Rational Algebraic Expressions Quiz
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Questions and Answers

What is a rational algebraic expression?

  • An expression that combines algebraic and geometric terms
  • An expression that can be written as a ratio of two polynomials (correct)
  • An expression that can only include integers
  • An expression that does not allow division by zero (correct)

    • What does it mean to cancel in a fraction?

    To divide the numerator and denominator by the same common factor

    What is the least common multiple (LCM) of two integers?

    The smallest positive number that is a common multiple of the integers

    What is the least common denominator (LCD) of two fractions?

    <p>The LCM of the two denominators</p> Signup and view all the answers

    What is a factor theorem?

    <p>x - n is a factor of a polynomial if the polynomial equals 0 when n is substituted for x</p> Signup and view all the answers

    What is a fractional equation?

    <p>An equation that has a variable in at least one denominator</p> Signup and view all the answers

    What is an extraneous solution?

    <p>A value of the variable that satisfies the transformed equation, but not the original one</p> Signup and view all the answers

    What is the domain in relation to a variable?

    <p>The set of numbers that can be values of the variable</p> Signup and view all the answers

    What is cross multiplication?

    <p>In a proportion, the product of the means equals the product of the extremes</p> Signup and view all the answers

    Average speed is calculated using the formula: Total distance / Total ____

    <p>Time</p> Signup and view all the answers

    Study Notes

    Rational Algebraic Expressions

    • A rational algebraic expression represents a ratio of two polynomials.
    • Important: The denominator polynomial must not equal zero.

    Canceling

    • Canceling in fractions involves dividing both numerator and denominator by a common factor.
    • For reals (a, b, c) (with (a \neq 0) and (c \neq 0)), the relationship ( \frac{ab}{ac} = \frac{b}{c} ) holds true.
    • This process simplifies the fraction.

    Least Common Multiple (LCM)

    • A common multiple of integers (a) and (b) is a number that can be expressed as ( \text{integer} \times a ) and ( \text{integer} \times b ).
    • The LCM is the smallest positive number that is a common multiple of (a) and (b).
    • The LCM can be computed by factoring integers into their prime components.

    Least Common Denominator (LCD)

    • The LCD of two fractions is derived from the LCM of their denominators.

    Factor Theorem

    • If (x - n) is a factor of a polynomial, then substituting (n) for (x) must make the polynomial equal to zero.

    Fractional Equation

    • A fractional equation has at least one variable present in its denominator, complicating the solution process.

    Extraneous Solution

    • An extraneous solution refers to a variable value that satisfies the transformed equation but does not fulfill the original equation.

    Domain

    • The domain of a variable encompasses all possible values that the variable can take.

    Cross Multiplication

    • In a proportion expressed as ( a:b = c:d ), the means' product equals the extremes' product; thus, if ( \frac{a}{b} = \frac{c}{d} ), then ( ad = bc ) applies.

    Average Speed

    • Average speed can be calculated using the formula: Total Distance / Total Time.

    Additional Note

    • The concept of fractional equations is reiterated, emphasizing that they include variables in the denominator.

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    Description

    Test your knowledge on rational algebraic expressions, including concepts like canceling fractions, least common multiple (LCM), least common denominator (LCD), and the factor theorem. This quiz will help reinforce your understanding of these crucial algebraic principles.

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