Fraction Solver
Solve and simplify complex fractions with full step-by-step arithmetic explanations for addition, subtraction, multiplication, and division.
Also covers: fraction to decimal calculator with steps and explanation · add subtract multiply fractions calculator · simplify fractions tool
Formula & How It Works
a/b + c/d = (a×d + c×b) ÷ (b×d)
- Subtraction uses the same common denominator: (a×d − c×b) ÷ (b×d).
- Multiplication is (a×c) ÷ (b×d), and division flips the second fraction to (a×d) ÷ (b×c).
- The answer is reduced by dividing the numerator and denominator by their greatest common divisor, then shown as a mixed number and a decimal.
Step-by-Step Example
Adding two unlike fractions: 1/2 + 1/3.
- 1.Cross-multiply
- 1 × 3 = 3 and 1 × 2 = 2
- 2.Add the numerators
- 3 + 2 = 5
- 3.Multiply the denominators
- 2 × 3 = 6
- 4.Simplify
- gcd(5, 6) = 1, so the fraction stays 5/6
1/2 + 1/3 = 5/6, which is about 0.8333 as a decimal.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator and then add the numerators. The general rule is a/b + c/d = (a×d + c×b) ÷ (b×d): for 1/2 + 1/3 that is (3 + 2) ÷ 6 = 5/6. The result is then reduced to lowest terms, which this tool does for you.
What is the easiest way to simplify an improper fraction?
Divide the numerator and denominator by their greatest common divisor — 8/12 becomes 2/3 because both divide by 4. If the numerator is larger than the denominator the fraction is improper and can also be written as a mixed number, so 7/4 is 1 3/4, and a decimal value is shown alongside.
How do you convert a fraction into a decimal?
Divide the numerator by the denominator: 3/8 is 3 ÷ 8 = 0.375. A reduced fraction gives a terminating decimal when its denominator is built only from 2s and 5s, and a repeating decimal otherwise — 1/3 is 0.333… and 1/6 is 0.1666…
About the Fraction Solver
Solve and simplify complex fractions with full step-by-step arithmetic explanations for addition, subtraction, multiplication, and division.
It runs entirely in your browser — nothing you type is sent to a server — and the result updates as you edit the inputs. Estimates are for educational and informational purposes only; see ourdisclaimer.
Common searches
- fractions
- arithmetic
- mixed number
- simplify
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