About the fractions calculation
Adding and subtracting fractions needs a common denominator; multiplying and dividing do not. That asymmetry is the source of most fraction errors — people cross-multiply when adding, or hunt for a common denominator when multiplying. Enter a simple fraction like 3/4 or a mixed number like 1 1/2.
Formula
a/b + c/d = (ad + bc) / bd
a/b − c/d = (ad − bc) / bd
a/b × c/d = ac / bd
a/b ÷ c/d = ad / bc (multiply by the reciprocal)
Then divide numerator and denominator by their greatest common divisor.Worked example
1/2 + 1/3: the common denominator is 6, giving 3/6 + 2/6 = 5/6. Multiplying instead: 1/2 × 1/3 = 1/6 — no common denominator needed.
Frequently asked questions
Why do I need a common denominator to add but not to multiply?
Because addition combines quantities that must be in the same units — sixths can only be added to sixths. Multiplication scales one fraction by another, which works directly on numerators and denominators without any conversion.
How do I divide by a fraction?
Multiply by its reciprocal — flip the second fraction and multiply. Dividing by 1/4 is the same as multiplying by 4, which is why dividing by a fraction smaller than one makes the answer bigger.
What is a mixed number?
A whole number alongside a proper fraction, like 1 1/2. It equals the improper fraction 3/2. Enter either form here — mixed numbers need a space between the whole part and the fraction.
Can I divide by zero?
No. A fraction with a zero denominator is undefined, and dividing by a fraction whose numerator is zero is equally undefined. This calculator refuses both rather than returning infinity.
Sources
- Standard rational number arithmetic