Fraction Calculator

Video Guide: Fraction Calculator

About Fraction Calculator

Welcome to the Fraction Calculator, a comprehensive free online tool for adding, subtracting, multiplying, and dividing fractions. Whether you are working with proper fractions, improper fractions, or mixed numbers, this calculator provides step-by-step solutions with visual diagrams to help you understand every calculation.

How to Use the Fraction Calculator

1. Enter the first fraction: Input the numerator (top number) and denominator (bottom number). For mixed numbers, also enter the whole number part.
2. Select the operation: Choose addition (+), subtraction (−), multiplication (×), or division (÷).
3. Enter the second fraction: Input the second fraction in the same way.
4. Calculate: Click the button to see your result with complete step-by-step explanation.
5. Review results: View the answer as a simplified fraction, mixed number, decimal, and percentage.

Fraction Operations Explained

Types of Fractions

• Proper Fractions: The numerator is smaller than the denominator (e.g., 3/4). These represent values less than 1.
• Improper Fractions: The numerator is equal to or greater than the denominator (e.g., 5/4, 7/3). These represent values of 1 or more.
• Mixed Numbers: A combination of a whole number and a proper fraction (e.g., 1 1/2, 2 3/4).

Converting Between Forms

Mixed Number to Improper Fraction

Multiply the whole number by the denominator, add the numerator, and place over the original denominator:

Improper Fraction to Mixed Number

Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator:

Simplifying Fractions

A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. To simplify, find the Greatest Common Factor (GCF) and divide both numbers by it:

Frequently Asked Questions

How do you add fractions with different denominators?

To add fractions with different denominators: 1) Find the Least Common Denominator (LCD) of both fractions. 2) Convert each fraction to an equivalent fraction with the LCD. 3) Add the numerators while keeping the common denominator. 4) Simplify the result if possible. For example, 1/4 + 1/3 = 3/12 + 4/12 = 7/12.

How do you multiply fractions?

To multiply fractions, simply multiply the numerators together and multiply the denominators together. Then simplify the result if possible. For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. You can also cross-cancel before multiplying to make the calculation easier.

How do you divide fractions?

To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. Remember: Keep the first fraction, Change to multiplication, Flip the second fraction (KCF method).

What is the difference between proper and improper fractions?

A proper fraction has a numerator smaller than its denominator (e.g., 3/4, representing less than 1 whole). An improper fraction has a numerator equal to or greater than its denominator (e.g., 5/4, representing 1 or more wholes). Improper fractions can be converted to mixed numbers: 5/4 = 1 1/4.

How do you convert a mixed number to an improper fraction?

To convert a mixed number to an improper fraction: 1) Multiply the whole number by the denominator. 2) Add the numerator to that product. 3) Place the result over the original denominator. For example, 2 3/4 = (2×4 + 3)/4 = 11/4.

Additional Resources

• Fraction - Wikipedia
• Fraction Arithmetic - Khan Academy
• Fractions - Math is Fun

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