Transcript UNIT 2 - PreAlgebrateachers.Com

UNIT 2
Chapter 4-1 Factors and Monomials
Vocabulary and Rules
Factors: Two or more numbers that are multiplied to form a product
4 • 8 = 32
Factors
Product
Vocabulary and Rules
• Divisibility Rules
• A number is divisible by:
• 2 if the ones digit is divisible by 2
Ex: 54
4 is divisible by 2
• 3 if the sum of the digits is divisible by 3 Ex: 72
7 + 2 = 9 and 9 is divisible by 3
• 5 if the ones digit is 0 or 5
Ex: 65
The ones digit is a 5
• 6 if the number is divisible by 2 and 3
Ex: 48
48 is divisible by 2 and 3
• 10 if the ones digit is 0
Ex. 120
The ones digit is 0.
Try some examples
• Determine whether 138 is divisible by 2, 3, 5, 6, or 10
Number
Divisible?
Reason
2
Yes
the ones digit is 8 and 8 is divisible by 2
3
Yes
1+3+8 is 12, and 12 is divisible by 2
5
No
The ones digit is 8, not 0 or 5
6
Yes
138 is divisible by 2 and 3
10
No
The ones digit is no 0
So, 138 is divisible by 2, 3, and 6.
You can also use divisibility rules to find factors
of a number
• List all the factors 82:
1 x 82
2 x 42
So the factors of 82 are 1, 2, 42, 82
• List all the factors of 72:
1x72
6 x 12
2x36
7 x (nothing)
3x24
8x9
4x18
9x8
You can stop finding factors when the numbers start repeating
5 x (nothing)
So the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Monomials
• A monomial is a number, variable, or a product of a number and/or variable.
• Example:
 4
Monomial because it’s a number
 Y
Monomial because it’s a variable
 -2 VK
Monomial because it’s a product of a number and variables
 2+R
Not a monomial because it shows addition
 4c – 5
Not a monomial because it shows subtraction
 2 (v + k) Not a monomial because both terms are added
Let’s Try Some Examples
Use divisibility rules to determine whether the number is divisible by 2, 3, 5, 6, or 10
1) 120
List the factors of given number
2) 90
Determine whether the expression is a monomial. Why or why not.
3) 110
4) b – c
5) xyz
Let’s Check Our Answers!
Use divisibility rules to determine whether the number is divisible by 2, 3, 5, 6, or 10
1) 120 Divisible by 2, 3, 5, 6, and 10
List the factors of given number
2) 90 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Determine whether the expression is a monomial. Why or why not.
3) 110
Yes, 110 is a number
4) b – c
No, shows subtraction
5) xyz
Yes, shows product of variables