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  42 =
 23 =

3. Section 4.3: Prime Factorization and Greatest Common Factor
By Ms. Dewey-Hoffman
October 14th, (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
825 = 5 • 5 • 3 • 11
825 = 52  3  11 with Prime Factorization. 3 11

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 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.

10. 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

11. 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.

12. Section 4.4: Simplifying Fractions
October 14th 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 =
3ab2/12ab =
2mn/6m =
24x2y/8xy =

20. Assignment #23
Pages 183: odd.
Pages 188: odd and