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# Section 4.1 And 4.2 Plus Warm Ups

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Section 4.1 and 4.2 plus Morning Warm Up. Finding Factors and Exponents. Welcome to the Exponential Jungle.

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### Section 4.1 And 4.2 Plus Warm Ups

1. 1. Chapter 4: Welcome to the Exponential Jungle By Ms. Dewey-Hoffman October 13 th , 2008 There are a ton of notes today, so get settled and get going.
2. 2. Warm Ups for Chapter 4 <ul><li>Find the Quotient: 147  3 = </li></ul><ul><li>Find the Quotient: 273/3 = </li></ul><ul><li>Find the Quotient: 450/10 = </li></ul><ul><li>Find the Product: 4 • 4 • 4 = </li></ul><ul><li>Find the Product: (-2)(-2)(-2) = </li></ul><ul><li>Find the Product: (10)(10)(10)(10) = </li></ul>
3. 3. Warm Ups for Chapter 4 <ul><li>Write TWO numbers, that when multiplied together, give this product: </li></ul><ul><li>12 </li></ul><ul><li>50 </li></ul><ul><li>36 </li></ul><ul><li>24 </li></ul>
4. 4. Section 4.1: Divisibility and Factors <ul><li>One integer is DIVISIBLE by another if the remainder is 0 when you divide. </li></ul><ul><li>Divisibility Rules for 2, 5, and 10 . </li></ul><ul><li>An integer is divisible by… </li></ul><ul><li>2, if it ends in 0, 2, 4, 6, and 8 . </li></ul><ul><li>5, if it ends in 0 or 5 . </li></ul><ul><li>10, if it ends in 0 . </li></ul>
5. 5. Examples: Divisibility Rules <ul><li>Is the first number divisible by the second? </li></ul><ul><li>567 and 2? </li></ul><ul><li>1,015 and 5? </li></ul><ul><li>111,120 and 10? </li></ul><ul><li>53 and 2? </li></ul><ul><li>1,118 and 2? </li></ul>
6. 6. Divisibility Rule for 3 and 9. <ul><li>See if you can pick out the pattern… </li></ul>Yes Yes Yes Yes 1 + 0 + 1 + 7 = 9 1,017 No No No No 2 + 1 + 5 = 8 215 Yes Yes Yes Yes 4 + 6 + 8 = 18 468 No Yes No Yes 2 + 8 + 2 = 12 282 Is the Number Divisible by: 3? 9? Is the Sum Divisible by: 3? 9? Sum of Digits Number
7. 7. Divisibility Rule for 3 and 9. <ul><li>From the pattern we saw before… </li></ul><ul><li>An integer is divisible by… </li></ul><ul><li>3, if the sum of its digits is divisible by 3 . </li></ul><ul><li>9, if the sum of its digits is divisible by 9 . </li></ul>
8. 8. Example Problems: <ul><li>Is the first number divisible by the second? Explain. </li></ul><ul><li>64 by 9? </li></ul><ul><li>472 by 3? </li></ul><ul><li>174 by 3? </li></ul><ul><li>43,542 by 9? </li></ul>
9. 9. Finding Factors <ul><li>One integer is a FACTOR of another integer if it divides that integer with remainder zero. </li></ul>number number number
10. 10. Finding Factors <ul><li>So find all the different combinations of factors </li></ul><ul><li>12? </li></ul><ul><li>16? </li></ul><ul><li>18? </li></ul><ul><li>24? </li></ul>1(12), 2(6), 3(4): so, 1, 2, 3, 4, 6, and 12 1(16), 2(8), 4(4): so, 1, 2, 4, and 16 1(18), 2(9), 3(6): so, 1, 2, 3, 6, 9, and 18 1(24), 2(12), 3(8), 4(6): so, 1, 2, 3, 4, 6, 8, 12, and 24
11. 11. Word Problem: <ul><li>There are 20 choral students singing at a school concert. Each row of singers much have the same number of students. If there are at least 5 students in each row, what are all the possible arrangements? </li></ul>
12. 12. List the positive factors of each number. <ul><li>10 </li></ul><ul><li>21 </li></ul><ul><li>31 </li></ul>1, 2, 5, 10 1, 3, 7, 21 1, 31
