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Lesson 26

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Lesson 26 Operations with Rational Expressions * MATH 2 HONORS - SANTOWSKI * Math 2 Honors - Santowski – PowerPoint PPT presentation

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Title: Lesson 26


1
Lesson 26 Operations with Rational Expressions
  • Math 2 Honors - Santowski

2
(A)Multiplying and Dividing With 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
  • ? 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
  • ex. (5/12) ? (15/64) - multiply by the reciprocal
    (5/12) x (64/15) ? (5/4x3) (4x16/3x5) ?
    (16/3x3) ? 16/9

3
(A) Multiplying and Dividing With Fractions
Example 1
  • the strategy that will be used - we must try to
    factor the expressions in the numerator and
    denominator
  • Example Simplify
  • But are there restrictions in this case? Why?

4
(A) Multiplying and Dividing With Fractions
Solution for Example 1
  • Example Simplify

5
(A) Multiplying and Dividing With Rational
Expressions Example 2
  • Simplify and state restrictions for

6
(A) Multiplying and Dividing With Rational
Expressions Solution for Example 2
  • Simplify

7
(A) Multiplying and Dividing With Rational
Expressions Example 3
  • Simplify and state restrictions for
  • Graphically, verify your answer

8
(A) Multiplying and Dividing With Rational
Expressions Solution for Example 3
  • Simplify

9
(A) Multiplying and Dividing With Rational
Expressions Solution for Example 3
10
(A) Multiplying and Dividing With Rational
Expressions Example 4
  • Simplify and state restrictions

11
(A) Multiplying and Dividing With Rational
Expressions Solution for Example 4
  • Simplify

12
(A) Multiplying and Dividing With Rational
Expressions Example 5
  • We introduce an idea called a complex fraction
  • Consider the 2 expressions
  • Is there any difference?
  • How do you then simplify a complex fraction?

13
(A) Multiplying and Dividing With Rational
Expressions Solution to Example 5
  • Simplify the complex fraction

14
(B) Adding Subtracting With Fractions
  • To add and subtract fractions
  • find a common denominator
  • convert fractions to equivalent fractions
    operate
  •  
  • 2/5 3/7 2(7) / 5(7) 3(5) / 7(5)
  • 14/35 15/35 29/35
  • 3/13 - 5/4 3(4) / 13(4) 5(13) / 4(13)
  • 12/52 65/52 -53/52

15
(B) Adding Subtracting With Rational
Expressions Example 1
  • Simplify and state restrictions

16
(B) Adding Subtracting With Rational
Expressions Solution for Example 1
  • Simplify and state restrictions

17
(B) Adding Subtracting With Rational
Expressions Example 2
  • Simplify and state restrictions
  • Graphically verify your work

18
(B) Adding Subtracting With Rational
Expressions Solution for Example 2
  • Simplify and state restrictions

19
(B) Adding Subtracting With Rational
Expressions Solution for Example 2
20
(B) Adding Subtracting With Rational
Expressions Example 3
  • Simplify and state restrictions for

21
(B) Adding Subtracting With Rational
Expressions Solution for Example 3
  • Simplify and state restrictions for

22
(B) Adding Subtracting With Rational
Expressions Example 4
  • Simplify and state restrictions

23
(B) Adding Subtracting With Rational
Expressions Solution for Example 4
  • Simplify and state restrictions

24
(B) Adding Subtracting With Rational
Expressions Example 5
  • Simplify and state restrictions

25
(B) Adding Subtracting With Rational
Expressions Solutions for Example 5
  • Simplify and state restrictions

26
(C) Adding Subtracting With Rational
Expressions Example 6
  • Mr S. and Mr. E set off at the same time on a 30K
    run. Mr. E. runs 1.4 km/h faster than Mr. S. Mr.
    E. finishes 2 hrs ahead of Mr. S. in spite of a
    20 minute rest in the race. How fast was each one
    running and how long did it take each person to
    run the race?

27
(C) Adding Subtracting With Rational
Expressions Solution to Example 6
  • Mr S. and Mr. E set off at the same time on a 30K
    walk. Mr. E. runs 1.4 km/h faster than Mr. S. Mr.
    E. finishes 2 hrs ahead of Mr. S. in spite of a
    20 minute rest in the race. How fast was each one
    running and how long did it take each person to
    run the race?
  • Equation is
  • Solution is vs 3.6 km/h and it took me 8 hours
    20 min

28
(D) Internet Links
  • Adding and Subtracting Rational Expressions from
    West Texas AM
  • Adding Subtracting Rationals Lesson - I from
    Purple Math
  • College Algebra Tutorial on Multiplying and
    Dividing Rational Expressions from West Texas AM
  • Multiplying Dividing Rationals Lesson - I from
    Purple Math

29
(E) Homework
  • Textbook, S8.4, p502, Q13,17-25odds, 31,33,44,46
  • Textbook, S8.5, p509, Q15,19,21,29,36,37,43,45,48-
    50
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