Adding and subtracting rational expressions with different denominator
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Lesson plan on Adding and subtracting rational expressions with different denominator
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Adding and subtracting rational expressions with different denominator
- 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 different denominator 3. relate rational expressions in real life situation II. Learning Content A. Subject Matter Addition and Subtraction ofRational Expressions with Different 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 B. Analysis mmReaction Guide
- 3. C.Abstraction When the denominators of the two rational algebraic expressions are different, we need to find the least common denominator (LCD) of the given expressions. The least common denominator must contain all prime factor of each denominator raised to the highest power. It is the common multiple of the denominator. Provided that the denominators are not equal to zero, then, Perform the indicated operation and simplify if possible. 1. 𝟏 𝟐𝒓 + 𝟐 𝟑𝒔 2. 𝟐 𝒓+𝟏 + 𝒙 𝒓−𝟏 3. 𝒙+𝟏 𝒙 +𝟐 - 𝒙−𝟏 𝒙−𝟐 𝒂 𝒃 + 𝒄 𝒅 = 𝒂𝒅 + 𝒄𝒅 𝒃𝒅 𝒂 𝒃 − 𝒄 𝒅 = 𝒂𝒅 − 𝒄𝒅 𝒃𝒅 Step 1 : Find the least common denominator (LCD). 𝟐𝒓 = ( 2 ) ( r ) 3s = (3) (s) LCD = (2) (r ) (3)(s) LCD = (2) (3) ( r ) (s) LCD = 6rs Step 2 : Express each fraction with the LCD as the denominator. 𝟏 𝟐𝒓 + 𝟐 𝟑𝒔 = 𝟏 ( 𝟑𝒔)+𝟐 (𝟐𝒓) 𝟔𝒓𝒔 𝟔𝒓𝒔 𝟐𝒓 = 3s 𝟔𝒓𝒔 𝟐𝒓 = 3s 𝟔𝒓𝒔 𝟑𝒔 = 2r Step 3 : Add the numerator and simplify when possible. 𝟏 𝟐𝒓 + 𝟐 𝟑𝒔 = 𝟏 ( 𝟑𝒔)+𝟐 (𝟐𝒓) 𝟔𝒓𝒔 = 𝟑𝒔+ 𝟒𝒓 𝟔𝒓𝒔 Observehow to add dissimilar fraction. Step 1 . Combine the denominator. 𝟐 𝒓+𝟏 + 𝒙 𝒓−𝟏 = (𝒓+𝟏) ( 𝒓−𝟏) Step 2 . Cross Multiply. 𝟐 𝒓+𝟏 + 𝒙 𝒓−𝟏 = 𝟐 ( 𝒓−𝟏 ) +𝒙 (𝒓+𝟏 ) (𝒓+𝟏) ( 𝒓−𝟏) Step 3 . Multiply the numerator. 