Questions and Answers
What is a rational algebraic expression?
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?
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What is a factor theorem?
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What is a fractional equation?
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What is an extraneous solution?
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What is the domain in relation to a variable?
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What is cross multiplication?
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Average speed is calculated using the formula: Total distance / Total ____
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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.