📘intermediate algebra review

key term - Fractions

Definition

A fraction is a numerical quantity that represents a part of a whole. It is expressed as a ratio of two numbers, the numerator and the denominator, which indicates how many equal parts the whole is divided into and how many of those parts are being considered.

5 Must Know Facts For Your Next Test

  1. Fractions can be used to represent parts of a whole, measurements, or the result of division.
  2. Fractions can be classified as proper, improper, or mixed, depending on the relationship between the numerator and denominator.
  3. Operations with fractions, such as multiplication and division, involve manipulating the numerators and denominators according to specific rules.
  4. Rational expressions are algebraic expressions that can be written as a fraction, and they follow the same rules as arithmetic fractions.
  5. Simplifying rational expressions involves reducing the fraction to its lowest terms by factoring and canceling common factors in the numerator and denominator.

Review Questions

  • Explain how fractions are used to represent parts of a whole and how they are classified.
    • Fractions are used to represent parts of a whole by dividing the whole into a number of equal parts and indicating how many of those parts are being considered. Fractions can be classified as proper fractions (when the numerator is less than the denominator), improper fractions (when the numerator is greater than or equal to the denominator), or mixed numbers (which have a whole number part and a fractional part). The classification of a fraction depends on the relationship between the numerator and denominator.
  • Describe the process of multiplying and dividing rational expressions, and explain how it relates to the operations with arithmetic fractions.
    • Multiplying and dividing rational expressions follows the same rules as multiplying and dividing arithmetic fractions. To multiply rational expressions, you multiply the numerators together and multiply the denominators together. To divide rational expressions, you invert the divisor (the fraction in the denominator) and then multiply the dividend (the fraction in the numerator) by the inverted divisor. This process is analogous to the operations with arithmetic fractions, where the numerators and denominators are manipulated according to the same rules.
  • Analyze the importance of simplifying rational expressions and explain the steps involved in this process.
    • Simplifying rational expressions is crucial because it allows for easier manipulation and comparison of these expressions. The process of simplifying rational expressions involves reducing the fraction to its lowest terms by factoring the numerator and denominator and then canceling any common factors. This step-by-step process ensures that the rational expression is in its most simplified form, making it easier to perform further operations, such as addition, subtraction, multiplication, and division. Simplifying rational expressions is a fundamental skill in algebra and is essential for understanding and working with more complex algebraic expressions.