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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

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
• 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
Expressions Example 1
• Simplify and state restrictions

16
Expressions Solution for Example 1
• Simplify and state restrictions

17
Expressions Example 2
• Simplify and state restrictions

18
Expressions Solution for Example 2
• Simplify and state restrictions

19
Expressions Solution for Example 2
20
Expressions Example 3
• Simplify and state restrictions for

21
Expressions Solution for Example 3
• Simplify and state restrictions for

22
Expressions Example 4
• Simplify and state restrictions

23
Expressions Solution for Example 4
• Simplify and state restrictions

24
Expressions Example 5
• Simplify and state restrictions

25
Expressions Solutions for Example 5
• Simplify and state restrictions

26
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
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
• 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