Fraction Calculator

Calculation Types

1. Arithmetic Operations

1. Enter the numerator and denominator for both fractions
2. Select the operation (addition, subtraction, multiplication, or division)
3. Click "Calculate" to see the result with step-by-step solution
4. View the simplified result, decimal equivalent, and mixed number (when applicable)

2. Simplify Fraction

1. Enter a fraction in the format 6/9, mixed number like 2 1/3, or whole number
2. Click "Calculate" to see the simplified form
3. The calculator finds the greatest common divisor to reduce the fraction

3. Convert to Decimal/Percentage

1. Enter any fraction, mixed number, or whole number
2. Click "Calculate" to see the decimal and percentage equivalents
3. Useful for comparing fractions or understanding their relative values

4. Compare Fractions

1. Enter two fractions using the numerator/denominator inputs
2. Click "Calculate" to see which fraction is larger
3. The result shows the comparison with decimal values for reference

Input Formats

• Regular fractions: 3/4, -2/5, 7/8
• Mixed numbers: 2 1/3, -1 2/5, 3 7/8
• Whole numbers: 5, -3, 10

Fractions represent parts of a whole and are fundamental to mathematics, cooking, construction, and many everyday activities. Understanding fraction operations helps you work with recipes, measurements, and proportional relationships.

What is a Fraction?

A fraction consists of two parts: the numerator (top number) shows how many parts you have, and the denominator (bottom number) shows how many parts make up the whole. For example, in 3/4, you have 3 out of 4 equal parts.

Types of Fractions

• Proper Fractions: Numerator is smaller than denominator (3/4, 2/5)
• Improper Fractions: Numerator is larger than or equal to denominator (5/4, 7/3)
• Mixed Numbers: Combination of whole number and proper fraction (2 1/3, 4 2/5)
• Equivalent Fractions: Different fractions representing the same value (1/2 = 2/4 = 3/6)

Fraction Operations Explained

Addition and Subtraction

To add or subtract fractions, you need a common denominator. Find the least common multiple of the denominators, convert both fractions, then add or subtract the numerators.

Multiplication

Multiply fractions by multiplying the numerators together and the denominators together. This is often easier than addition/subtraction because no common denominator is needed.

Division

To divide fractions, multiply by the reciprocal (flip) of the second fraction. So a/b ÷ c/d becomes a/b × d/c.

Real-World Applications

• Cooking: Scaling recipes up or down (doubling 1/3 cup flour)
• Construction: Measuring lumber and materials (adding 2 3/4 + 1 1/8 inches)
• Finance: Calculating portions of investments or expenses
• Time: Working with partial hours (1/2 hour + 1/4 hour)
• Science: Mixing solutions and calculating concentrations

Fraction Operation Formulas

• •Always simplify your final answer to make it easier to understand and use
• •For addition and subtraction, find the least common multiple (LCM) of denominators for efficiency
• •When multiplying fractions, you can simplify before multiplying to make calculations easier
• •Remember: dividing by a fraction is the same as multiplying by its reciprocal
• •Mixed numbers are often more intuitive than improper fractions for practical applications
• •Cross-multiply to quickly compare which of two fractions is larger
• •Convert fractions to decimals when you need to use them in calculations with decimal numbers
• •Practice with common fractions like 1/2, 1/3, 1/4 to build intuition for fraction relationships