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

Warm Ups: Simplify or Evaluate 15 + (4+6)2  5 = (4 + 8)2  42 = -32 + 5  23 =

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

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.

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.

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?

Factor Trees Use a factor tree to write the prime factorization of 825. 825 5 165 5 33 825 = 5 • 5 • 3 • 11 825 = 52  3  11 with Prime Factorization. 3 11

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.

Find the GCF for 40 and 60: 40 60 2 20 2 30 2 10 2 15 2 5 3 5 40 = 2  2  2  5 or 40 = 23  5 60 = 2  2  3  5 or 60 = 22  3  5 So, 2  2  5 = 22  5 = 20, The GCF of 40 and 60 is 20.

Find the GCF for 6a3b and 4a2b Write the Prime Factorization. 6a3b = 2•3•a•a•a•b 4a2b = 2•2•a•a • b What are the GCF? GCF = 2 • a2 • b The GCF of 6a3b and 4a2b = 2a2b

Example Problems: Use Prime Factorization to find the GCF: 12 and 87 15m2n and 45m 12: 3 • 4 87: 3 • 29 3 is the only Common Factor so it is the GCF 15m2n: 3 • 5 • m • m • n 45m: 3 • 3 • 5 • m 3, 5, m are the common factors, so 15m is the GCF.

Section 4.4: Simplifying Fractions October 14th Notes Continued

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)

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

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.

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

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.

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

Write in Simplest Form. y/xy = 3ab2/12ab = 2mn/6m = 24x2y/8xy =

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