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-HoffmanOctober 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

3 11• 825 = 5 • 5 • 3 • 11

• 825 = 52 3 11 with Prime Factorization.

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 10

2 5

2 30

2 15

3 5

40 = 2 2 2 5or

40 = 23 5

60 = 2 2 3 5or

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.

1. 6a3b = 2•3•a•a•a•b2. 4a2b = 2•2•a•a • b

• What are the GCF?1. GCF = 2 • a2 • b

2. The GCF of 6a3b and 4a2b = 2a2b

Example Problems:

• Use Prime Factorization to find the GCF:

1. 12 and 87

2. 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.

1. 5/15 =

2. 10/12 =

3. 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.