Adding Similar Rational Expressions
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The document outlines a lesson plan for teaching the addition and subtraction of rational expressions with the same denominator to 8th grade math students. It includes intended learning outcomes, learning content on rational expressions, sample problems and solutions, and an evaluation section to assess student understanding. The lesson aims to have students differentiate between rational and non-rational expressions, perform operations on rational expressions with the same denominator, and apply rational expressions to real-life situations.
Adding Similar Rational Expressions
- 1. Republic of the Philippines 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 Learning Outcomes Through varied learning activities, the grade 8 students with at least80 % ofaccuracy shall able to: 1. differentiate rational expressions from non-rational expressions 2. add and subtract rational expressions with same denominator 3. relate rational expressions in real life situation II. Learning Content A. Subject Matter Addition and Subtraction ofRational Expressions with The Same 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 http://www.mesacc.edu/~scotz47781/mat120/notes/rational/dividing/dividing.html#:~:text=Exam ple%201%20%E2%80%93%20Simplify%3A- ,Step%201%3A%20Completely%20factor%20both%20the%20numerators%20and%20denominators %20of,Cancel%20or%20reduce%20the%20fractions. C. Materials Learners’ Module; Google Classroom; powerpointpresentation; google forms III. Learning Experiences A. Activity mmFlow Chart
- 3. B. Analysis 1. Does every step have a mathematical conceptinvolved? 2. What makes that mathematical conceptimportantto every step? 3. Can mathematical conceptin every step be interchanged? How? 4. Can you make another method in adding or subtracting rational algebraic expressions? How? B. Abstraction In adding and subtractingrational expressions with same denominators, perform the operation in the numerator and keep the denominator. The resulting sum and difference must be reduced to lowest terms whenever possible. Provided the denominator is not equal to zero, then Perform the indicated operations. 1. 𝟑 𝟓 + 𝟏 𝟓 2. 𝟑𝒙+𝟐 𝒙+ 𝟓 + 𝟒𝒙 𝒙+ 𝟓 3. 