UnitConv

Fraction Calculator

Add, subtract, multiply and divide fractions with step-by-step work

Result
56
Decimal:0.833333

Step-by-step work

  1. 1
    Problem
    1/2 + 1/3
  2. 2
    Find a common denominator (LCM)
    LCM(2, 3) = 6
  3. 3
    Rewrite over the common denominator
    1/2 = 3/6, 1/3 = 2/6
  4. 4
    Combine the numerators
    3/6 + 2/6 = 5/6

Fraction rules

a/b + c/d = (a·d + c·b) / (b·d)
a/b × c/d = (a·c) / (b·d)
a/b ÷ c/d = (a·d) / (b·c)

Addition and subtraction need a common denominator; multiplication and division work directly. The result is then reduced by the greatest common divisor.

What is a Fraction Calculator?

A fraction calculator works out the result of adding, subtracting, multiplying or dividing two fractions and gives you the answer in three handy forms: a fully reduced fraction, a mixed number, and a decimal. Fractions are everywhere in everyday math — recipes, measurements, money and probability — yet doing the arithmetic by hand means juggling common denominators and reducing by the greatest common divisor. This tool does all of that instantly and, crucially, shows the full step-by-step work so you can learn the method rather than just copy the answer. It handles negative numerators and guards against undefined cases such as a zero denominator.

How to use this calculator

1. Type the numerator (top) and denominator (bottom) of the first fraction. 2. Choose the operation: + (add), − (subtract), × (multiply) or ÷ (divide). 3. Type the second fraction. The answer updates instantly. Read the reduced fraction, the mixed number and the decimal, and open the step-by-step work to see how the common denominator and the reduction were found.

How fractions are calculated

To add or subtract, the fractions need the same denominator. The calculator finds the least common multiple (LCM) of the two denominators, rewrites each fraction over that common denominator, then adds or subtracts the numerators: a/b ± c/d = (a·d ± c·b) / (b·d). Multiplication is direct — multiply numerators and multiply denominators: a/b × c/d = (a·c) / (b·d). To divide, multiply by the reciprocal (flip the second fraction): a/b ÷ c/d = a/b × d/c = (a·d) / (b·c). Finally the result is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD). For example, 1/2 + 1/3 has LCM 6, giving 3/6 + 2/6 = 5/6, which is already in lowest terms.

Reading your result

The big fraction at the top is the answer in lowest terms — numerator and denominator share no common factor greater than 1. If the value is larger than one whole, the mixed number form shows it as a whole number plus a proper fraction (for example 3/2 = 1 1/2), which is often easier to picture. The decimal gives the same value as a number you can use directly in measurements or further calculations; note that some fractions, like 1/3, do not have an exact finite decimal, so the decimal is rounded. A negative sign on either input flips the sign of the result accordingly.

Frequently Asked Questions

How do I add fractions with different denominators? ▾

Find the least common multiple of the two denominators, rewrite both fractions over that common denominator, add the numerators, then reduce. For 1/2 + 1/3 the common denominator is 6, giving 3/6 + 2/6 = 5/6.

How do I divide one fraction by another? ▾

Keep the first fraction, flip the second (use its reciprocal), and multiply. So 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 6/4 = 3/2 = 1.5.

What does it mean to reduce a fraction? ▾

Reducing means dividing the numerator and denominator by their greatest common divisor so the fraction is in its simplest form. For example 2/4 reduces to 1/2 because both divide by 2.

Can I use negative fractions or get a whole number? ▾

Yes. A negative sign on a numerator is supported and carries through the calculation. If the result has a denominator of 1, it is shown as a whole number instead of a fraction.