13. 13. Section 4.2: Exponents <ul><li>You can use EXPONENTS to show repeated multiplication. </li></ul><ul><li>(Just like multiplication can show repeated addition). </li></ul><ul><li>A POWER has two parts: </li></ul><ul><li>A BASE: the factor. </li></ul><ul><li>And an EXPONENT: the number of times the base (or factor) is multiplied by itself. </li></ul>
14. 14. Exponents: Exponential Notation <ul><li>So show me the EXPANDED version of 2 to the 6 th power. Or 2 6 . </li></ul><ul><li>2 • 2 • 2 • 2 • 2 • 2 = 64 = 2 6 </li></ul>
15. 15. Exponents…Show me! <ul><li>Exponential Notation. </li></ul><ul><li>And Value. (The answer). </li></ul><ul><li>Twelve to the first power. </li></ul><ul><li>Six to the second power, or six squared. </li></ul><ul><li>The opposite of the quantity seven to the fourth power. </li></ul><ul><li>Negative eight to the fifth power. </li></ul>
16. 16. Exponential Notation and Answers <ul><li>Twelve to the first power. </li></ul><ul><li>12 1 , 12 </li></ul><ul><li>Six to the second power, or six squared. </li></ul><ul><li>6 2 , 6 • 6 = 36 </li></ul><ul><li>The opposite of the quantity seven to the fourth power. </li></ul><ul><li>-7 4 , - (7 • 7 • 7 • 7) 4 = - (2,401) = -2,401 </li></ul><ul><li>Negative eight to the fifth power. </li></ul><ul><li>(-8) 5 , (-8)(-8)(-8)(-8)(-8) = -32,768 </li></ul>
17. 17. Writing Exponential Notation <ul><li>Remember to include the Negative Sign. </li></ul><ul><li>(-5)(-5)(-5) = (-5) 3 </li></ul><ul><li>Rewrite the expression using the commutative and associative properties. </li></ul><ul><li>-2 • a • b • a • a = </li></ul><ul><li>-2 • a • a • a • b = -2a 3 b </li></ul>
18. 18. Exponents and Negative Integers <ul><li>So when you multiply 2 negative numbers…what do you get? </li></ul><ul><li>A positive number </li></ul><ul><li>When you multiply 3 negative numbers…what do you get? </li></ul><ul><li>A negative number </li></ul>
19. 19. Exponents and Negative Numbers <ul><li>When you multiply an EVEN number of negative integers, the answer will be positive. </li></ul><ul><li>When you multiply an ODD number of negative integers, the answer will be negative. </li></ul>
20. 20. Example Problems <ul><li>Write these in exponential notation… </li></ul><ul><li>6 • 6 • 6 • 6 = </li></ul><ul><li>(-3)(-3)(-3) = </li></ul><ul><li>4 • y • x • y = 4y 2 x </li></ul>
21. 21. Word Problem: <ul><li>A microscope can magnify a specimen 10 3 times. How many times is that? </li></ul>
22. 22. Example Problems: <ul><li>Simplify: 6 2 </li></ul><ul><li>Evaluate: - a 4 , for a = 2 </li></ul><ul><li>Evaluate: (-a) 4 , for a = 2 </li></ul>
23. 23. Orders of Operations <ul><li>Work inside the grouping symbols </li></ul><ul><li>Simplify any terms with exponents. </li></ul><ul><li>Multiply and divide in order from left to right. </li></ul><ul><li>Add and subtract in order from left to right. </li></ul>
24. 24. Example Problem: <ul><li>4(3+2) 2 = </li></ul><ul><li>Grouping Symbols: 3+2 = 5 </li></ul><ul><li>Exponents: 5 2 = 5 • 5 = 25 </li></ul><ul><li>Multiplying/Dividing: 4 • 25 = 100. </li></ul><ul><li>Addition/Subtraction?: Nope </li></ul><ul><li>So, 100 is the answer. </li></ul>
25. 25. Example Problem: <ul><li>-2x 3 + 4y, for x = -2 and y = 3. </li></ul><ul><li>Substitute Variables: -2(-2) 3 + 4(3) </li></ul><ul><li>Grouping Symbols: None </li></ul><ul><li>Exponents: (-2) 3 = (-2)(-2)(-2) = -8 </li></ul><ul><li> -2(-8)+ 4(3) </li></ul><ul><li>Multiplication/Division: 16 + 12 = 28 </li></ul><ul><li>Addition/Subtraction: None </li></ul><ul><li>So, 28 is the answer. </li></ul>
26. 26. Assignment #22: <ul><li>Pages 174-175: 15-29 Odd. </li></ul><ul><li>Pages 178-179: 13-43 Odd. </li></ul>