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Calculators

Fraction Calculator

Calculate and simplify arithmetic with two fractions.

Fraction Calculator tool

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About This Tool

Use this fraction calculator for the four basic arithmetic operations while keeping the answer exact. Enter a numerator and denominator for each fraction, choose addition, subtraction, multiplication, or division, and the result is automatically reduced to lowest terms. The tool also shows a decimal equivalent for quick comparison, while the simplified fraction remains the exact answer to use in math work, recipes, measurements, homework checks, or step-by-step practice.

How To Use It

  1. Enter the numerator and denominator of the first fraction and the second fraction.
  2. Choose Add, Subtract, Multiply, or Divide.
  3. Read the simplified exact fraction and its decimal equivalent, then copy the fraction if needed.
  4. Use whole-number numerators and denominators. Convert mixed numbers such as 2 1/3 to improper fractions such as 7/3 before entering them.
  5. If an answer is negative, the calculator keeps the minus sign on the numerator and leaves the denominator positive.

Examples

1/2 + 1/3

Use a common denominator of 6: 3/6 + 2/6 = 5/6, so the simplified result is 5/6.

3/4 × 2/5

Multiply numerators and denominators: 6/20, then reduce by 2 to get 3/10.

2/3 ÷ 4/5

Multiply by the reciprocal of the second fraction: 2/3 × 5/4 = 10/12 = 5/6.

5/6 − 3/4

Use a common denominator of 12: 10/12 − 9/12 = 1/12, so the result is already in lowest terms.

-2/9 + 5/6

The calculator supports negative numerators and denominators. Here the common denominator is 18, so -4/18 + 15/18 = 11/18.

Useful Notes

Adding and subtracting fractions

Fractions need a common denominator before their numerators can be combined. For a/b + c/d, the direct calculation is (ad + bc) / bd; subtraction uses (ad − bc) / bd. The final fraction is then reduced.

Common denominators do not have to be least common denominators

The direct formulas use bd as a common denominator, then reduce the final answer. In hand calculations you may prefer the least common denominator to keep numbers smaller; both approaches produce the same simplified result when done exactly.

Multiplying and dividing fractions

Multiplication uses (a × c) / (b × d). Division multiplies the first fraction by the reciprocal of the second: (a × d) / (b × c). Dividing by a zero fraction is undefined and is rejected.

How simplification works

The numerator and denominator are divided by their greatest common divisor. A negative sign is kept on the numerator, and a zero result is normalized to 0/1 so equivalent answers have one consistent form.

Exact integer limits

Inputs must be whole numbers within JavaScript's safe-integer range. Intermediate calculations use exact BigInt arithmetic and the answer is reduced before checking the output range. If the simplified numerator or denominator exceeds the safe-integer range, the calculator stops instead of displaying a potentially rounded integer as exact.

Mixed numbers and decimals

The input fields represent one numerator and one denominator for each fraction. Convert mixed numbers to improper fractions before calculating, and convert decimal measurements to fractions first when you need an exact fraction result.

FAQ

Can the denominator be zero?

No. A fraction with a zero denominator is undefined, so the calculator asks you to use a non-zero denominator.

Can I use negative fractions?

Yes. Enter a negative numerator or denominator. The simplified result normalizes the sign so the denominator is positive.

Why is the decimal sometimes rounded?

Many fractions, such as 1/3, have repeating decimal expansions. The fraction result is exact; the decimal display is a compact numerical approximation.

Does the calculator simplify the answer automatically?

Yes. Every result is reduced to lowest terms using the greatest common divisor.

Can I enter mixed numbers like 2 1/3?

Not directly. Convert the mixed number to an improper fraction first. For example, 2 1/3 becomes 7/3 because 2 × 3 + 1 = 7.

Is the displayed decimal the exact answer?

The simplified fraction is the exact answer. The decimal display is included for comparison and may be rounded when the decimal repeats or is too long to show compactly.