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# Section 4.3 And 4.4 Plus Warm Ups

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Section 4.3 and 4.4, plus Warm Up from Sections 4.1 and 4.2. Greatest Common Factors and Simplifying Fractions.

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### Section 4.3 And 4.4 Plus Warm Ups

1. 1. Warm Ups: Write in Exponential Notation <ul><li>c • b • 4 • b • b = </li></ul><ul><li>-5 • x • x • 3 • y • y = </li></ul><ul><li>d cubed = </li></ul>
2. 2. Warm Ups: Simplify or Evaluate <ul><li>15 + (4+6) 2  5 = </li></ul><ul><li>(4 + 8) 2  4 2 = </li></ul><ul><li>-3 2 + 5  2 3 = </li></ul>
3. 3. Section 4.3: Prime Factorization and Greatest Common Factor By Ms. Dewey-Hoffman October 14 th , (Tuesday)
4. 4. Finding Prime Factorizations <ul><li>A PRIME NUMBER is a positive integer, greater than 1, with exactly two factors. 1 and itself. </li></ul><ul><li>3, 5, 7, and 9 are examples of prime numbers. </li></ul><ul><li>A COMPOSITE NUMBER is a positive integer greater than 1 with more than two factors. </li></ul><ul><li>4, 6, 8, 9, and 10 are composite numbers. </li></ul><ul><li>The number 1 is neither PRIME or COMPOSITE. </li></ul>
5. 5. Tell whether each number is Prime or Composite. <ul><li>23? </li></ul><ul><li>Prime: it only has two factors, 1 and 23. </li></ul><ul><li>129? </li></ul><ul><li>Composite: it has more than two factors: 1, 3, 43, and 129. </li></ul><ul><li>54? </li></ul><ul><li>Composite: 1, 2, 27, 6, 9, etc. </li></ul>
6. 6. Prime Factorization <ul><li>Writing a COMPOSITE NUMBER as a PRODUCT of its PRIME FACTORS shows the PRIME FACTORIZATION of the number. </li></ul><ul><li>OR… </li></ul><ul><li>Breaking a composite number into prime factors is Prime Factorization. </li></ul><ul><li>Remember Factor Trees? </li></ul>
7. 7. Factor Trees <ul><li>Use a factor tree to write the prime factorization of 825. </li></ul>825 5 165 5 33 3 11 <ul><li>825 = 5 • 5 • 3 • 11 </li></ul><ul><li>825 = 5 2  3  11 with Prime Factorization. </li></ul>
8. 8. Greatest Common Factor (GCF) <ul><li>You can use PRIME FACTORIZATION to find the Greatest Common Factor . </li></ul><ul><li>Any factors that are the same for two or more numbers are COMMON FACTORS. </li></ul><ul><li>A Common Factor for 12 and 10 is 2. </li></ul><ul><li>Common Factors for 12 and 24 </li></ul><ul><li>are: </li></ul><ul><li>2, 3, 4, 6, and 12. </li></ul><ul><li>12 is the GREATEST COMMON FACTOR. </li></ul>
9. 9. Find the GCF for 40 and 60: 40 60 2 20 2 10 2 5 2 30 2 15 3 5 40 = 2  2  2  5 or 40 = 2 3  5 60 = 2  2  3  5 or 60 = 2 2  3  5 So, 2  2  5 = 2 2  5 = 20, The GCF of 40 and 60 is 20.
10. 10. Find the GCF for 6a 3 b and 4a 2 b <ul><li>Write the Prime Factorization. </li></ul><ul><li>6a 3 b = 2•3•a•a•a•b </li></ul><ul><li>4a 2 b = 2 •2•a•a • b </li></ul><ul><li>What are the GCF? </li></ul><ul><li>GCF = 2 • a 2 • b </li></ul><ul><li>The GCF of 6a 3 b and 4a 2 b = 2 a 2 b </li></ul>
11. 11. Example Problems: <ul><li>Use Prime Factorization to find the GCF: </li></ul><ul><li>12 and 87 </li></ul><ul><li>15m 2 n and 45m </li></ul>12: 3 • 4 87: 3 • 29 3 is the only Common Factor so it is the GCF 15m 2 n: 3 • 5 • m • m • n 45m : 3 • 3 • 5 • m 3, 5, m are the common factors, so 15m is the GCF.
12. 12. Section 4.4: Simplifying Fractions October 14 th Notes Continued
13. 13. Finding Equivalent Fractions <ul><li>Hopefully this is Review! </li></ul><ul><li>Find equivalent fractions by multiplying or dividing the numerator and denominator by the same nonzero factor. </li></ul><ul><li>4/12 = (Multiply) </li></ul><ul><li>4/12 = (Divide) </li></ul>
14. 14. Example Problems: <ul><li>Find two fractions equivalent to each fraction. </li></ul><ul><li>5/15 = </li></ul><ul><li>10/12 = </li></ul><ul><li>14/20 = </li></ul>
15. 15. Fractions in Simplest Form <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>Use GCF to write a fraction in simplest form. </li></ul>
16. 16. Try these: <ul><li>6/8 </li></ul><ul><li>9/12 </li></ul><ul><li>28/35 </li></ul>
17. 17. Word Problem… <ul><li>You survey your friends about their favorite sandwich and find that 8 out of 12, or 8/12, prefer peanut butter. Write this fraction in simplest form. </li></ul>
18. 18. Simplest form of Variable Fractions <ul><li>You can simplify fractions that contain variables. </li></ul><ul><li>Assume that no expression has a denominator that equals zero. </li></ul>
19. 19. Write in Simplest Form. <ul><li>y/xy = </li></ul><ul><li>3ab 2 /12ab = </li></ul><ul><li>2mn/6m = </li></ul><ul><li>24x 2 y/8xy = </li></ul>
20. 20. Assignment #23 <ul><li>Pages 183: 23-43 odd. </li></ul><ul><li>Pages 188: 19-35 odd and 36. </li></ul>