Fraction calculator
Add, subtract, multiply, or divide two fractions and see the simplified result plus its decimal equivalent.
What this calculator covers
Use this fraction calculator when you want the result reduced instead of left as a raw numerator and denominator pair.
The walkthrough keeps the operation rule visible so it is easy to verify whether the problem needed a common denominator, cross multiplication, or a reciprocal.
Frequently asked questions
- Why do addition and subtraction require a common denominator but multiplication does not?
- Adding or subtracting fractions requires matching denominators because you are counting pieces of the same size — mismatched denominators would be like adding thirds and quarters directly. Multiplication does not need this because it scales one fraction by another, and the denominators simply multiply straight across.
- How does dividing fractions work?
- Division flips the second fraction into its reciprocal and then multiplies. So a/b ÷ c/d becomes a/b × d/c. The reciprocal step converts the division into multiplication, which the same cross-multiplication rule handles.
- What does it mean when the result simplifies to a whole number?
- When the denominator of the result reduces to 1, the fraction is equivalent to an integer. For example, 3/4 × 4/3 simplifies to 12/12, which reduces to 1. The calculator displays the whole number directly in that case.
- Can I enter negative numerators or denominators?
- Yes. The calculator accepts negative whole numbers in either position. Signs are kept on the numerator in the simplified result, and a negative denominator is converted to a positive denominator by flipping both signs before the operation is applied.
Tool
Run the calculation
Result
RESULT · FRACTION
â„–110
Primary result
5/6
1/2 + 1/3 simplifies to 5/6, which is 0.833333 in decimal form.
- Operation
- 1/2 + 1/3
- Simplified fraction
- 5/6
- Decimal equivalent
- 0.833333
Step-by-step solution
- 1.Interpret the problem as addition: 1/2 + 1/3.
- 2.Apply the fraction rule a/b + c/d = (ad + bc) / bd to combine the numerators and denominators correctly.
- 3.Reduce the raw result to 5/6 and read the decimal equivalent as 0.833333.
Walkthrough
Visual walkthrough
Fraction work stays transparent when the combination rule and the final reduction are kept separate.
01
Write both fractions in reduced form
1/2 + 1/3
Start from the reduced inputs so any common factors are already stripped out before the main operation.
02
Apply the matching fraction rule
a/b + c/d = (ad + bc) / bd
Addition and subtraction use a shared denominator, while multiplication and division work across the numerators and denominators.
03
Reduce and translate to decimal
Divide the numerator and denominator by their greatest common divisor, then convert the simplified result to decimal form.
5/6 = 0.833333