MATH 90 CHAPTER 7 Name:.
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1 MATH 90 CHAPTER 7 Name:. 7.1 Reducing Rational Epressions Need To Know Idea of rational epressions w/ restrictions Review reducing number fraction Review polynomial factoring methods How to reduce rational epressions Idea of Rational Epressions A rational epression is simply a polynomial fraction. The denominator can NOT be zero which requires us to place restriction on the s we plug into the polynomials fractions Review Reducing Fraction Reduce By shortcut How to Reduce 1. Factor. Divide common. Show all steps Scott Eckert pg. 1
2 Review Factoring Polynomials (A) (B) (c) Factor GCF Look at the Number of Terms Two Terms Use Formula 1. A B = (A + B)(A B). A + B can t factor Three Terms Guess, check, and revise Formulas 1. A + AB + B = (A + B). A AB + B = (A B) Four Terms By Grouping Method Always Factor Completely. Try to factor more! Reducing Rational Epressions Reduce to lowest terms 45 y 5 9 y How to Reduce 1. Factor. Divide common Reducing Rational Epressions Reduce to lowest terms 5a 15 10a How to Reduce 1. Factor. Divide common Scott Eckert pg.
3 Reducing Rational Epressions Reduce to lowest terms 3 3 7a 3b 7b 3a How to Reduce 1. Factor. Divide common 7. Rational Epression Multiplication & Division Need To Know Review reducing fractions (canceling) Review multiplication and division of fractions Multiplying and dividing rational epressions Scott Eckert pg. 3
4 Reducing Fractions (Canceling) Reduce each: a 1 3 a Recall: Multiplying Fractions - Review a c b d ac bd Multiply Factions 1. Reduce a) Factor b) Divide common. Multiply/simplify Eamples Multiply Rational Epressions Multiply Factions 1. Reduce a) Factor b) Divide common. Multiply/simplify Multiply a10 a 3 a 3a Scott Eckert pg. 4
5 Multiply Rational Epressions Multiply Factions 1. Reduce a) Factor b) Divide common. Multiply/simplify Multiply Recall: Dividing Fractions - Review a c a d b d b c Divide Factions 1. Change division into multiplication. Multiply by the reciprocal of the second fraction Eamples Divide Rational Epressions a b c a d d b c Divide 3 4t 1 t t 1 t Scott Eckert pg. 5
6 7.6 and 7.7 Proportions Need To Know Special Focus on Proportions Idea of proportions How to solve proportion Solving proportion word problems Ratios and Proportions A ratio is a way to compare two numbers. We write a ratio of a and b as: a to b or a b A proportions is an equation of two ratios. Eamples Yes or No: Solving Proportions Solve proportions by cross multiplying the equations Scott Eckert pg. 6
7 Solving Proportions Solve proportions by cross multiplying the equations. 3 w 10 w7 w7 18 Apply Proportions Triangles ABC and XYZ are similar. Solve for side a. a Steps 1. Familiarize. Translate 3. Carry out 4. Check 5. State answer Tools 1. Keywords. Drawing 3. Simpler problem 4. Tables/Patterns 5. Charts 6. Guess 7. Verbal Model Scott Eckert pg. 7
8 Apply Proportions To estimate the number of trout in a lake, a naturalist catches, tags and releases 11 trout. Later, 8 trout are caught; 3 of the have tags. Estimate the number of trout in the lake. Steps 1. Familiarize. Translate 3. Carry out 4. Check 5. State answer Tools 1. Keywords. Drawing 3. Simpler problem 4. Tables/Patterns 5. Charts 6. Guess 7. Verbal Model Apply Proportions A manufacturer knows that during production, 8 out of 100 parts made are defective. If they plan to produce 1,650 parts, how many can they epect to be defective. Steps 1. Familiarize. Translate 3. Carry out 4. Check 5. State answer Tools 1. Keywords. Drawing 3. Simpler problem 4. Tables/Patterns 5. Charts 6. Guess 7. Verbal Model Scott Eckert pg. 8
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