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Multiplication and Division of Rational Algebraic Expressions

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Multiplication and Division of Rational Algebraic Expressions

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Questions and Answers

What is the first step in multiplying rational algebraic expressions?

Multiply the numerators and denominators

Simplify the expression

Factor the numerator and denominator (correct)

Cancel out common factors

In dividing fractions, what should you do with the divisor?

Divide the divisor by the original fraction

Multiply the divisor by 2

Add the divisor to the original fraction

Get the reciprocal of the divisor (correct)

What is the shortcut method for multiplying rational algebraic expressions?

Divide by common factors first

Simplify the expression before multiplying

Factor the terms and then multiply remaining terms

Directly multiply all terms without factoring (correct)

What is the importance of recalling the multiplication and division of fractions when dealing with rational algebraic expressions?

To ensure denominators do not equal zero Signup and view all the answers

What should be done if there are common factors in the numerator and denominator when multiplying rational algebraic expressions?

Divide or cancel out common factors Signup and view all the answers

Why is factoring numerators and denominators important when dividing rational algebraic expressions?

To cancel out common factors easily Signup and view all the answers

Study Notes

The text discusses the multiplication and division of rational algebraic expressions and the importance of recalling the multiplication and division of fractions.
To multiply fractions: multiply the numerators and denominators, ensure denominators do not equal zero, and simplify if possible.
In multiplying rational algebraic expressions: factor the numerator and denominator, divide or cancel out common factors, and multiply remaining terms.
In the example given, the text walks through the process of multiplying 5/10*5/a^3 using the long way method, and then using the shortcut method.
In dividing fractions: get the reciprocal of the divisor, multiply the reciprocal of the divisor and the original fraction.
The text also covers dividing rational algebraic expressions, factoring numerators and denominators, and cancelling common factors.
The text ends with an example of dividing x^2 - 9 / x - 3 by x + 3 / 3 and the importance of getting the reciprocal of the divisor and following the steps of multiplying rational algebraic expressions.

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Description

This quiz covers the multiplication and division of rational algebraic expressions, including the multiplication and division of fractions. It discusses the methods to multiply fractions and rational algebraic expressions, as well as the process of dividing fractions and rational algebraic expressions. Examples are provided to illustrate the steps and importance of recalling the multiplication and division of fractions.