Fraction Calculator
Add, subtract, multiply or divide two fractions, with the result simplified and shown as a decimal.
- 1/20.5
- 1/30.3333
- Result (5/6)0.8333
1/2 + 1/3 = 5/6 — shown here as decimals so you can see how the result compares to each fraction you started with.
- Decimal0.8333
About the Fraction Calculator
Fractions turn up anywhere a whole gets split into parts and the parts need combining: a recipe that needs 2/3 of a cup doubled, a woodworker adding 3/8" and 5/16" of lumber thickness, a student working through an algebra problem set that keeps the answer unsimplified until the very last step. Unlike decimals, fractions carry the exact value — 1/3 stays exact where 0.333... doesn't — which is exactly why they're still taught and still used anywhere precision matters.
This calculator handles the four basic operations — add, subtract, multiply, divide — on two fractions, and does the two things that make fraction arithmetic tedious by hand: finding a common denominator for addition and subtraction, and simplifying the result down to lowest terms afterward. It also shows the decimal equivalent, so you can sanity-check the fraction answer against the number you'd get from a plain calculator.
It's built for checking homework against a known operation, converting a recipe or measurement mid-project, or just avoiding a common-denominator mistake when the two denominators don't share an obvious factor.
How it’s calculated
Addition and subtraction need a common denominator first. Rather than finding the least common denominator, this calculator uses the reliable general approach: multiply the two denominators together to get a common one, cross-multiply the numerators to match, then simplify at the end. a/b + c/d becomes (a×d + c×b) / (b×d).
Multiplication is the simplest operation — multiply the numerators together and the denominators together, no common denominator needed: (a/b) × (c/d) = (a×c) / (b×d).
Division flips the second fraction and multiplies: (a/b) ÷ (c/d) = (a/b) × (d/c). This works because dividing by a number is the same as multiplying by its reciprocal — flipping c/d to d/c is exactly what 'divide by' means when you're not allowed to divide directly by a fraction.
Every result gets simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), so 6/8 comes back as 3/4 rather than sitting unreduced.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions so they share a common denominator, then add the numerators and keep that denominator. The simplest reliable way is to multiply each numerator by the other fraction's denominator and multiply the denominators together — the calculator's addition mode does exactly this.
Why do you flip and multiply to divide fractions?
Dividing by a fraction is the same operation as multiplying by its reciprocal, because a/b ÷ c/d asks 'how many c/d fit into a/b,' and multiplying by d/c answers that directly. Flipping c/d to d/c is just applying that equivalence.
How do I simplify a fraction to lowest terms?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. 12/18 has a GCD of 6, so it simplifies to 2/3 — the calculator does this automatically on every result.
How do I convert an improper fraction to a mixed number?
Divide the numerator by the denominator — the whole-number quotient is the mixed number's whole part, and the remainder over the original denominator is the fractional part. 11/4 is 2 remainder 3, so it becomes 2¾.
How do I convert a decimal to a fraction?
Write the decimal over a power of 10 matching its number of decimal places (0.75 becomes 75/100), then simplify by dividing both numbers by their GCD — 75/100 reduces to 3/4.
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