𝟓𝒓 +𝟐 𝒓+ 𝟒 − 𝟏𝟎𝒓 𝒓+ 𝟒 4. 𝟐𝒘+ 𝟒 𝒘 𝟐−𝟔𝒘+𝟗 − 𝒘−𝟏 𝒘 𝟐−𝟔𝒘+𝟗 𝒂 𝒃 + 𝒄 𝒃 = 𝒂 + 𝒄 𝒃 𝒂 𝒃 − 𝒄 𝒃 = 𝒂 − 𝒄 𝒃 Step 1 : Since the denominator is the same, add the numerator and copy the denominator. 𝟑 𝟓 + 𝟏 𝟓 = 𝟑+𝟏 𝟓 = 𝟒 𝟓 Step 1 : Sincethedenominatoris the same, combinethe numeratorandkeep thedenominator. 𝟑𝒙+𝟐 𝒙+ 𝟓 + 𝟒𝒙 𝒙+ 𝟓 = 𝟑𝒙+𝟐+𝟒𝒙 𝒙+ 𝟓 Step 2 : Combineliketerms. 𝟑𝒙+𝟐 𝒙+ 𝟓 + 𝟒𝒙 𝒙+ 𝟓 = 𝟑𝒙+𝟒𝒙+𝟐 𝒙+ 𝟓 = 𝟕𝒙+𝟐 𝒙+ 𝟓 Step 1 : Since thedenominatoris the same, combinethe numeratorandkeep thedenominator. 𝟓𝒓 +𝟐 𝒓+ 𝟒 − 𝟏𝟎𝒓 𝒓+ 𝟒 = 𝟓𝒓 +𝟐 −𝟏𝟎𝒓 𝒓+ 𝟒 Step 2 : Combineliketerms. 𝟓𝒓 +𝟐 𝒓+ 𝟒 − 𝟏𝟎𝒓 𝒓+ 𝟒 = 𝟓𝒓 −𝟏𝟎𝒓 + 𝟐 𝒓+ 𝟒 = −𝟓𝒓+𝟐 𝒓+ 𝟒 When you subtract two numbers, just follow the KCC Rules ; Example: 5r -10r *Keep the Subtrahend 5r *Change the operation from minus to add (5r+ * Change the sign ofthe minuend toits opposite sign from +10r to-10r 5r +-10r, and proceed to the rules ofaddition. 5r +-10r =-5r Solution: 𝟐𝒘+ 𝟒 𝒘 𝟐−𝟔𝒘+𝟗 − 𝒘−𝟏 𝒘 𝟐−𝟔𝒘+𝟗 = 𝟐𝒘+ 𝟒 − (𝒘−𝟏) 𝒘 𝟐−𝟔𝒘+𝟗 = 𝟐𝒘+ 𝟒−𝒘+𝟏 𝒘 𝟐−𝟔𝒘+𝟗 = 𝒘+ 𝟑 𝒘 𝟐−𝟔𝒘+𝟗 Multiply negative to each term Combine liketerms
- 4. 5. 𝒆 + 𝟓 𝒇 𝟐+𝟗 − 𝟔𝒆+𝟐 𝒇 𝟐+𝟗 C. Application Perform the indicated rational expressions. 𝟏. 𝟕 𝟗 + 𝟏 𝟗 2. 𝟒𝒎+𝟐 𝒏+ 𝟓 + 𝟗𝒎+𝟐 𝒏+ 𝟓 𝟑. 𝒑 −𝟐 𝒒− 𝟐 − 𝟑𝒑 𝒒− 𝟐 𝟒. 𝟏𝟐𝒎 𝟐 𝟓𝒏 𝟐 + 𝟏𝟐𝒎 𝟑 𝟐𝟓𝒏 𝟑 IV. Evaluation Perform the indicated operation for rational expressions with like denominators. 1. 𝟓𝒌 𝟏𝟎𝒍 − 𝟐𝒌 𝟏𝟎𝒍 5. 𝟓𝒛− 𝟒 𝒛 𝟐− 𝟏 − 𝟒𝒛−𝟑 𝒛 𝟐− 𝟏 2. 𝟏𝟓𝒕 𝟐𝒖 𝟐 + 𝟗 𝟐𝒖 𝟐 6. 𝟐𝒗+𝟏 (𝒗+𝟏) + 𝒗 𝟐 (𝒗+𝟏) 3. 𝒑 𝟐 𝒑 + 𝟐 − 𝟖 +𝟐𝒑 𝒑+𝟐 7. 𝒂 𝟐 𝒂+𝒃 + 𝟐𝒂𝒃+𝒃 𝟐 𝒂+𝒃 4. 𝒆 + 𝟏𝟐 𝟗 + 𝟐𝒆−𝟑 𝟗 𝟖. 𝟒𝒒+ 𝟑 𝒒 𝟐− 𝟐𝟓 + 𝟐−𝟑𝒒 𝒒 𝟐− 𝟐𝟓 Skill Booster! Solution: 𝒆 + 𝟓 𝒇 𝟐+𝟗 − 𝟔𝒆+𝟐 𝒇 𝟐+𝟗 = 𝒆 + 𝟓 − (𝟔𝒆 + 𝟐) 𝒇 𝟐 +𝟗 = ---------------- = ---------------- Multiply negative to each term Combine liketerms * When you multiply unlike terms, the resultis negative. Example: (-1 )(w)= -w *When you multiply like terms, the result is positive. Example: (-1)(-1)=1 *When you add unlike terms, the sign used in the result willbe based which absolute num. is greater. Examples: e+-6e= -5e We use -5esince -6e has the greater absolute value and its sign is negative. Solution: Solution: Solution: Solution:
- 5. V. Assignment Rewrite the solution in the first box. Write your solution in the second box. In the third box, write your explanation on how your solution corrects the original one.