Fraction Calculator
Add, subtract, multiply, and divide fractions. Get results as simplified fractions and decimals with step-by-step clarity.
Result (Fraction)
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Result (Decimal) —
Simplified Fraction —
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Result (Simplified)
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Decimal —
Common Denominator Used —
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Three-Fraction Result
Final Result (Simplified) —
Decimal —
Mixed Number —
Percentage —
Arithmetic Properties
Final GCD —
LCD (Least Common Denom) —
Step-by-Step —
How to Use This Calculator
Enter the numerator and denominator for each fraction, select your operation, and click Calculate. The result is shown as both a fraction and a decimal.
Formula
Add/Subtract: (ad ± bc) / bd • Multiply: ac / bd • Divide: ad / bc
Example
1/2 + 1/3 = 5/6 ≈ 0.8333
Frequently Asked Questions
- First find the Least Common Denominator (LCD) — the smallest number that both denominators divide into evenly. Convert each fraction to an equivalent fraction with the LCD, then add the numerators and keep the LCD. Example: 1/2 + 1/3. The LCD of 2 and 3 is 6. Convert: 1/2 = 3/6 and 1/3 = 2/6. Add: 3/6 + 2/6 = 5/6. A common mistake is adding both numerators and denominators separately (1+1)/(2+3) = 2/5, which is wrong. Always find the common denominator first.
- Divide both the numerator and denominator by their Greatest Common Divisor (GCD). The GCD is the largest number that divides both evenly. Example: simplify 18/24. GCD(18, 24) = 6. Divide both by 6: 18/6 = 3 and 24/6 = 4, giving 3/4. If you are unsure of the GCD, keep dividing by small primes (2, 3, 5…) until no common factors remain. A fully simplified fraction has a GCD of 1 — no further reduction is possible.
- Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator: (a/b) × (c/d) = (a×c)/(b×d). Example: 3/4 × 2/5 = 6/20 = 3/10 after simplification. A useful shortcut is to "cross-simplify" before multiplying — if 3 and 6 share a common factor, simplify them first to reduce the numbers you work with. Multiplication does not require a common denominator, unlike addition and subtraction.
- Multiply the first fraction by the reciprocal (flip) of the second: (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc. Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. Remember the phrase "Keep, Change, Flip" — Keep the first fraction, Change the division sign to multiplication, Flip the second fraction. Never flip the first fraction, and always simplify the final answer if possible.
- An improper fraction has a numerator that is greater than or equal to its denominator, such as 7/4 or 9/9. It represents a value of 1 or more. To convert to a mixed number, divide numerator by denominator: 7 ÷ 4 = 1 remainder 3, giving the mixed number 1 3/4. Improper fractions are mathematically equivalent to mixed numbers and are often preferred in calculations because they are easier to multiply and divide. For example, adding 1 3/4 + 2 1/2 is easier as 7/4 + 5/2 = 7/4 + 10/4 = 17/4 = 4 1/4.