Calculators
Fraction Calculator
Calculate and simplify arithmetic with two fractions.
Simplified result
5/6
Decimal: 0.833333333333
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. A decimal equivalent is also shown for quick comparison, while the simplified fraction remains the exact result.
How To Use It
- Enter the numerator and denominator of the first fraction and the second fraction.
- Choose Add, Subtract, Multiply, or Divide.
- Read the simplified exact fraction and its decimal equivalent, then copy the fraction if needed.
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.
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.
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. If an intermediate exact numerator or denominator would exceed that range, the calculator stops instead of displaying a potentially rounded integer as exact.
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.
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