Uploaded byLorie Jane Letada
Multiplying Rational Expressions
This document contains a lesson plan for teaching multiplying rational expressions in Math 8. The lesson plan outlines the intended learning outcomes, learning content including subject matter and references, learning experiences such as classifying rational expressions, and an assignment for students to practice multiplying rational expressions. The lesson plan provides step-by-step instructions for multiplying rational expressions by factoring, canceling common factors, and simplifying the resulting expression.
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Introduction to a semi-detailed lesson plan for Math 8 at Quiot National High School in the Philippines.
Intended learning outcomes focusing on rational expressions: differentiate, multiply, and apply in real life. References and materials included.
Abstraction and steps for multiplying rational expressions, rules similar to fractions, and example problems for practice.
Evaluation exercises for multiplying rational expressions, simplification steps, and additional skill booster assignment.
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Multiplying Rational Expressions
- 1. Republic of thePhilippines Department of Education Region VII Central Visayas Division of Cebu City Quiot National High School Bogo, Quiot, Cebu City A Semi-Detailed Lesson Plan In Math 8 ___________________ Date of Teaching ____________________ Time of Teaching Quiot National High School- Afternoon Session Venue of Teaching Prepared by: LORIE JANE L. LETADA Teacher 1 Observed by: ELEANOR D. GALLARDO ASSISTANT PRINCIPAL
- 2. I. Intended LearningOutcomes Through varied learning activities, the grade 8 students with at least80 % ofaccuracy shall able to: 1. differentiate rational expressions from non-rational expressions 2. multiply rational expressions 3. Relate multiply rational expressions in real life situation II. Learning Content A. Subject Matter Multiplying Rational Expressions B. Reference Diaz, Z., Mojica M. (2013) . Next Century Mathematics 8; Quezon City ; Phoenix Publishing House , Inc; Mathematics 8 Learner’s Module K-12; DepEd K-12 Modified Curriculum Guide and Teacher’s Guide for Mathematics 8 https://www.mathsisfun.com/simplifying-fractions.html C. Materials Learners’ Module; Google Classroom; powerpointpresentation; google forms III. Learning Experiences A. Activity B. Analysis 1. How many expressions did you place in the column ofrational algebraic expressions? 2. How many expressions did you place under the column ofnot rational algebraic expression column? 3. How did you differentiate a rational algebraic expression from a not rational algebraic expression? 4. Were you able to place each expression in its appropriate column? 5. What difficulty did you encounter in classifying the expressions? mmClassify Me!
