Fraction Calculator Online Free Tool
Fraction Calculator
Fraction Calculator
The fraction calculator adds, subtracts, multiplies, and divides fractions and mixed numbers. It shows the step-by-step process and gives the result in simplified form. It also converts between fractions, decimals, and percentages.
Fraction Operations
| Operation | Method | Example |
|---|---|---|
| Addition | Find common denominator, add numerators | 1/3 + 1/4 = 4/12 + 3/12 = 7/12 |
| Subtraction | Find common denominator, subtract numerators | 3/4 - 1/3 = 9/12 - 4/12 = 5/12 |
| Multiplication | Multiply numerators, multiply denominators | 2/3 x 3/5 = 6/15 = 2/5 |
| Division | Flip the second fraction, then multiply | 2/3 / 4/5 = 2/3 x 5/4 = 10/12 = 5/6 |
How to Simplify Fractions
A fraction is simplified when the numerator and denominator share no common factors other than 1. Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For 12/18: GCF of 12 and 18 is 6. 12/6 = 2. 18/6 = 3. Simplified form: 2/3.
Simplified Fraction = (Numerator / GCF) / (Denominator / GCF)
Example: 24/36. GCF = 12. Simplified = (24/12) / (36/12) = 2/3.
Common Fraction to Decimal Conversions
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/3 | 0.667 | 66.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
Mixed Numbers
A mixed number has a whole part and a fraction part: 2 3/4. To use it in a calculation, convert to an improper fraction: multiply the whole number by the denominator, add the numerator, keep the same denominator. 2 3/4 = (2x4 + 3)/4 = 11/4.
Mixed Number to Improper: (Whole x Denominator + Numerator) / Denominator
Example: 3 2/5 = (3x5 + 2)/5 = 17/5. Back to mixed: 17 / 5 = 3 remainder 2 = 3 2/5.
Frequently Asked Questions
How do you add fractions with different denominators?⌄
Find the least common denominator (LCD) of the two fractions. Convert each fraction to an equivalent fraction with the LCD as the denominator. Then add the numerators. Example: 1/4 + 1/6. LCD = 12. Convert: 3/12 + 2/12 = 5/12.
How do you multiply fractions?⌄
Multiply the numerators together and the denominators together. Simplify the result. Example: 3/4 x 2/5 = (3x2)/(4x5) = 6/20 = 3/10.
How do you divide fractions?⌄
Flip the second fraction (take its reciprocal), then multiply. Example: 3/4 / 2/3 = 3/4 x 3/2 = 9/8 = 1 1/8.
How do you convert a fraction to a decimal?⌄
Divide the numerator by the denominator. 3/8 = 3 / 8 = 0.375. 7/4 = 7 / 4 = 1.75. For repeating decimals like 1/3, the result is 0.333... (the dots indicate the pattern repeats infinitely).
What is an improper fraction?⌄
An improper fraction has a numerator larger than or equal to the denominator: 7/4, 11/3, 5/5. It represents a value of 1 or more. To convert to a mixed number, divide the numerator by the denominator. 11/4 = 2 remainder 3 = 2 3/4.