Fraction Calculator
Add, subtract, multiply, and divide fractions — simplified instantly with steps
Fraction Formulas Explained
Always simplify: after any operation, divide the numerator and denominator by their greatest common divisor (GCD) to get the simplest form.
Common Fraction Operations Reference
| Operation | Unsimplified | Simplified | Decimal |
|---|---|---|---|
| 1/2 + 1/3 | 5/6 | 5/6 | 0.8333 |
| 1/2 + 1/4 | 6/8 | 3/4 | 0.75 |
| 3/4 − 1/8 | 5/8 | 5/8 | 0.625 |
| 2/3 − 1/3 | 1/3 | 1/3 | 0.3333 |
| 2/3 × 3/5 | 6/15 | 2/5 | 0.4 |
| 1/2 × 1/2 | 1/4 | 1/4 | 0.25 |
| 1/2 ÷ 3/4 | 4/6 | 2/3 | 0.6667 |
| 3/4 ÷ 1/2 | 6/4 | 3/2 | 1.5 |
Frequently Asked Questions
How do you add fractions with different denominators?
Find a common denominator (multiply the two denominators, or use their LCM), convert each fraction, then add the numerators. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do you subtract fractions?
Convert both fractions to a common denominator, then subtract the numerators and keep the denominator. Example: 3/4 − 1/8 = 6/8 − 1/8 = 5/8.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. Example: 2/3 × 3/5 = 6/15 = 2/5.
How do you divide fractions?
Multiply the first fraction by the reciprocal (flip) of the second. Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
What is 1/2 + 1/3?
1/2 + 1/3 = 5/6. Common denominator is 6: 1/2 = 3/6 and 1/3 = 2/6, so 3/6 + 2/6 = 5/6, already in simplest form.
What is 3/4 minus 1/8?
3/4 − 1/8 = 5/8. Convert 3/4 to eighths: 6/8. Then 6/8 − 1/8 = 5/8.
How do you simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. Example: 6/15 — GCD(6,15)=3, so 6÷3 / 15÷3 = 2/5.
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The quotient is the whole number; the remainder over the original denominator is the fraction part. Example: 11/4 = 2 remainder 3, so 11/4 = 2 3/4.
Can you add fractions with negative numerators?
Yes. Treat the negative sign as part of the numerator and follow the same common-denominator process. Example: −1/2 + 1/4 = −2/4 + 1/4 = −1/4.
What is a common denominator?
A shared multiple of two or more denominators that lets fractions be added or subtracted directly. The easiest one is the product of both denominators; the LCM gives smaller numbers.
Why do you flip the second fraction when dividing?
Dividing by a fraction equals multiplying by its reciprocal, since a/b ÷ c/d = a/b × d/c. Flipping the divisor turns division into easier-to-compute multiplication.
What is 2/3 times 3/5?
2/3 × 3/5 = 6/15, which simplifies to 2/5 by dividing both numbers by their GCD of 3.