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Multiplying and Dividing Rational Expressions definitions

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  • Rational Expression
    A mathematical phrase with a numerator and denominator, both containing polynomials or numbers, often simplified by factoring and canceling.
  • Numerator
    The top part of a fraction or rational expression, representing the quantity being divided.
  • Denominator
    The bottom part of a fraction or rational expression, indicating the value by which the numerator is divided.
  • Prime Factor
    A basic building block of numbers or polynomials, used to break down expressions for simplification.
  • Difference of Squares
    A factoring pattern where two squared terms are subtracted, resulting in two binomial factors.
  • Reciprocal
    A flipped version of a fraction or rational expression, used in division to convert the operation to multiplication.
  • Simplification
    The process of reducing a rational expression to its most basic form by factoring and canceling common terms.
  • Common Factor
    A term or number present in both the numerator and denominator, which can be canceled to simplify expressions.
  • Quotient
    The result obtained after dividing one rational expression by another.
  • Divisor
    The expression or number by which another is divided in a rational expression.
  • Variable
    A symbol, often a letter, representing an unknown value in rational expressions.
  • Polynomial
    An algebraic expression consisting of variables and coefficients, used in both numerators and denominators.
  • Factoring
    The method of breaking down numbers or polynomials into simpler components to aid in simplification.
  • Multiplication
    The operation of combining numerators and denominators directly across to form a new rational expression.
  • Keep Change Flip
    A memory tool for division: retain the first expression, switch division to multiplication, and invert the second expression.