a percentage?
Convert the fraction to a decimal first (divide numerator by denominator), then multiply by 100, for example, 3/8 = 0.375 = 37.5%.
How do I simplify a fraction?
Divide both the numerator and denominator by their greatest common factor until no further common factor remains.
How do I use a mixed number in a calculation?
Convert it to an improper fraction first, then apply the standard addition, subtraction, multiplication, or division rules.
Try It Above
Enter your fractions in the calculator above to get the result for addition, subtraction, multiplication, division, or simplification instantly. Results are for general calculation purposes only.