- 3. C. Abstraction To multiplyrational expressions, recall the rules for multiplying fractions. If the denominators are not equal to zero, then we simply multiply the numerators and denominators. The same rule applies to rational expressions. If a, b, c, and d represent polynomials where b ≠ 0 and d ≠ 0. Then, Multiply each rational expression and simplify. 1. 𝟓 𝟏𝟐 ∗ 𝟖 𝟏𝟓 = 2. 𝟏𝟓 𝟐𝒚 𝟐 ∗ 𝒚 𝟒 𝟐𝟎𝒚 𝟐 = 3. 𝟒𝒙 𝟐 −𝟗 𝒙 𝟐 −𝟓𝒙+𝟔 ∗ 𝟑𝒙−𝟔 𝟖𝒙+𝟏𝟐 = 𝟒. 𝟑𝒔 𝟒𝒔+𝟏 ∗ 𝟐𝒔+𝟏 𝟑𝒔 𝟐 = D. Application Multiply each rational expression and simplify. 1. 𝟔 𝟏𝟎 ∗ 𝟓 𝟏𝟓 = 𝒂 𝒃 ∗ 𝒄 𝒅 = 𝒂𝒄 𝒃𝒅 Step 1 Factor each expression. 𝟓 𝟏𝟐 ∗ 𝟖 𝟏𝟓 = 𝟓 ( 𝟒)(𝟑) ∗ ( 𝟒) (𝟐) ( 𝟑) (𝟓) Step 2 Cancel all common factors. 𝟓 ( 𝟒)(𝟑) * ( 𝟒) (𝟐) ( 𝟑) (𝟓) Step 3: Write what is left. 𝟓 𝟏𝟐 ∗ 𝟖 𝟏𝟓 = 𝟐 ( 𝟑) (𝟑) = 𝟐 𝟗 Step 1: Factor each expression. 𝟏𝟓 𝟐𝒚 𝟐 ∗ 𝒚 𝟒 𝟐𝟎𝒚 𝟐 = ( 𝟓 )( 𝟑) ( 𝟐)(𝒚 𝟐) ∗ ( 𝒚 𝟐)(𝒚 𝟐 ) ( 𝟓)( 𝟒)(𝒚 𝟐) Step 2 Cancel all common factors. 𝟏𝟓 𝟐𝒚 𝟐 ∗ 𝒚 𝟒 𝟐𝟎𝒚 𝟐 = ( 𝟓 ) ( 𝟑) ( 𝟐) (𝒚 𝟐) ∗ ( 𝒚 𝟐) (𝒚 𝟐 ) ( 𝟓) ( 𝟒) (𝒚 𝟐) Step 3: Write what is left. 𝟏𝟓 𝟐𝒚 𝟐 ∗ 𝒚 𝟒 𝟐𝟎𝒚 𝟐 = 𝟑 (𝟐)(𝟒) = 𝟑 𝟖 Step 1: Factor each expression. 𝟒𝒙 𝟐 −𝟗 𝒙 𝟐 −𝟓𝒙+𝟔 ∗ 𝟑𝒙−𝟔 𝟖𝒙+𝟏𝟐 = ( 𝟐𝒙−𝟑 )(𝟐𝒙+𝟑) ( 𝒙−𝟑)(𝒙−𝟐) * 𝟑 ( 𝒙−𝟐 ) 𝟒(𝟐𝒙+𝟑) Step 2 : Cancel all common factors. 𝟒𝒙 𝟐 −𝟗 𝒙 𝟐 −𝟓𝒙+𝟔 ∗ 𝟑𝒙−𝟔 𝟖𝒙+𝟏𝟐 = ( 𝟐𝒙−𝟑 )(𝟐𝒙+𝟑) ( 𝒙−𝟑)(𝒙−𝟐) * 𝟑 ( 𝒙−𝟐 ) 𝟒(𝟐𝒙+𝟑) Step 3: Write what is left. 𝟒𝒙 𝟐 −𝟗 𝒙 𝟐−𝟓𝒙+𝟔 ∗ 𝟑𝒙−𝟔 𝟖𝒙+𝟏𝟐 = ( 𝟐𝒙−𝟑 ) ( 𝒙−𝟑) ∗ 𝟑 𝟒 = 𝟑 ( 𝟐𝒙−𝟑 ) 𝟒 ( 𝒙−𝟑 ) Step 1: Factor each expression. 𝟑𝒔 𝟒𝒔+𝟐 ∗ 𝟐𝒔+𝟏 𝟑𝒔 𝟐 = 𝟑𝒔 𝟐(𝟐𝒔+𝟏) ∗ (𝟐𝒔+𝟏) 𝒔 ( 𝟑𝒔 ) Step 2 : Cancel all common factors. 𝟑𝒔 𝟒𝒔+𝟐 ∗ 𝟐𝒔+𝟏 𝟑𝒔 𝟐 = 𝟑𝒔 𝟐(𝟐𝒔+𝟏) ∗ (𝟐𝒔+𝟏) 𝒔 ( 𝟑𝒔 ) 𝟑𝒔 𝟒𝒔+𝟐 ∗ 𝟐𝒔+𝟏 𝟑𝒔 𝟐 = 𝟏 𝟐 ( 𝒔) = 𝟏 𝟐𝒔 Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. Step 1 Factor each expression. Step 2 Cancel all common factors. Step 3: Write what is left.
- 4. 𝟐. 𝟏𝟐 𝟑𝒘 𝟑 ∗ 𝟒𝒘𝟒 𝟏𝟓𝒘 𝟐 = 𝟑. 𝒙+𝟓 𝟒 ∗ 𝟏𝟐𝒙 𝟐 𝒙 𝟐+𝟕𝒙+𝟏𝟎 = 𝟒. 𝟑 𝒙−𝒚 ∗ (𝒙−𝒚 ) 𝟐 𝟔 = IV. Evaluation Multiply each rational expression and simplify. 1. 𝟏𝟒 𝟐𝟕 ∗ 𝟑 𝟕 = 5. (𝒓 𝟐 +𝟑𝒓+𝟐 ) 𝒓−𝟏 * 𝒓+𝟑 𝒓 𝟐+𝟓𝒓+𝟔 = 2. 𝟏𝟐𝒏 𝟒𝒎 𝟐 ∗ 𝟖𝒎 𝟒 𝟏𝟓𝒏 𝟐 = 6. (𝒂 𝟐 −𝟏 ) 𝟏𝟔 𝒂 * (𝟒𝒂 𝟐 𝟕𝒂+𝟕 = 3. 𝟏𝟐𝒏 𝟒𝒎 𝟐 ∗ 𝟖𝒎 𝟒 𝟏𝟓𝒏 𝟐 = 7. (𝒚 𝟐 +𝟒𝒚+𝟒 ) 𝒚+𝟑 * 𝟒𝒚+𝟏𝟐 𝒚+𝟐 = = 4. 𝟐𝒎+𝟓 𝟑𝒎−𝟔 * (𝒎 𝟐 +𝒎−𝟔 ) 𝟒 = V. Assignment Skill Booster! Step 1: Factor each expression. Step 2 : Cancel all common factors. Step 3: Write what is left. Step 1: Factor each expression. Step 2 : Cancel all common factors. Step 3: Write what is left. Step 1: Factor each expression. Step 2 : Cancel all common factors. Step 3: Write what is left.