Fraction Calculator
Fraction Calculator
The fraction calculator performs addition, subtraction, multiplication, and division on two fractions and returns the simplified result.
Conversion Formula
Addition/subtraction: cross-multiply to get a common denominator. Multiplication: multiply straight across. Division: multiply by the reciprocal. All results are simplified by dividing by the GCD.
Step-by-Step Examples
1/4 + 1/3 = 7/12
(1×3 + 1×4) / (4×3) = 7/12, already simplified.
2/3 × 3/4 = 1/2
(2×3) / (3×4) = 6/12, simplified by GCD 6 to 1/2.
5/6 ÷ 2/3 = 5/4
5/6 × 3/2 = 15/12, simplified by GCD 3 to 5/4.
History
Fractions have been used since ancient Egypt (around 1800 BC), where they primarily used unit fractions (fractions with numerator 1).
Common Use Cases
- Cooking and recipe scaling
- Construction measurements
- Music theory (time signatures)
- Academic math problems
Frequently Asked Questions
How do I add fractions?
Find a common denominator, add the numerators, and simplify. For example, 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
How do I subtract fractions?
Find a common denominator, subtract the numerators, and simplify.
How do I multiply fractions?
Multiply the numerators together and the denominators together, then simplify.
How do I divide fractions?
Multiply the first fraction by the reciprocal (flipped version) of the second fraction.
What is a common denominator?
A common denominator is a shared multiple of two denominators that allows fractions to be added or subtracted.
What does it mean to simplify a fraction?
Dividing both the numerator and denominator by their greatest common divisor (GCD) to get the smallest equivalent fraction.
Can the result be negative?
Yes. If the result of the operation is negative, the numerator will be negative in the simplified result.
What is the GCD?
The Greatest Common Divisor is the largest number that divides evenly into both the numerator and denominator.