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📘intermediate algebra review

key term - Clear Fractions

Citation:

Definition

Clear fractions refer to the process of simplifying or reducing fractions to their simplest form by identifying and removing any common factors between the numerator and denominator. This is an important step in solving linear equations, as it helps to eliminate unnecessary complexity and make the equations easier to manipulate and solve.

5 Must Know Facts For Your Next Test

  1. Clearing fractions is essential for solving linear equations, as it allows for easier manipulation and simplification of the equation.
  2. The process of clearing fractions involves identifying the greatest common factor (GCF) between the numerator and denominator, and then dividing both the numerator and denominator by the GCF.
  3. Clearing fractions can be done by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, effectively eliminating the fractions.
  4. Proper clearing of fractions ensures that the equation remains balanced and that the solution remains valid.
  5. Clearing fractions can also be used to simplify complex expressions involving fractions, making them easier to work with and understand.

Review Questions

  • Explain the purpose of clearing fractions in the context of solving linear equations.
    • Clearing fractions is an essential step in solving linear equations because it helps to simplify the equation and make it easier to manipulate. By identifying and removing any common factors between the numerator and denominator of the fractions, the equation becomes more straightforward and the solution can be found more efficiently. This process ensures that the equation remains balanced and the final solution is valid.
  • Describe the process of clearing fractions, including the role of the greatest common factor (GCF).
    • The process of clearing fractions involves identifying the greatest common factor (GCF) between the numerator and denominator of the fraction. Once the GCF is determined, both the numerator and denominator are divided by the GCF, effectively simplifying the fraction. This step is crucial in solving linear equations, as it eliminates unnecessary complexity and makes the equation easier to manipulate and solve. By clearing fractions, the equation remains balanced, and the final solution is valid.
  • Analyze the importance of properly clearing fractions in the context of solving linear equations, and explain how it contributes to the overall accuracy and validity of the solution.
    • Properly clearing fractions is crucial in solving linear equations because it ensures the accuracy and validity of the final solution. When fractions are not cleared correctly, the equation can become more complex and difficult to manipulate, leading to potential errors in the solution. By identifying and removing the greatest common factor between the numerator and denominator, the equation is simplified, making it easier to solve. This process also preserves the balance of the equation, ensuring that the final solution is valid and represents the true solution to the original problem. Clearing fractions is an essential step in the problem-solving process, as it contributes to the overall rigor and reliability of the solution.