MS Algebra Ch Simplifying Rational Expressions. Mr. Deyo
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1 MS Algebra Ch Simplifying Rational Expressions Mr. Deyo
2 Title: 11.2 Simplifying Rational Expressions Date: Learning Target By the end of the period, I will simplify rational expressions and determine their excluded values. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.
3 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 11.2 Pg ) Section TxtBk. Problems #3-9 Odd Notes Copied on blank sheet #13-23 Odd Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due
4 Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1. How are the two images similar? 2. How are they different? 3. How can these two images be related to math?
5 1) Rational Expression Vocabulary 2) Excluded Value 3) Simplest Form 4) Factors
6 Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example Word List Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing
7 Daily Warm-Up Exercises Factor the polynomial. x 2 + 8x+ 15 For use with pages xxx xxx 2x 2 +15x 8
8 Daily Warm-Up Exercises Factor the polynomial. x 2 + 8x+ 15 For use with pages xxx xxx 2x 2 +15x 8 ANSWER ( x +3) ( x + 5) ANSWER ( x + 8) ( 2x 1)
9 Notes: A rational expression is in simplest form if the numerator and denominator have no factors in common other than 1. A number that makes a rational expression undefined is called an excluded value. (makes the Denominator = 0)
10 Problem(s) A Find excluded values Find the excluded values, if any, of the expression. a. b. x+8 10x 5 2y +14
11 Problem(s) A Find excluded values Find the excluded values, if any, of the expression. a. b. x+8 10x 5 2y +14 SOLUTION a. b. The expression is undefined when 10x = 0 or x = 0. The excluded value is 0. The expression is undefined when 2y + 14 = 0 or y = -7. The excluded value is -7.
12 Problem(s) B Find excluded values Find the excluded values, if any, of the expression. c. 4v d. 7w + 2 v 2 9 8w 2 +w +5
13 Problem(s) B Find excluded values Find the excluded values, if any, of the expression. c. 4v d. 7w + 2 v 2 9 8w 2 +w +5 SOLUTION c. The excluded values is -3 and 3. d. There are no excluded values.
14 Guided Practice Find the excluded values, if any, of the expression. n 6 2m 2n 2 5n 12 m 2 4
15 Guided Practice Find the excluded values, if any, of the expression. n 6 2m 2n 2 5n 12 m 2 4 ANSWER ANSWER 3 2, 4 2, 2
16 Storm Check (Think, Write, Discuss, Report) Why are excluded values important when simplifying rational expressions? Excluded values are important when simplifying rational expressions because.
17 Title: 11.2 Simplifying Rational Expressions Date: Learning Target By the end of the period, I will simplify rational expressions and determine their excluded values. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.
18 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 11.2 Pg ) Section TxtBk. Problems #4-10 Even Notes Copied on blank sheet #14-24 Even Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due
19 1) Rational Expression Vocabulary 2) Excluded Value 3) Simplest Form 4) Factors
20 Problem(s) A Simplify expressions by dividing out monomials Simplify the rational expression, if possible. State the excluded values. a. r b. 5x c. 6m 3 12m 2 2r 5( x +2) 18m 2
21 Problem(s) A Simplify expressions by dividing out monomials Simplify the rational expression, if possible. State the excluded values. a. r b. 5x c. 6m 3 12m 2 2r 5( x +2) 18m 2 SOLUTION r r a. = 2r 2r b. 5x 5( x + 2 ) = 5 5 x ( x + 2) c. = 6m2 ( m 2 ) 6 3 m 2 = 1 2 = x x + 2 = 6m2 ( m 2 ) 6 3 m 2 = m 3 2 The excluded value is 0. The excluded value is 2. The excluded value is 0.
22 Problem(s) B Simplify the rational expression, if possible. State the excluded values. 4a 3 c 2c 22a 6 + 5
23 Problem(s) B Simplify the rational expression, if possible. State the excluded values. 4a 3 c 2c 22a ANSWER ANSWER 2 11a 3 2c ; 0 c + 5 ; 5
24 Guided Practice Simplify the rational expression, if possible. State the excluded values. 2s 2 + 8s 3s x 3 8x + 16x 2
25 Guided Practice Simplify the rational expression, if possible. State the excluded values. 2s 2 + 8s 3s x 3 8x + 16x 2 ANSWER 2s 3 ; 4 ANSWER x x ; 0, 2
26 Storm Check (Think, Write, Discuss, Report) How can you tell if you have arrived at the simplest form of your rational expression? I have arrived at the simplest form of my rational expression when.
27 Title: 11.2 Simplifying Rational Expressions Date: Learning Target By the end of the period, I will simplify rational expressions and determine their excluded values. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.
28 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 11.2 Pg ) Section TxtBk. Problems Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due
29 1) Rational Expression Vocabulary 2) Excluded Value 3) Simplest Form 4) Factors
30 Standard Review Multiple Choice Practice Simplify to lowest terms. 6x x x 2 1 2(3x + 5) 3x 1 2(x + 5) 3x 1 2(x + 1) 9(x 1) 2(x + 5) 3x + 1
31 Standard Review Multiple Choice Practice SOLUTION 6x x x 2 1 = 2(x + 5) (3x + 1) (3x 1) (3x + 1) Factor numerator and denominator. = 2(x + 5) (3x + 1) (3x 1) (3x + 1) Divide out common factor. = 2(x + 5) 3x 1 Simplify. ANSWER The correct answer is B.
32 Problem A Recognize opposites Simplify and state the excluded values. x 2 7x x 2
33 Problem A Recognize opposites x 2 7x Simplify and state the excluded values. x 2 x 2 7x x 2 = (x 3) (x 4) (4 x) (4 + x) Factor numerator and denominator. (x 3) (x 4) = = (x 4) (4 + x) Rewrite 4 x as (x 4). (x 3) (x 4) (x 4) (4 + x) Divide out common factor. x 3 = (4 + x) Simplify. = x 3 x + 4 a a Write as. b b ANSWER The excluded values are 4 and 4.
34 Problem B Simplify the rational expression. State the excluded values. x 2 + 3x + 2 x 2 + 7x + 10
35 Problem B Simplify the rational expression. State the excluded values. x 2 + 3x + 2 x 2 + 7x + 10 ANSWER x + 1 ; 2, 5 x + 5
36 Guided Practice Simplify the rational expression. State the excluded values. y 2 64 y 2 16y z z 2 z 2 3z 10
37 Guided Practice Simplify the rational expression. State the excluded values. y 2 64 y 2 16y z z 2 z 2 3z 10 ANSWER ANSWER y + 8 z + 1 ; 8 ; 5, 2 y 8 z + 2
38 1) Rational Expression Vocabulary 2) Excluded Value 3) Simplest Form 4) Factors
39 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 11.2 Pg ) Section TxtBk. Problems #24-34 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due
40 Title: 11.2 Simplifying Rational Expressions Date: Learning Target By the end of the period, I will simplify rational expressions and determine their excluded values. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.
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