Math & Statistics
Fraction Calculator ā Add, Subtract, Multiply & Divide Fractions
Use our free Fraction Calculator to quickly solve fraction problems. Add, subtract, multiply, divide, and simplify fractions with step-by-step results for easy learning.
How to Calculate with Fractions
A fraction represents a part of a whole, written as numerator/denominator. The numerator (top) shows how many parts you have; the denominator (bottom) shows how many equal parts make the whole. For example, 3/4 means 3 out of 4 equal parts.
Key rules: To add/subtract fractions, find a common denominator first. To multiply, multiply numerators together and denominators together. To divide, flip the second fraction and multiply. Always simplify your final answer by dividing both parts by their greatest common divisor (GCD).
First Fraction
Second Fraction
How to Use This Calculator
- Enter the numerator and denominator for the first fraction
- Select the operation (+, ā, Ć, Ć·)
- Enter the numerator and denominator for the second fraction
- Click Calculate to see the simplified result, decimal, and percentage
Common Use Cases
- Homework & math class
- Cooking & recipe scaling
- Construction measurements
- Financial calculations
- Science & engineering
- Sewing & fabric cutting
Fraction Operation Rules
| Operation | Formula | Example | Result |
|---|---|---|---|
| Addition | a/b + c/d = (ad + bc) / bd | 1/4 + 1/2 | 3/4 |
| Subtraction | a/b ā c/d = (ad ā bc) / bd | 3/4 ā 1/2 | 1/4 |
| Multiplication | a/b Ć c/d = ac / bd | 2/3 Ć 3/4 | 1/2 |
| Division | a/b Ć· c/d = a/b Ć d/c | 1/2 Ć· 1/4 | 2 |
Common Fractions & Decimal Equivalents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 2/3 | 0.666... | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| Fraction | Decimal | Percent |
|---|---|---|
| 1/5 | 0.2 | 20% |
| 1/6 | 0.166... | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
How to Simplify Fractions
To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). A fraction is fully simplified when the GCD is 1.
| Original | Find GCD | Divide Both | Simplified |
|---|---|---|---|
| 12/18 | GCD(12,18) = 6 | 12Ć·6 / 18Ć·6 | 2/3 |
| 15/25 | GCD(15,25) = 5 | 15Ć·5 / 25Ć·5 | 3/5 |
| 24/36 | GCD(24,36) = 12 | 24Ć·12 / 36Ć·12 | 2/3 |
| 8/20 | GCD(8,20) = 4 | 8Ć·4 / 20Ć·4 | 2/5 |
FAQ ā Fraction Calculator
How do I add fractions with different denominators?
Find the Least Common Denominator (LCD) of both fractions. Convert each fraction to an equivalent fraction with the LCD as the denominator. Then add the numerators and keep the common denominator. Example: 1/4 + 1/3 ā LCD is 12 ā 3/12 + 4/12 = 7/12.
Why do I flip the second fraction when dividing?
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a/b is b/a. So a/b Ć· c/d = a/b Ć d/c. This rule comes from the definition of division: how many times does c/d fit into a/b?
What's the difference between proper and improper fractions?
A proper fraction has a numerator smaller than its denominator (e.g., 3/4). An improper fraction has a numerator equal to or larger than its denominator (e.g., 5/4). Improper fractions can be converted to mixed numbers: 5/4 = 1Ā¼.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and place over the original denominator. Example: 2Ā¾ ā (2Ć4 + 3)/4 = 11/4. To reverse: divide numerator by denominator to get the whole number, remainder becomes the new numerator.
What is the Greatest Common Divisor (GCD)?
The GCD is the largest number that divides both the numerator and denominator evenly. To find it, list factors of both numbers and pick the largest common one, or use the Euclidean algorithm. The GCD of 12 and 18 is 6.
Can I multiply fractions without finding a common denominator?
Yes! Unlike addition and subtraction, multiplication doesn't require a common denominator. Simply multiply numerators together and denominators together: 2/3 Ć 4/5 = 8/15. You can simplify before or after multiplying.
How do I convert a decimal to a fraction?
Write the decimal over a power of 10 based on decimal places, then simplify. Example: 0.75 = 75/100 = 3/4. For repeating decimals like 0.333..., recognize the pattern: 0.333... = 1/3. Use algebra for complex repeating decimals.
What does it mean to simplify a fraction?
Simplifying (or reducing) a fraction means dividing both numerator and denominator by their GCD until no common factors remain. A simplified fraction is in "lowest terms." Example: 8/12 ā divide both by 4 ā 2/3.
How do I compare two fractions?
Convert both fractions to the same denominator, then compare numerators. Alternatively, cross-multiply: for a/b vs c/d, compare aĆd with bĆc. If aĆd > bĆc, then a/b > c/d. Example: 2/3 vs 3/5 ā 2Ć5=10, 3Ć3=9 ā 10>9 ā 2/3 > 3/5.
Why is my answer showing as a mixed number?
When the result is an improper fraction (numerator ā„ denominator), this calculator displays it as a mixed number for easier interpretation. For example, 7/4 is shown as 1Ā¾. Both forms are mathematically equivalent.