Algebraic Fractions

Definition

Algebraic fractions are mathematical expressions that represent the division of one algebraic expression by another. They consist of a numerator, which is the dividend, and a denominator, which is the divisor, separated by a fraction bar. Algebraic fractions are a fundamental concept in solving equations with fraction or decimal coefficients.

5 Must Know Facts For Your Next Test

1. Algebraic fractions can be simplified by factoring the numerator and denominator and canceling common factors.
2. The rules for operations with algebraic fractions (addition, subtraction, multiplication, and division) are similar to those for numerical fractions.
3. Solving equations with algebraic fractions often requires cross-multiplying to isolate the variable.
4. The least common denominator (LCD) must be found when adding or subtracting algebraic fractions with different denominators.
5. Algebraic fractions can be converted to decimal form by dividing the numerator by the denominator.

Review Questions

• Explain the process of simplifying an algebraic fraction.
  • To simplify an algebraic fraction, first factor the numerator and denominator to identify any common factors. Then, cancel out the common factors to obtain the simplified form of the fraction. This reduces the fraction to its lowest terms and makes it easier to perform operations with the fraction.
• Describe the steps involved in solving an equation with algebraic fractions.
  • To solve an equation with algebraic fractions, first find the least common denominator (LCD) of all the fractions in the equation. Then, use the LCD to rewrite each fraction with a common denominator. Next, cross-multiply to isolate the variable term, and finally, solve for the variable by performing the necessary algebraic operations.
• Analyze the relationship between algebraic fractions and rational expressions.
  • Algebraic fractions and rational expressions are closely related, as a rational expression can be written in the form of an algebraic fraction. Both involve the division of one algebraic expression by another, and the rules for operations with these expressions are similar. Understanding the properties of algebraic fractions is essential for working with rational expressions and solving more complex equations and inequalities.

Related terms

Numerator: The expression above the fraction bar in an algebraic fraction, representing the dividend.

Denominator: The expression below the fraction bar in an algebraic fraction, representing the divisor.

Rational Expression: A mathematical expression that can be written as a ratio of two polynomial expressions.