Section 1-2 Divisibility Patterns
A whole number is divisible by another number if the remainder is 0 when the
first number is divided by the second.
Divisibility Rules
A whole number is divisible by Examples
2 if the ones digit is divisible by 2
2,4,6,8,10,12...
3 if the sum of the digits is divisible by 3
3,6,9,12,15,18 ( 1+8)=9
4 if the number formed by the last two digits is divisible by 4 112, 684....
5 if the ones digit is 0 or 5 10,
20, 55...
6 if the number is divisible by both 2 and 3
6,12,18...
9 if the sum of the digits is divisible by 9 27,
36, 45 ( 4+5)=9
10 if the ones digit is 0
20,30,40...
A whole number is even if it is divisible by 2. It is odd if it is not
divisible by 2.
1-3 PRIME FACTORS
When two or more numbers are multiplied, each number is called a factor of
the product.
7 6
1x7 1x6
2x3
So the factors of 7 are:1 and 7 So the factors of 6
are:1,2,3,6
A whole number that has exactly two unique factors, 1 and the number itself
is called a prime number.
A number greater than 1 with more than two factors is a composite number.
Every composite number can be expressed as a product of prime numbers. This
is called a prime factorization of the number. A factor tree can be used.
1-4 Powers and Exponents
A product of prime factors can be written using exponents and a base.
32=2x2x2x2x2= 25-exponent
base
Numbers expressed using exponents are called powers.
Powers Words Expression
Value
25 2 to the fifth power 2x2x2x2x2
32
32 3 to the second power or 3 squared 3x3
9
103 10 to the third power or 10 cubed 10x10x10
100
* The symbol . means miltiplication
1. Write 3.3.3.3 using ans exponent. Find the value
2. Write 45 as a product of the same factor. Then find the value.
3.Science
The approximate daytime surface temperature on the moon can be written as 28
Farenheit. What is this temperature?
4. Write the prime factorization of 72 using exponents.
1-5 Order of Operations
Order of Operations tells you which operation to perform first so that
everyone gets the same final answer.
PLEASE EXCUSE MY DEAR AUNT SALLY
P=Parentheses
E=Exponents
M=Multiply or divide from left to right
D=Divide or multiply from left to right
A=Add or subtract from left to right
S=Subtract or add from left to right
Example 1
4+3 x 5=
10-2 + 8=
3 x 62 + 4=
(27 +2) x 42=
1-6 ALGEBRA: Variables and Exponents
Algebra is a language of symbols. One symbol that is often used is a
variable. A variable is a symbol, usually a letter, used to represent a
number.
An algebraic expression are combinations of variables, numbers, and at least
one operation.
1-7: Algebra: Solving Equations
Objective: To solve equations by using mental math and guess and check
strategy
We looked at algebraic expressions, today we are going to solve algebraic
equations.
Equations contain an equals sign.
Some equations can be solved mentally.
Example: Solve 5 + h=12 mentally
Your turn: 18- d =10
We can guess and check
s + 49 = 61
Estimate= s+ 50=60, s should be about 10
Try 10 Try 11 Try 12
