How this calculator works
Fractions stay exact through the operation; the result is reduced only after the arithmetic is complete.
- Step 1Read both values2 1/3 and 3/4A mixed number becomes one signed numerator over a positive denominator.
- Step 2Apply the operation7/3 × 3/4Multiply the numerators and denominators, or use a common denominator for addition and subtraction.
- Step 3Reduce and show7/4 = 1 3/4The GCD reduces the fraction; long division supplies an exact or clearly shortened decimal.
For addition and subtraction, the calculator finds the least common denominator (LCD), rewrites each numerator to that denominator, then combines the numerators. Multiplication is across; division multiplies by the reciprocal.
What the result leaves out
- No decimal inputEnter rational values as integers, fractions or mixed numbers so the calculation remains exact.
- Two numbers at a timeUse the result as an input to continue a longer calculation.
Worked example
For 1/2 + 1/3, LCD = lcm(2, 3) = 6. The numerators can then be added.
- Addition with an LCD
a/b + c/d = (a × LCD/b + c × LCD/d) / LCD
- Step 1Exact fraction calculationLCD = lcm(2, 3) = 6.
- Step 2Exact fraction calculationRewrite: 3/6 + 2/6.
- Step 3Exact fraction calculationCross-multiply to the LCD: 1 × 3 = 3; 1 × 2 = 2.
- Step 4Exact fraction calculationCombine numerators: 3 + 2 = 5.
- Step 5Exact fraction calculationSimplify by the GCD 1: 5/6 → 5/6.
The decimal is 0.8(3). Parentheses show the digits that repeat, rather than suggesting that the decimal ends.
Reading your result
- Fraction5/6The exact ratio, reduced to lowest terms.
- Mixed number5/6A whole part and a fraction when the result is improper.
- Decimal0.8(3)A base-ten view; repeating digits appear in parentheses.
An ellipsis means the decimal expansion continues beyond the display limit. Use the fraction for an exact value, especially when continuing another calculation.
Related number tools
Fractions, ratios, decimals and percentages are different ways of writing the same parts of a whole.
Adding fractions needs a common denominator, which is the lowest common multiple; the LCM and HCF calculator shows how to find it. To simplify or scale a ratio, use the ratio calculator.
To turn a fraction into a decimal by hand, the long division calculator shows each step and any recurring digits. For percent questions, try the percentage calculator.
Common mistakes
Mistake: Adding the top and bottom numbers separately.
Instead: Convert to a common denominator, then add or subtract only the numerators.
Mistake: Treating −1 1/2 as −1 + 1/2.
Instead: The sign applies to the whole mixed number: −(1 + 1/2).
Mistake: Dividing top by top and bottom by bottom.
Instead: Keep the first fraction, invert the second and multiply.
Frequently asked questions
Can I enter an improper fraction?
Yes. Enter a value such as 7/3. The result includes a mixed-number form when it has a whole part.
How do I enter a negative mixed number?
Put the minus sign before the whole part, for example −2 1/3. The sign applies to the complete value.
Why is the decimal written with parentheses?
A block such as (3) marks digits that repeat indefinitely. A long period may be shortened with an ellipsis; the fraction remains exact.
What happens if I divide by zero?
The calculator shows an error and does not display a numeric result. A denominator of zero in either input is also rejected.
How large can my inputs be?
Each whole, numerator and denominator component can contain at most 30 digits. This limit applies to typed components, not to exact intermediate products.
Are my inputs sent to a server?
No. The calculation runs in your browser and the values are not sent to us.
Sources and method
This page follows the standard fraction notation, reduction and arithmetic rules described by Wolfram MathWorld’s fraction reference and its greatest common divisor reference. Its examples are generated from the calculator logic and checked with independent cross-product arithmetic.
Read how we test our calculators, or browse more maths calculators.