Rewrite Equation Without Fraction Calculator
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Reviewed by Calculator Editorial Team
Eliminating fractions from equations can simplify solving them, especially when dealing with complex fractions or multiple fractions in a single equation. This calculator helps you rewrite equations without fractions by finding a common denominator and eliminating the denominators through multiplication.
How to Use This Calculator
To use the rewrite equation without fraction calculator:
- Enter your equation in the provided field. For example:
x/2 + 3/4 = 5/6 - Click the "Calculate" button to process the equation
- View the simplified equation without fractions in the results section
- Review the step-by-step solution provided
The calculator will automatically identify the denominators in your equation and eliminate them by finding the least common denominator (LCD) and multiplying each term by this value.
How It Works
The process of rewriting an equation without fractions involves these key steps:
- Identify all denominators in the equation
- Find the least common denominator (LCD) of all denominators
- Multiply every term in the equation by the LCD
- Simplify the resulting equation
This method ensures that all fractions are eliminated while maintaining the equality of the original equation.
Worked Examples
Example 1: Simple Equation
Original equation: x/2 + 3/4 = 5/6
- Denominators: 2, 4, 6
- LCD: LCM(2,4,6) = 12
- Multiply each term by 12:
12×(x/2) + 12×(3/4) = 12×(5/6) - Simplify:
6x + 9 = 10
Final simplified equation: 6x + 9 = 10
Example 2: Complex Equation
Original equation: (2x + 1)/3 - (x - 2)/4 = (3x - 1)/6
- Denominators: 3, 4, 6
- LCD: LCM(3,4,6) = 12
- Multiply each term by 12:
12×[(2x + 1)/3] - 12×[(x - 2)/4] = 12×[(3x - 1)/6] - Simplify:
4(2x + 1) - 3(x - 2) = 2(3x - 1) - Expand:
8x + 4 - 3x + 6 = 6x - 2 - Combine like terms:
5x + 10 = 6x - 2
Final simplified equation: 5x + 10 = 6x - 2
Frequently Asked Questions
Why should I rewrite equations without fractions?
Rewriting equations without fractions simplifies solving them, especially when dealing with complex fractions or multiple fractions in a single equation. It makes the equations easier to work with and solve.
What is the least common denominator (LCD)?
The least common denominator (LCD) is the smallest number that is a multiple of all denominators in an equation. It's used to eliminate fractions by multiplying each term in the equation by this number.
Can this calculator handle variables in equations?
Yes, this calculator can handle equations with variables. It will identify the denominators and eliminate them while keeping the variables in the equation.
What if my equation has negative denominators?
The calculator will handle negative denominators correctly. It will find the LCD and multiply each term by the absolute value of the LCD to ensure all denominators are eliminated.