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Algebra

This guide covers the fundamental processes of multiplying and dividing rational expressions and fractions. Learn how to multiply fractions by multiplying numerators and denominators, along with strategies for simplifying by reducing and cross-canceling common factors. Additionally, discover how to divide fractions by multiplying by the reciprocal of the divisor, applying the same principles to rational expressions. Practice problems are included to reinforce your understanding and prepare for upcoming quizzes.

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Algebra

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  1. Algebra 11.5 Multiplying and Dividing Rational Expressions

  2. Multiplying Fractions When you multiply fractions, you multiply: NUMERATOR x NUMERATOR DENOMINATOR x DENOMINATOR But first, you can simplify by reducing fractions and cross-canceling common factors. 5 25 1 5 8 x = 32 15 12 4 3

  3. Multiplying Rational Expressions When you multiply rational expressions, you use the same process. You factor completely, then divide out common factors. 5 x 7 y x x Factored

  4. Try these. x x 3 x x

  5. Dividing Fractions When you divide fractions, you multiply by the reciprocal of the divisor: 4 28 16 16 7 4 21 ∙ = ÷ = 3 21 9 9 4 3 1

  6. Dividing Rational Expressions When you divide rational expressions, you use the same process. You rewrite the expression to multiply by the reciprocal, then multiply as usual. 5 x 7 x

  7. Try these. x²- 1 Think of this term as 1 x x x x

  8. Homework pg. 673 #12-34 Quiz 11.4-11.6 on Friday

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