The document covers prime factorization and greatest common factor (GCF), highlighting that a prime number has exactly two factors while a composite number has more than two. It explains how to find the GCF using prime factorization and provides examples for practice, including equivalent fractions and simplifying fractions. Additionally, it includes assignment instructions to reinforce concepts learned.

1. Warm Ups: Write in Exponential Notation c • b • 4 • b • b = -5 • x • x • 3 • y • y = d cubed =

2. Warm Ups: Simplify or Evaluate 15 + (4+6) 2  5 = (4 + 8) 2  4 2 = -3 2 + 5  2 3 =

3. Section 4.3: Prime Factorization and Greatest Common Factor By Ms. Dewey-Hoffman October 14 th , (Tuesday)

4. Finding Prime Factorizations A PRIME NUMBER is a positive integer, greater than 1, with exactly two factors. 1 and itself. 3, 5, 7, and 9 are examples of prime numbers. A COMPOSITE NUMBER is a positive integer greater than 1 with more than two factors. 4, 6, 8, 9, and 10 are composite numbers. The number 1 is neither PRIME or COMPOSITE.

5. Tell whether each number is Prime or Composite. 23? Prime: it only has two factors, 1 and 23. 129? Composite: it has more than two factors: 1, 3, 43, and 129. 54? Composite: 1, 2, 27, 6, 9, etc.

6. Prime Factorization Writing a COMPOSITE NUMBER as a PRODUCT of its PRIME FACTORS shows the PRIME FACTORIZATION of the number. OR… Breaking a composite number into prime factors is Prime Factorization. Remember Factor Trees?

7. Factor Trees Use a factor tree to write the prime factorization of 825. 825 5 165 5 33 3 11 825 = 5 • 5 • 3 • 11 825 = 5 2  3  11 with Prime Factorization.

8. Greatest Common Factor (GCF) You can use PRIME FACTORIZATION to find the Greatest Common Factor . Any factors that are the same for two or more numbers are COMMON FACTORS. A Common Factor for 12 and 10 is 2. Common Factors for 12 and 24 are: 2, 3, 4, 6, and 12. 12 is the GREATEST COMMON FACTOR.

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. Find the GCF for 6a 3 b and 4a 2 b Write the Prime Factorization. 6a 3 b = 2•3•a•a•a•b 4a 2 b = 2 •2•a•a • b What are the GCF? GCF = 2 • a 2 • b The GCF of 6a 3 b and 4a 2 b = 2 a 2 b

11. Example Problems: Use Prime Factorization to find the GCF: 12 and 87 15m 2 n and 45m 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. Section 4.4: Simplifying Fractions October 14 th Notes Continued

13. Finding Equivalent Fractions Hopefully this is Review! Find equivalent fractions by multiplying or dividing the numerator and denominator by the same nonzero factor. 4/12 = (Multiply) 4/12 = (Divide)

14. Example Problems: Find two fractions equivalent to each fraction. 5/15 = 10/12 = 14/20 =

15. Fractions in Simplest Form A fraction is in simplest form when the numerator and the denominator have no factors in common other than 1 . Use GCF to write a fraction in simplest form.

16. Try these: 6/8 9/12 28/35

17. Word Problem… 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.

18. Simplest form of Variable Fractions You can simplify fractions that contain variables. Assume that no expression has a denominator that equals zero.

19. Write in Simplest Form. y/xy = 3ab 2 /12ab = 2mn/6m = 24x 2 y/8xy =

20. Assignment #23 Pages 183: 23-43 odd. Pages 188: 19-35 odd and 36.