𝟐 𝒓+𝟏 + 𝒙 𝒓−𝟏 = 𝟐 ( 𝒓−𝟏 ) +𝒙 (𝒓+𝟏 ) (𝒓+𝟏) ( 𝒓−𝟏) = 𝟐 𝒓−𝟏 + 𝒙𝒓 +𝒙 (𝒓+𝟏) ( 𝒓−𝟏) = 𝟐 𝒓+𝒙+𝒙𝒓−𝟏 (𝒓+𝟏) ( 𝒓−𝟏) You can only add or subtract ifthey have the same variables and exponents regardless ofits numerical coefficients Example: 𝟐𝒙 𝟑 and 𝟑𝒙 𝟑 Step 1 . Combine the denominator. 𝒙+𝟏 𝒙 +𝟐 - 𝒙−𝟏 𝒙−𝟐 = ( 𝒙+𝟏)−(𝒙−𝟏) ( 𝒙 +𝟐) (𝒙−𝟐 ) Step 2 . Cross Multiply. 𝒙+𝟏 𝒙 +𝟐 - 𝒙−𝟏 𝒙−𝟐 = [( 𝒙+𝟏)( 𝒙−𝟐 ) ]−[ ( 𝒙−𝟏)( 𝒙+𝟐 )] ( 𝒙 +𝟐)( 𝒙−𝟐)
- 4. n 4. 𝒄 +𝟏 𝒅− 𝟐 - 𝒅 −𝟏 𝒄 − 𝟑 D. Application Perform the indicated rational expressions. 𝟏. 𝒘 +𝟑 𝒒− 𝟏 + 𝒒 −𝟏 𝒘+ 𝟑 2. 𝟒𝒎+𝟐 𝒎+ 𝟓 + 𝟗𝒎+𝟐 𝒏+ 𝟓 𝟑. 𝒑 −𝟐 𝒓− 𝟐 − 𝟑𝒑 𝒒− 𝟐 𝟒. 𝟏𝟐𝒎 𝟐 𝒏 𝟐 + 𝟏𝟐𝒎 𝟑 𝟓𝒏 𝟑 Solution: Solution: Solution: Solution: Step 3 . Multiply the numerator. 𝒙+𝟏 𝒙 +𝟐 - 𝒙−𝟏 𝒙−𝟐 = [( 𝒙+𝟏)( 𝒙−𝟐 ) ]−[ ( 𝒙−𝟏)( 𝒙+𝟐 )] ( 𝒙 +𝟐)( 𝒙−𝟐) 𝒙+𝟏 𝒙 +𝟐 - 𝒙−𝟏 𝒙−𝟐 = ( 𝒙 𝟐 −𝟐𝒙−𝟐) −( 𝒙 𝟐 −𝟐𝒙−𝟐 ) 𝒙 𝟐 −𝟒 Use FOIL method to simplify these the numerator. Use FOIL method to simplify these the denominator. Step 4. Simplify the numerator. 𝒙+𝟏 𝒙 +𝟐 - 𝒙−𝟏 𝒙−𝟐 = ( 𝒙 𝟐 −𝟐𝒙−𝟐) −( 𝒙 𝟐 −𝟐𝒙−𝟐 ) 𝒙 𝟐 −𝟒 𝒙+𝟏 𝒙 +𝟐 - 𝒙−𝟏 𝒙−𝟐 = 𝒙 𝟐 −𝟐𝒙−𝟐 − 𝒙 𝟐 + 𝟐𝒙 +𝟐 𝒙 𝟐 −𝟒 𝒙+𝟏 𝒙 +𝟐 - 𝒙−𝟏 𝒙−𝟐 = 𝟎 𝒙 𝟐 −𝟒 = 0 Multiply negative toeachterms. Combine like terms, Solution: 𝒄 +𝟏 𝒅− 𝟐 - 𝒅 −𝟏 𝒄 − 𝟑 = [( 𝒄 +𝟏)( 𝒄−𝟑)]−[( 𝒅−𝟏)(𝒅−𝟐) ( 𝒅− 𝟐)(𝒄−𝟑 ) = (𝒄 𝟐 −𝟐𝒄−𝟑 ) −(𝒅 𝟐 −𝟐𝒅+𝟐) 𝒄𝒅−𝟐𝒄−𝟑𝒅+𝟔 = 𝒄 𝟐 −𝟐𝒄−𝟑 − 𝒅 𝟐 +𝟐𝒅−𝟐 𝒄𝒅−𝟐𝒄−𝟑𝒅+𝟔 = 𝒄 𝟐 − 𝒅 𝟐 −𝟐𝒄 +𝟐𝒅−𝟓 𝒄𝒅−𝟐𝒄−𝟑𝒅+𝟔 Cross multiply Get the LCD Use FOIL Method Unlike Terms are terms that are not in group ;example −4𝑦3 and 5𝑥3 because the variables are different
- 5. IV. Evaluation Perform the indicated operation and simplify. 𝟏. 𝟏 𝟓𝒑 + 𝟐 𝟐𝒒 4. 𝟐𝒔 𝒓 +𝟓 - 𝟓𝒓 𝒔 −𝟓 𝟐. 𝒙 𝟒𝒉 + 𝟐 𝟑𝒊 5. 𝒂 +𝟑 𝒃− 𝟏 + 𝒃 −𝟏 𝒂+ 𝟑 𝟑. 𝟑𝒑 𝒑 +𝟐 - 𝟐 𝒑−𝟑 6. 𝒇 +𝟏 𝒈− 𝟐 + 𝟐𝒇 𝒈 + 𝟑 V. Assignment Write a reflection about what you have learned so far on Addition and subtraction of Rational Expressions with different denominators. Skill Booster!