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# Chapter 4 Review Part 2

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Chapter 4 Review, Part 2: October 22, 2008 Lecture Notes. Covers Rational Numbers, Multiplying, Dividing and taking Power of a Power, Scientific Notation, and Word Problems.

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### Chapter 4 Review Part 2

1. 1. Chapter 4 Review: Part 2 October 22 nd 2008 Ms. Dewey-Hoffman
2. 2. Simplifying Fractions (4.4) <ul><li>Equivalent fractions are fractions that look the same, but when simplified both give the same fraction in simplest form. </li></ul><ul><li>A fraction is in Simplest Form when the numerator and the denominator have no factors in common other than 1. </li></ul><ul><li>When simplifying fractions, write the factors. </li></ul><ul><li>Cancel out the common factors on the top and bottom. </li></ul>
3. 3. Try These: <ul><li>25n 3 a 5 /100n 2 a 10 = </li></ul><ul><li>9h 2 b/18ha = </li></ul><ul><li>309t 4 s 2 /6t 4 s = </li></ul>
4. 4. Reasoning Strategies (4.5) <ul><li>Word Problems! </li></ul><ul><li>Look for all of the possibilities. </li></ul><ul><li>Make sure you have them all. </li></ul><ul><li>If it helps: Make Diagrams </li></ul><ul><li>If it helps: Shorten things. </li></ul><ul><li>Example: Sammy, Jenny and Ben. Shorten to S, J and B. </li></ul>
5. 5. Baseball Games <ul><li>There are seven baseball teams in a league. Each team plays each of the other teams twice. What is the total number of games played? </li></ul><ul><li>Team 7: 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1. </li></ul><ul><li>2x6 = 12 Games. </li></ul><ul><li>Team 6: 5, 5, 4, 4, 3, 3, 2, 2, 1, 1. </li></ul><ul><li>2x5 = 10 Games </li></ul><ul><li>Team 5: …Figure out the pattern. How many Games? </li></ul><ul><li>42 Games Total. </li></ul>
6. 6. 4.6: Rational Numbers <ul><li>Rational Number: any number that can be written as a fraction, decimal, or ratio </li></ul><ul><li>(hence RATIO nal Number) </li></ul><ul><li>There are an unlimited number of equivalent fractions for every rational number. </li></ul><ul><li>Also, remember you can graph rational numbers on a number line. </li></ul>
7. 7. Rational Numbers and Variables <ul><li>To evaluate fractions with variables: </li></ul><ul><li>Remember that the fraction bar is a grouping symbol! </li></ul><ul><li>First: substitute for variables. </li></ul><ul><li>Second: Simplify above and blow the line. </li></ul><ul><li>Third: Write the fraction in simplest form. </li></ul>
8. 8. Try These: <ul><li>(x 2 + y) + 5 / 25, for x = 10, y = 20 </li></ul><ul><li>45 – t / t – 52, for t = 28 </li></ul><ul><li>3  3  y / y + 36, for y = 9 </li></ul>
9. 9. 4.7: Exponents and Multiplication <ul><li>Multiplying two powers with the same base? </li></ul><ul><li>Just add the exponents. </li></ul><ul><li>5 2  5 8 = 5 10 </li></ul><ul><li>x 4  x 7 = x 11 </li></ul><ul><li>Taking the Power of a Power? </li></ul><ul><li>Just multiply both exponents.   </li></ul><ul><li>(3 4 ) 3 = 3 12 </li></ul><ul><li>(m 9 ) 2 = m 18 </li></ul>
10. 10. Try These: <ul><li>-7x 6  -5x 8 </li></ul><ul><li>(d 5 ) 8 </li></ul><ul><li>x _  x 12 = x 15 </li></ul><ul><li>(r 4 ) _ = r 20 </li></ul>
11. 11. 4.8: Exponents and Division <ul><li>When dividing two powers with the same base: Subtract the exponents. </li></ul><ul><li>When dividing exponents and you come across a negative exponent… </li></ul><ul><li>Put the negative exponent below a fraction bar. </li></ul><ul><li>Positive exponents above the fraction bar. </li></ul><ul><li>Negative exponents go below the fraction bar. </li></ul><ul><li>If you get rid of everything above or below the fraction bar it is now 1. </li></ul>
12. 12. Try These: <ul><li>5x 2 / 10x -5 </li></ul><ul><li>6 7 / 6 11   </li></ul><ul><li>42a 6 b 7 / 7a 3 b 3 </li></ul><ul><li>Write as a Fraction: 4t 3 y -4 </li></ul><ul><li>Write without a Fraction: 21x 6 r 5 / 7x 7 r 2 </li></ul>
13. 13. 4.9: Scientific Notation <ul><li>Re-writing numbers, either extremely large or small, using powers of 10. </li></ul><ul><li>Negative powers of 10 are small numbers, less then 1 and greater than 0. </li></ul><ul><li>Positive powers of 10 are large numbers, much greater than 1. </li></ul>
14. 14. Standard   Scientific <ul><li>Scientific  Standard, a negative exponent says move the decimal to the left. </li></ul><ul><li>Scientific  Standard, a positive exponent says move the decimal to the right. </li></ul><ul><li>Standard  Scientific, really small number means negative exponent. </li></ul><ul><li>Standard  Scientific, large number means positive exponent. </li></ul>
15. 15. Order and Compare <ul><li>Re-write in Scientific Notation </li></ul><ul><li>Compare Exponents </li></ul><ul><li>Compare Decimals </li></ul><ul><li>Put in Order as Directed </li></ul><ul><li>Re-write with Original Numbers </li></ul>
16. 16. Multiplying in Scientific Notation <ul><li>When multiplying Scientific Notation… </li></ul><ul><li>BREAK INTO FACTORS!!!! </li></ul><ul><li>Then MULTIPLY! </li></ul>
17. 17. Try These: <ul><li>8.43 x 10 6 </li></ul><ul><li>2 x 10 -4 </li></ul><ul><li>(7 x 10 2 )(17 x 10 16 ) </li></ul><ul><li>0.0000000005067 </li></ul><ul><li>3,405,000,000 </li></ul>
18. 18. Assignment #28 <ul><li>Pages: 217-218: 26-66 All. PLUS! </li></ul><ul><li>Definitions to the bolded words in those three sections: Equivalent Fractions, Simplest Form, Rational Number, and Scientific Notation.  </li></ul><ul><li>We’re going to do a game on Friday, sorry Folks. </li></ul><ul><li>Chapter 4 Test Tomorrow. </li></ul><ul><li>Extra Credit is: Page 219: All. (1-76). </li></ul>