Fraction Calculator
0
| Step | Result |
|---|
How Fraction Arithmetic Works
Adding or subtracting fractions requires a common denominator: each fraction is rewritten over the least common multiple of the two denominators before the numerators are combined. Multiplying fractions is more direct — multiply the numerators together and the denominators together. Dividing by a fraction is defined as multiplying by its reciprocal (flipping the second fraction's numerator and denominator), which is why 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 2. Every result shown above is then reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor, found with the Euclidean algorithm.
A Common Misconception
A frequent mistake is adding fractions "straight across" — for example treating 1/2 + 1/3 as 2/5. Fractions are ratios, not counts, so numerators can only be added once both fractions represent parts of the same-sized whole (the same denominator). The correct answer, 1/2 + 1/3 = 5/6, only appears once both fractions are converted to sixths (3/6 + 2/6).
Related Tools
To reduce a single fraction to lowest terms by hand, it helps to see the greatest common factor explicitly — try the GCF calculator. If you need the least common multiple used to find a common denominator for more than two fractions, the LCM calculator handles that directly.
Frequently Asked Questions
How do you divide fractions?
To divide by a fraction, multiply by its reciprocal instead. Flip the second fraction's numerator and denominator, then multiply straight across: for example, 1/2 divided by 3/4 becomes 1/2 times 4/3 = 4/6, which simplifies to 2/3.
Why does the calculator show three different result formats?
The simplified fraction (lowest terms) is the standard mathematical answer, the decimal equivalent is useful for quick comparisons or calculator entry, and the mixed number format (whole number plus a proper fraction) is often preferred in everyday measurements like cooking or carpentry.