Fraction calculator
Add, subtract, multiply or divide fractions like 1/3 and 1/6 and get an exactly reduced result plus a mixed-number form.
- Runs in your browser
- No upload
- Instant result
Assumptions & formula
Formula and assumptions
a/b ± c/d = (ad±bc)/bd; × = ac/bd; ÷ = ad/bc; gcd
Results
Enter values and press Calculate to see the result here.
How to use this calculator
- Set inputs and units
Enter one fraction in each field, using slash notation such as 1/3 and -2/5, then choose add, subtract, multiply or divide. Whole numbers such as 2 are accepted. Convert a mixed number first: 1 3/4 becomes 7/4; -1 3/4 becomes -7/4.
- Calculate
Check this worked example: 1/3 +1/6 =1/2; 2/4 → reduced1/2
- Results
Read the exact reduced fraction and its mixed-number form. For example, 7/4 is 1 3/4; a minus sign applies to the whole mixed number. Negative denominators are normalized so the reduced fraction carries any minus sign in its numerator.
Questions and limits
How do the four fraction operations work?
For a/b and c/d, add with (ad+bc)/bd, subtract with (ad−bc)/bd, multiply with ac/bd, or divide with ad/bc. Addition and subtraction need a common denominator; multiplication and division do not. Reduce the result by dividing numerator and denominator by their greatest common divisor. For example, 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.
Which input errors should I correct?
Denominators can't be zero. Division also rejects a second fraction whose numerator is zero.
What does this calculation leave out?
Use integers or integer fractions. Each integer may use at most 100 characters, including a leading sign. Decimal inputs such as 0.5, mixed-number inputs such as 1 1/2, and variables are not accepted; convert them to fractions first. The calculator returns exact results and a general formula, rather than generating a separate worked solution for every input.