Rational Algebraic Expressions Quiz

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?

The LCM of the two denominators Signup and view all the answers

What is a factor theorem?

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

What is a fractional equation?

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

What is an extraneous solution?

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

What is the domain in relation to a variable?

The set of numbers that can be values of the variable Signup and view all the answers

What is cross multiplication?

In a proportion, the product of the means equals the product of the extremes Signup and view all the answers

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

Time 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.

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.