Fraction Calculator
Do arithmetic with fractions and get the answer fully simplified — as a proper fraction, a mixed number and a decimal. The result shows the cross-multiplication steps so you can follow the working.
How to use this calculator
- Enter the first fraction's numerator (top) and denominator (bottom).
- Choose the operation: add, subtract, multiply or divide.
- Enter the second fraction and press Calculate.
- For mixed numbers like 2¾, convert first: 2¾ = 11/4 (whole × denominator + numerator).
Formula used
Addition and subtraction use cross-multiplication to reach a common denominator; division multiplies by the reciprocal. The result is then reduced by dividing top and bottom by their greatest common divisor (GCD).
Example calculation
3/4 + 5/6: cross-multiply → (3×6 + 5×4) / (4×6) = (18 + 20) / 24 = 38/24.
GCD of 38 and 24 is 2 → simplified to 19/12, which is the mixed number 1 7/12 ≈ 1.5833.
Working with fractions
A fraction expresses division: 3/4 means 3 ÷ 4. Adding and subtracting fractions requires a common denominator — you can only add pieces of the same size — which is why those operations feel harder than multiplying, where you simply multiply straight across.
Simplifying means dividing numerator and denominator by their greatest common divisor, giving the smallest equivalent fraction. It's the same value in lowest terms — 38/24, 19/12 and 1.5833… are all one number written three ways.
Why use this calculator?
- Get simplified results with the working shown — ideal for checking homework step by step.
- See the answer as a fraction, mixed number and decimal simultaneously.
- Avoid the classic common-denominator slip that causes most fraction mistakes.
Frequently asked questions
How do I add fractions with different denominators?
Cross-multiply: multiply each numerator by the other fraction's denominator, add the results, and put them over the product of both denominators. 1/3 + 1/4 = (1×4 + 1×3)/(3×4) = 7/12. Then simplify if possible.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For 38/24, the GCD is 2, so it simplifies to 19/12. If the GCD is 1, the fraction is already in lowest terms.
How do I divide fractions?
Multiply by the reciprocal — flip the second fraction and multiply: (3/4) ÷ (5/6) = (3/4) × (6/5) = 18/20 = 9/10. "Keep, change, flip" is the classroom mnemonic.
How do I enter a mixed number like 2¾?
Convert it to an improper fraction first: multiply the whole number by the denominator and add the numerator. 2¾ = (2×4 + 3)/4 = 11/4. Enter 11 and 4.