Fraction Calculator
Enter two fractions with optional whole numbers and pick an operation. Results show instantly with step-by-step work, visual bars, and all formats.
Common Fraction Equivalents
Quick reference for common fractions with their decimal and percentage equivalents.
How to Work with Fractions
Adding and Subtracting Fractions
To add or subtract fractions, you need a common denominator:
- Find the least common denominator (LCD) of both fractions
- Convert each fraction to an equivalent fraction with the LCD
- Add or subtract the numerators
- Keep the denominator the same
- Simplify the result if possible
Example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12
Multiplying Fractions
Multiplication is simpler -- no common denominator needed:
- Multiply the numerators together
- Multiply the denominators together
- Simplify the result
Example: 2/3 x 3/4 = (2x3)/(3x4) = 6/12 = 1/2
Dividing Fractions
Division uses the "flip and multiply" method:
- Keep the first fraction as is
- Flip the second fraction (reciprocal)
- Multiply the fractions
- Simplify the result
Example: 2/3 / 1/4 = 2/3 x 4/1 = 8/3 = 2 2/3
Simplifying Fractions
To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD). For example, 8/12 simplifies to 2/3 because GCD(8,12) = 4, so 8/4 = 2 and 12/4 = 3.
Converting Mixed Numbers
A mixed number like 2 1/3 can be converted to an improper fraction: multiply the whole number by the denominator, add the numerator, and place over the original denominator. So 2 1/3 = (2x3 + 1)/3 = 7/3.
Frequently Asked Questions
How do you add fractions?
To add fractions, first find a common denominator. Convert both fractions to equivalent fractions with that denominator, then add the numerators. For example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
How do you multiply fractions?
To multiply fractions, multiply the numerators together and multiply the denominators together. For example: 2/3 x 3/4 = (2x3)/(3x4) = 6/12 = 1/2 after simplification.
How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal (flip) of the second fraction. For example: 2/3 / 1/4 = 2/3 x 4/1 = 8/3 = 2 2/3 as a mixed number.
What is a mixed number?
A mixed number combines a whole number and a fraction, like 2 1/3. It represents 2 + 1/3 = 7/3 as an improper fraction. Mixed numbers are easier to visualize for values greater than 1.
How do you simplify fractions?
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example: 8/12 simplified is 2/3, because GCD(8,12) = 4, and 8/4 = 2, 12/4 = 3.
What is the least common denominator?
The least common denominator (LCD) is the smallest number that both denominators divide into evenly. It is the least common multiple (LCM) of the two denominators. For 1/4 and 1/6, the LCD is 12.
Can this calculator handle mixed numbers?
Yes. Enter the whole number part in the first field, then the fraction part. The calculator will convert it to an improper fraction for calculation and show the result in both formats.
Does this calculator simplify fractions automatically?
Yes. All results are automatically simplified to their lowest terms by dividing both numerator and denominator by their greatest common divisor.
Privacy & Limitations
- All calculations run entirely in your browser -- nothing is sent to any server.
- Results are estimates and may vary based on actual conditions.
Related Tools
- Decimal to Fraction Converter -- Convert decimals to fractions and vice versa
- Fraction Visualizer -- Visualize a fraction and see the simplified form
- Long Division Calculator -- Perform long division with step-by-step process
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This tool FAQ
How do you add fractions?
To add fractions, first find a common denominator. Convert both fractions to equivalent fractions with that denominator, then add the numerators. For example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
How do you multiply fractions?
To multiply fractions, multiply the numerators together and multiply the denominators together. For example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2 after simplification.
How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal (flip) of the second fraction. For example: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2 2/3 as a mixed number.
What is a mixed number?
A mixed number combines a whole number and a fraction, like 2 1/3. It represents 2 + 1/3 = 7/3 as an improper fraction. Mixed numbers are easier to visualize for values greater than 1.
How do you simplify fractions?
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example: 8/12 simplified is 2/3, because GCD(8,12) = 4, and 8÷4 = 2, 12÷4 = 3.
What is the least common denominator?
The least common denominator (LCD) is the smallest number that both denominators divide into evenly. It is the least common multiple (LCM) of the two denominators. For 1/4 and 1/6, the LCD is 12.