key term - Clearing Fractions

Definition

Clearing fractions is the process of removing or eliminating fractions from an equation or expression in order to simplify and solve the problem. This technique is commonly used when dealing with equations or expressions that contain fractions, as it allows for easier manipulation and solution-finding.

5 Must Know Facts For Your Next Test

1. Clearing fractions is a crucial step in solving equations with fractions or decimals, as it allows for the equation to be simplified and solved more easily.
2. The process of clearing fractions involves finding the least common denominator (LCD) of all the fractions in the equation and then converting the fractions to equivalent fractions with the LCD.
3. Cross-multiplication is a common technique used to clear fractions, where the numerator of one fraction is multiplied by the denominator of the other fraction, and vice versa, to eliminate the fractions.
4. Clearing fractions is also an important step in solving rational equations, as it allows for the equation to be simplified and solved more efficiently.
5. The ability to clear fractions is a fundamental skill in algebra and is essential for success in solving a wide range of mathematical problems.

Review Questions

• Explain the purpose of clearing fractions in the context of solving equations with fractions or decimals.
  • The purpose of clearing fractions when solving equations with fractions or decimals is to eliminate the fractions or decimals from the equation, allowing for easier manipulation and solution-finding. By converting the fractions or decimals to equivalent expressions with a common denominator, the equation can be simplified and solved more efficiently. This process is crucial in ensuring that the final solution is accurate and meets the requirements of the problem.
• Describe the steps involved in clearing fractions when solving rational equations.
  • When solving rational equations, the process of clearing fractions involves the following steps: 1) Identify the least common denominator (LCD) of all the fractions in the equation. 2) Convert each fraction to an equivalent fraction with the LCD as the denominator. 3) Multiply each term in the equation by the LCD to eliminate the fractions. 4) Simplify the resulting equation and solve for the unknown variable. By clearing the fractions in this manner, the rational equation can be transformed into a simpler, polynomial equation that can be solved using standard algebraic techniques.
• Analyze how clearing fractions is related to solving proportion and similar figure applications.
  • In the context of solving proportion and similar figure applications, clearing fractions is an essential step. Proportions are often expressed as fractions, and clearing these fractions is necessary to solve for the unknown value. Additionally, when working with similar figures, the ratios of corresponding sides are expressed as fractions. Clearing these fractions allows for the establishment of an equivalent expression, which can then be used to determine the missing dimensions of the similar figures. By clearing fractions, the relationships between the quantities in the proportion or similar figure problem can be more easily manipulated and solved.

Related terms

Least Common Denominator (LCD):

The least common denominator is the smallest positive integer that is divisible by all the denominators in a set of fractions. This is a crucial step in clearing fractions, as the fractions must be converted to equivalent fractions with a common denominator.

Cross-Multiplication:

Cross-multiplication is a technique used to clear fractions by multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa, to eliminate the fractions and create an equivalent expression.

Rational Equation:

A rational equation is an equation that contains one or more fractions. Clearing fractions is a necessary step in solving rational equations, as it allows for the equation to be simplified and solved.