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Evaluate The Expression Fractions Calculator with Negative and Mixed Numbers

Reviewed by Calculator Editorial Team

This calculator evaluates mathematical expressions containing fractions, negative numbers, and mixed numbers. It handles operations like addition, subtraction, multiplication, and division with proper fraction simplification and mixed number conversion.

How to Use This Calculator

To evaluate a mathematical expression with fractions, negative numbers, and mixed numbers:

  1. Enter your expression in the input field. For example: (3/4 - 1/2) * -2 + 1 1/2
  2. Click the "Calculate" button to evaluate the expression
  3. View the result in both fraction and decimal forms
  4. Use the "Reset" button to clear the calculator for a new calculation

The calculator will handle all operations in the correct order of operations (PEMDAS/BODMAS) and properly convert between fractions and mixed numbers as needed.

Formula Used

The calculator evaluates expressions using standard mathematical operations with these rules:

1. Parentheses/Brackets first 2. Exponents/Orders 3. Multiplication and Division (left to right) 4. Addition and Subtraction (left to right)

For fractions, the calculator performs operations by finding a common denominator when needed and simplifying results to their lowest terms.

Mixed numbers are converted to improper fractions for calculation and then converted back to mixed numbers in the result when appropriate.

Worked Examples

Example 1: Simple Fraction Operation

Expression: 1/2 + 3/4

Calculation:

  1. Find common denominator (4): (2/4 + 3/4)
  2. Add numerators: 5/4
  3. Result: 1 1/4 (mixed number)

Example 2: Negative Fraction Operation

Expression: -2/3 * 4/5

Calculation:

  1. Multiply numerators and denominators: (-2 * 4)/(3 * 5) = -8/15
  2. Result: -8/15 (already simplified)

Example 3: Mixed Number Operation

Expression: 2 1/2 - 1 3/4

Calculation:

  1. Convert to improper fractions: (5/2 - 7/4)
  2. Find common denominator (4): (10/4 - 7/4)
  3. Subtract numerators: 3/4
  4. Result: 3/4 (proper fraction)

Frequently Asked Questions

Can this calculator handle complex expressions with multiple operations?
Yes, the calculator follows the standard order of operations (PEMDAS/BODMAS) to evaluate expressions with multiple operations correctly.
How does the calculator simplify fractions?
The calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by this value to simplify fractions to their lowest terms.
Can I use decimal numbers in the expression?
Yes, the calculator can handle decimal numbers and will convert them to fractions for calculation when needed.
What if I enter an invalid expression?
The calculator will display an error message if the expression is invalid or cannot be evaluated.