Fraction Calculator
Fraction calculator
Calculate, convert, and simplify fractions with exact rational results.
InputsAddTwo-value arithmeticLive
Spaces around `/` are allowed. Denominators cannot be zero.
Simplified result
23/20
3/4 + 2/5 = 23/20
Live
Mixed
1 3/20
Decimal
1.15
Percent
115%
Steps, decimal precision & visual
Calculation steps
- Find the least common denominator: LCM(4, 5) = 20.
- Rewrite the fractions as 15/20 and 8/20.
- Add the numerators: 15 + 8 = 23.
- The result is already in lowest terms.
- Final result: 23/20.
Rounded decimal: 1.15
Fractional part3/20
15% of the next whole.
Formula
a/b ± c/d = (ad ± bc)/bd (a/b) x (c/d) = ac/bd (a/b) ÷ (c/d) = ad/bc Symbol legend
| Symbol | Meaning | Unit | Copy |
|---|---|---|---|
a, c | Numerators | integer | |
b, d | Denominators (non-zero) | integer | |
\pm | Addition or subtraction operation | - | |
\times, \div | Multiplication or division operation | - |
- For addition and subtraction, convert to a common denominator using cross multiplication.
- For multiplication, multiply numerators together and denominators together.
- For division, multiply by the reciprocal of the second fraction and simplify the result.
Example
Worked example: 3/4 + 2/5
- 1 Common denominator is 4 x 5 = 20
- 2 Adjusted numerators: 3 x 5 = 15 and 2 x 4 = 8
- 3 Sum numerator: 15 + 8 = 23, so result is 23/20
3/4 + 2/5 = 23/20 = 1.15.
How
- Choose Calculate for two-value arithmetic or Convert & simplify for one value.
- Enter a fraction, mixed number, whole number, finite decimal, or repeating decimal such as 0.(3).
- Read the exact fraction, mixed number, decimal pattern, and percent, then open the steps when needed.
Avoid
- Writing a repeating decimal without parentheses; use 0.(3) for 0.333....
- Using a zero denominator, which is undefined.
- For division, forgetting that dividing by a fraction means multiplying by its reciprocal.
FAQ
Does this calculator simplify fractions automatically?
Yes. Every valid result is reduced to lowest terms before display.
Can I enter negative fractions?
Yes. Negative fractions, mixed numbers, and decimals are supported and normalized in the result.
Can this convert a decimal to a fraction?
Yes. Finite decimals are converted exactly, and repeating decimals can use parentheses, such as 0.(3) for one third.
Why does division sometimes fail?
Division is invalid when the second fraction equals zero because that would divide by zero.
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