Rewrite Equations Without Fractions Calculator
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Reviewed by Calculator Editorial Team
Eliminating fractions from equations can simplify solving them, especially when dealing with variables. This calculator helps you rewrite equations without fractions by finding a common denominator and multiplying through. Learn the step-by-step process and see how it works with practical examples.
How to Use This Calculator
To eliminate fractions from your equation, follow these steps:
- Enter your equation in the input field. For example:
x/3 + 2/5 = 1 - Select the operation type (addition, subtraction, multiplication, or division)
- Click "Calculate" to see the fraction-free version of your equation
- Review the step-by-step solution and the final result
This calculator works best with simple linear equations. For more complex equations, you may need to use additional algebraic techniques.
The Method for Eliminating Fractions
The process of eliminating fractions from an equation involves finding a common denominator and multiplying every term by that denominator. Here's how it works:
- Identify all the denominators in the equation
- Find the least common denominator (LCD) of all the denominators
- Multiply every term in the equation by the LCD
- Simplify the resulting equation
LCD = Least Common Denominator of b, d, f
Multiply each term by LCD:
(LCD × a)/b + (LCD × c)/d = (LCD × e)/f
Simplify each term:
(LCD × a)/(LCD × b) + (LCD × c)/(LCD × d) = (LCD × e)/(LCD × f)
Final equation: a/(b/LCD) + c/(d/LCD) = e/(f/LCD)
The result is an equation with whole numbers that's easier to solve.
Worked Examples
Example 1: Simple Addition
Original equation: 1/2 + 3/4 = 5/6
- Denominators: 2, 4, 6
- LCD: 12
- Multiply each term by 12:
1/2 × 12 = 6
3/4 × 12 = 9
5/6 × 12 = 10 - Result: 6 + 9 = 10
Example 2: With Variables
Original equation: x/3 + 2/5 = 1
- Denominators: 3, 5, 1
- LCD: 15
- Multiply each term by 15:
x/3 × 15 = 5x
2/5 × 15 = 6
1 × 15 = 15 - Result: 5x + 6 = 15
| Original Equation | Simplified Equation | LCD Used |
|---|---|---|
| 1/2 + 3/4 = 5/6 | 6 + 9 = 10 | 12 |
| x/3 + 2/5 = 1 | 5x + 6 = 15 | 15 |
Frequently Asked Questions
Why should I eliminate fractions from equations?
Eliminating fractions makes equations easier to solve, especially when dealing with variables. It reduces the complexity of the equation and makes it easier to perform operations like addition and subtraction.
What if my equation has negative fractions?
The process is the same for negative fractions. You still find the LCD and multiply each term by it. The negative signs will remain in place.
Can this method be used for all types of equations?
This method works best for linear equations with simple fractions. For more complex equations, you may need to use additional algebraic techniques.