Bell Work: Rules of Membership

1
Bell Work Rules of Membership

• What are the rules that allow a prime number to
  be a prime number?
• What are the rules that allow a composite number
  to be a composite number?
• Sort the following numbers into groups according
  to your rules of membership.
• Explain why you put them there.
• Did any numbers not fit? Why?

• 0
• 1
• 19
• 21
• 23
• 25

27 43 47 54 55 97
2
Mrs. ORegans Rules of Membership
PRIME NUMBERS
COMPOSITE NUMBERS
DOES NOT BELONG
0
21
19
1
25
27
23
47
43
54
55
97
3
Prime number Prime number What do you see? I see
no other factors Except for one and
me. Composite number Composite number What do
you see? I see at least three factors Including
one and me.
4
Greatest Common Factor

• Lesson 4-4
• (continued)

5
Todays Math Standard

• Number Sense 2.4
• Determine the least common multiple and the
  greatest common divisor of whole numbers use
  them to solve problems with fractions (e.g., to
  find a common denominator to add two fractions or
  to find the reduced form for a fraction).

6
Key Vocabulary

• Greatest
• biggest
• Common
• shared
• Factor
• One of the numbers multiplied to get a product
• Factor Factor Product

7
The Greatest Common Factor (GCF)is also known as
theGreatest Common Divisor (GCD)
Factor Factor Product
8
Steps to finding the GCF

• Make a factor tree for each of the numbers
• Write out the prime factorization of each number
• Write the factors from least to greatest
• Make a Venn diagram
• Place the exponents in the correct part of the
  Venn
• Look at the overlap area of the Venn diagram
• If there are no factors, then the GCF is 1
• If there is one factor, then that is the GCF
• If there is more than one factor, then multiply
  all the factors together

9
What is the GCF of 60 and 96?
10
96
60
32
3
30
2
8
4
2
15
4
2
2
2
3
5
2
2
2 ? 2 ? 3 ? 5
2 ? 2 ? 2 ? 2 ? 2 ? 3
11
96
60
32
3
30
2
8
4
2
15
4
2
2
2
3
5
2
2
2 ? 2 ? 3 ? 5
2 ? 2 ? 2 ? 2 ? 2 ? 3
12
96
60
2
2
5
2
2
3
2
2 ? 2 ? 3 ? 5
2 ? 2 ? 2 ? 2 ? 2 ? 3
GCF 2 x 2 x 3 12
13
Yesterdays Challenge Problem
Use what you know about multiplying whole numbers
by variables and exponents to find the GCF for
the following two monomials
15xy2
45x3y
xy2
45
x3y
15
x3
y
5
3
9
x
y2
5
3
3
y
x
x
x
y
3 ? 5 ? x ? y ? y
3 ? 3 ? 5 ? x ? x ? x ? y
14
Yesterdays Challenge Problem
15xy2
45x3y
xy2
45
x3y
15
x3
y
5
3
9
x
y2
5
3
3
y
x
x
x
y
3 ? 5 ? x ? y ? y
3 ? 3 ? 5 ? x ? x ? x ? y
15
Yesterdays Challenge Problem
15xy2
45x3y
3
3
5
y
x
x
y
x
3 ? 5 ? x ? y ? y
3 ? 3 ? 5 ? x ? x ? x ? y
GCF 15xy