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1 OCF.01.9 - Multiplying and Dividing Rational Expressions MCR3U - Santowski.

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Presentation on theme: "1 OCF.01.9 - Multiplying and Dividing Rational Expressions MCR3U - Santowski."— Presentation transcript:

1 1 OCF.01.9 - Multiplying and Dividing Rational Expressions MCR3U - Santowski

2 2 (A) Review of Factoring - Common Factoring when we expand, we multiply two (or more) polynomials together to come up with a single polynomial when we expand, we multiply two (or more) polynomials together to come up with a single polynomial when we factor, we do the opposite - we go from a single polynomial to a product of a pair (or more) of polynomials when we factor, we do the opposite - we go from a single polynomial to a product of a pair (or more) of polynomials to factor means to find numbers that multiply together to give a product  ex. factors of 24 are 2x12 i.e. (2)(12), 1x24, 3x8, 4x6 to factor means to find numbers that multiply together to give a product  ex. factors of 24 are 2x12 i.e. (2)(12), 1x24, 3x8, 4x6 the greatest common factor is the largest factor of a set of given number  ex. GCF of 24 and 36 is 12 although 2,3,4,6 are all common factors  ex. GCF of 8x 2 y and 12axy 2 is 4xy the greatest common factor is the largest factor of a set of given number  ex. GCF of 24 and 36 is 12 although 2,3,4,6 are all common factors  ex. GCF of 8x 2 y and 12axy 2 is 4xy when we factor algebraic expressions, the first step is to find and GCF for all the terms when we factor algebraic expressions, the first step is to find and GCF for all the terms ex. factor 24x 2 + 6x ex. factor 24x 2 + 6x ex. factor 5a 2 - 15ab 2 + 30a 2 b 2 ex. factor 5a 2 - 15ab 2 + 30a 2 b 2 ex. factor and check by expanding 3x 2 - 9x + 15x 2 y ex. factor and check by expanding 3x 2 - 9x + 15x 2 y ex. factor 5(x + 3) + 2x(x + 3) ex. factor 5(x + 3) + 2x(x + 3)

3 3 (B) Review of Factoring - Factoring Simple Trinomials find a pair of numbers that satisfy the given set of conditions: find a pair of numbers that satisfy the given set of conditions: multiply to 10 and add to 7 multiply to 10 and add to 7 multiply to 3 and add to 4 multiply to 3 and add to 4 multiply to 5 and add to 6 multiply to 5 and add to 6 multiply to -8 and add to 2 multiply to -8 and add to 2 multiply to -8 and add to –2 multiply to -8 and add to –2 multiply to -12 and add to –1 multiply to -12 and add to –1 multiply to -12 and add to 1 multiply to -12 and add to 1 factor x 2 + 2x + 1 factor x 2 + 2x + 1 factor x 2 - 4x – 3 factor x 2 - 4x – 3 factor a 2 + 3a – 40 factor a 2 + 3a – 40 factor d 2 + 12d – 160 factor d 2 + 12d – 160 factor g 2 - 2g + 36 factor g 2 - 2g + 36

4 4 (C) Review of Factoring - Factoring Trinomials When a  1 Recall the expansion using FOIL Recall the expansion using FOIL ex. (2b - 5)(4b + 3) ex. (2b - 5)(4b + 3) = 2b x (4b + 3) – 5 x (4b + 3) = 2b x (4b + 3) – 5 x (4b + 3) = (2b)(4b) + (2b)(3) + (-5)(4b) + (-5)(3) = (2b)(4b) + (2b)(3) + (-5)(4b) + (-5)(3) = 8b 2 + 6b - 20b - 15 = 8b 2 + 6b - 20b - 15 = 8b 2 - 14b - 15 = 8b 2 - 14b - 15 observe that the -14b term came from two terms, 6b and -20b and observe that the product of (-20)(6) = the product of (8)(-15) = -120 observe that the -14b term came from two terms, 6b and -20b and observe that the product of (-20)(6) = the product of (8)(-15) = -120 so, to factor 8b 2 - 14b -15, we work through the reverse procedure. so, to factor 8b 2 - 14b -15, we work through the reverse procedure. 8b 2 - 14b - 15 8b 2 - 14b - 15 = 8b 2 + 6b - 20b - 15 = 8b 2 + 6b - 20b - 15 = 2b(4b + 3) -5(4b + 3) = 2b(4b + 3) -5(4b + 3) = (4b + 3)(2b - 5) = (4b + 3)(2b - 5) In the decomposition method, we decompose the middle term into two terms and then proceed using factoring by grouping. In the decomposition method, we decompose the middle term into two terms and then proceed using factoring by grouping. ex. Factor 6x 2 - 17x + 10 ex. Factor 6x 2 - 17x + 10 ex. Factor 6x 3 – 32x 2 + 10x ex. Factor 6x 3 – 32x 2 + 10x

5 5 (D) Review of Multiplying and Dividing With Fractions recall how to divide and multiply rational numbers - fractions recall how to divide and multiply rational numbers - fractions ex. (6/5) x (25/42) - multiply the numerator and then multiply the denominator  (150/210) = 5/7 ex. (6/5) x (25/42) - multiply the numerator and then multiply the denominator  (150/210) = 5/7  OR look to cancel COMMON FACTORS between the numerator and denominators prior to multiplying  OR look to cancel COMMON FACTORS between the numerator and denominators prior to multiplying  (6/5) x (5x5)/(6x7) = (1/1) x (5/7) = 5/7  (6/5) x (5x5)/(6x7) = (1/1) x (5/7) = 5/7 ex. (5/12)  (15/64) - multiply by the reciprocal (5/12) x (64/15)  (5/4x3) ÷ (4x16/3x5)  (16/3x3)  16/9 ex. (5/12)  (15/64) - multiply by the reciprocal (5/12) x (64/15)  (5/4x3) ÷ (4x16/3x5)  (16/3x3)  16/9

6 6 (E) Multiplying and Dividing Rational Expression2 – Example 1 the same strategy that was introduced yesterday will be employed again - we must try to factor the expressions in the numerator and denominator the same strategy that was introduced yesterday will be employed again - we must try to factor the expressions in the numerator and denominator Example: Simplify Example: Simplify

7 7 (E) Multiplying and Dividing Rational Expressions – Example 2 Simplify Simplify

8 8 (E) Multiplying and Dividing Rational Expressions – Example 3 Simplify Simplify

9 9 (E) Multiplying and Dividing Rational Expressions – Example 4 Simplify Simplify

10 10 (F) Internet Links College Algebra Tutorial on Multiplying and Dividing Rational Expressions from West Texas A&M College Algebra Tutorial on Multiplying and Dividing Rational Expressions from West Texas A&M College Algebra Tutorial on Multiplying and Dividing Rational Expressions from West Texas A&M College Algebra Tutorial on Multiplying and Dividing Rational Expressions from West Texas A&M Multiplying & Dividing Rationals Lesson - I from Purple Math Multiplying & Dividing Rationals Lesson - I from Purple Math Multiplying & Dividing Rationals Lesson - I from Purple Math Multiplying & Dividing Rationals Lesson - I from Purple Math

11 11 (G) Homework Page 106, Q5,9,12,15,16 Page 106, Q5,9,12,15,16 Do eol for each question Do eol for each question Nelson Text, p359, Q1-5 eol, 7-9 eol, 12, 17 Nelson Text, p359, Q1-5 eol, 7-9 eol, 12, 17


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