Reduce - Evaluate. Example B

Transcription

1 Reduce - Evaluate Rational Expressions: Quotient of two 94

2 Reduce Reduce Fractions To reduce fractions we common 95

3 Reduce - Monomials Quotient Rule of Exponents: 96

4 Reduce - Polynomials To reduce we common This means we must first 97

5 Multiply and Divide - Fractions First common Then multiply Division is the same, with one extra step at the start: by the 98

6 Multiply and Divide - Monomials With monomials we can use 99

7 Multiply and Divide - Polynomials To divide out factors, we must first 100

8 Multiply and Divide Both at Once To divide: Be sure to before 101

9 LCD - Numbers Prime Factorization: To find the LCD use factors with exponents. 102

10 LCD - Monomials Use factors with exponents 103

11 LCD - Polynomials Use factors with exponents This means we must first 104

12 Add and Subtract - Fractions To add or subtract we the denominators by by the missing. 105

13 Add and Subtract Common Denominator Add the and keep the When subtracting we will first the negative Don t forget to 106

14 Add and Subtract Different Denominators To add or subtract we the denominators by by the missing. This means we may have to to find the LCD! 107

15 Rational Equations Clear Denominator Recall: Clear fractions by multiplying by 81

16 Rational Equations Factoring Denominator To identify all the factors in the we may have to the 82

17 Rational Equations Extraneous Solutions Because we are working with fractions, the cannot be 83

18 Formulas Two Step Formulas Solving Formulas: Treat other variables like. Final answer is an Example: and 17

19 Formulas Multi-Step Formulas Strategy: 18

20 Formulas Fractions Clear fractions by May have to first! 19

21 Distance/Revenue Distance Problems Distance Table: To solve: Divide by A man rode his bike to a park 60 miles away. On the return trip he went 2 mph slower which made the trip take 1 hour longer. How fast did he ride to the park? After driving through a construction zone for 45 miles, a woman realized that if she had driven just 6 mph faster she would have arrived 2 hours sooner. How fast did she drive? (practice problems on the next page) 89

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23 Distance/Revenue Steams and Wind Downwind/stream: Upwind/stream: Zoe rows a boat downstream for 80 miles. The return trip upstream took 12 hours longer. If the current flows at 3 mph, how fast does Zoe row in still water? Darius flies a plane against a headwind for 5084 miles. The return trip with the wind took 20 hours less time. If the wind speed is 10mph, how fast does Darius fly the plane when there is no wind? (practice problems on the next page) 91

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25 Work Problems One Unknown Time Adam does a job in 4 hours. Each hour he does of the job. Betty does a job in 12 hours. Each hour he does of the job. Together, each hour they do of the job. This means it takes them, working together, hours to do the entire job. Work Equation: Use! Catherine can paint a house in 15 hours. Dan can paint it in 30 hours. How long will it take them working together? Even can clean a room in 3 hours. If his sister Faith helps, it takes them hours. How long will it take Faith working alone? 84

26 Work Problems Two Unknown Times Be sure to clearly identify who is the! Tony does a job in 16 hours less time than Marissa, and they can do it together in 15 hours. How long will it take each to do the job alone? Alex can complete his project in 21 hours less than Hillary. If they work together it can get done in 10 hours. How long does it take each working alone? 85