Fraction Calculator
Add, subtract, multiply, or divide fractions with automatic simplification.
0.833333
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About this calculator
What Is a Fraction?
A fraction describes a part of a whole. It is written as one number over another, such as 3/8: the top number (the numerator) says how many equal parts you have, and the bottom number (the denominator) says how many equal parts make up the whole. Picture a pie cut into 8 slices — eating 3 leaves 5/8. The denominator can never be zero, because dividing into zero equal parts has no meaning. This fraction calculator adds, subtracts, multiplies, divides and simplifies fractions and mixed numbers, showing the answer in simplest form.
How to Add and Subtract Fractions
Fractions can only be added or subtracted when they share a denominator. One reliable method is a/b ± c/d = (ad ± bc) ÷ bd. A tidier method is to find the least common multiple (LCM) of the denominators and rewrite each fraction over it. For 1/4 + 1/6 + 1/2 the LCM of 4, 6 and 2 is 12, so you rewrite the fractions as 3/12 + 2/12 + 6/12 = 11/12.
How to Multiply Fractions
Multiplication is the easy one: multiply the numerators together and the denominators together. a/b × c/d = ac/bd. For example, 2/3 × 3/5 = 6/15, which simplifies to 2/5. No common denominator is needed.
How to Divide Fractions
Dividing by a fraction is the same as multiplying by its reciprocal — the fraction flipped upside down. a/b ÷ c/d = a/b × d/c = ad/bc. So 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, or 1 7/8 as a mixed number.
Simplifying Fractions
A fraction is in lowest terms when the numerator and denominator share no common factor except 1. To simplify, divide both by their greatest common factor (see the GCF Calculator). 220/440 becomes 1/2. Answers are normally given in simplest form, and as a mixed number when the fraction is improper (the numerator is larger than the denominator).
Fractions and Decimals
To turn a fraction into a decimal, divide the numerator by the denominator: 3/8 = 0.375. To go the other way, write the decimal over a power of ten and simplify — 0.75 = 75/100 = 3/4. Some fractions, like 1/3, repeat forever as decimals, which is one reason fractions are more exact for many calculations. Use the Ratio Calculator to compare quantities as fractions of each other.
Worked example
1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6, already in simplest form since 5 and 6 share no common factor — equivalent to 0.833333 as a decimal.
Frequently asked questions
How does this add fractions with different denominators?
It cross-multiplies to a common denominator first: a/b + c/d = (a×d + c×b) / (b×d), then simplifies the result to its lowest terms.
How does fraction division work?
Dividing by a fraction is the same as multiplying by its reciprocal: a/b ÷ c/d = a/b × d/c.
Why is my result automatically simplified?
The calculator divides both the numerator and denominator by their greatest common factor, so you always get the fraction in lowest terms rather than an unreduced one.
Can I enter negative fractions?
Yes — a negative numerator or denominator is handled correctly and the sign carries through to the simplified result.
