Expanding the walls of our classroom. This is an interactive learning ecology for students and parents in our Algebra 2 class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.
Section 1.1: Basic Concepts. -Natural Numbers otherwise known as counting numbers {1,2,3,4,5,6,...} -Whole Numbers {0,1,2,3,4,5,6,...} -Integers {...,-3,-2,-1,0,1,2,3,...} -Rational Numbers {p/q⎮p and q are integers, q≠0} Examples:4/1,1.3,-9/2,16/8 or 2,√ -Irrational Numbers {x⎮x is a real number that is not rational} Examples: √x, -√2, pi. -Real Numbers {x⎮x is represented by a point on a number line}
1.2: Operations on Real Numbers Adding Real Numbers. Like Signs- to add two numbers with the same sign, add their absolute values, The sign of the answer (either +or -) is the same as the sign of the two numbers. Unlike Signs-to add two numbers with different signs, subtract the smaller absolute value from the larger. The sign of the answer is the same as the sign of the number with the larger absolute value.
Multiplying Real Numbers Like Signs the product of two numbers with the same sign is positive. Unlike Signs The product of two numbers with different signs is negative.
Dividing Real Numbers Like signs The quotient of two nonzero numbers with the same sign is positive. Unlike signs The quotient of two nonzero numbers with different signs is negative.
1.3 Exponents, Roots, and Order of Operations Exponential Expression If a is a real number and n is a natural number, a^n= n factors of a. Where n is the exponent, a is the base, and a^n is an exponential expression. Exponents are also called powers.
Order of Operations 1. Work separately above and below any fraction bar. 2. If grouping symbols such as parentheses, square brackets, or absolute value bars are present, start with the innermost set and work outward. 3. Evaluate all powers, roots, and absolute values. 4. Do any multiplications or divisions in order, working from left to right. 5. Do any additions or subtractions in order, working from left to right.
Inverse Properties For any real number a, there is a single real number -a such that a+(-a)=0 and -a+a=0 The inverse "undoes" addition with the result 0. For any nonzero real number a, there is a single real number 1/a such that a x 1/a=1 and 1/a X a= 1 The inverse "undoes: multiplication with the result 1.
Identity Properties For any real number a, a+0=0+a=a Start with a number a; add o. The answer is identical to a. Also, a x 1=1 x a=a Start with a number a;multiply by 1. The answer is identical to a.
Commutative and Associative Properties For any real numbers a, b, and c, a+b=b+a and ab=ba, these two are the commutative property. Interchange the order of the two terms or factors.
KEY TERMS FOR CHAPTER 1. set elements empty set variable set-builder notation number line coordinate graph additiv inverse signed numbers absolute value equation inequality sum difference product reciprocals quotient factors exponent base exponential expression square root algebraic expression term like terms coefficient combining like terms
Thanks so much for posting about the different properties because they are really important to remember! Also if anyone needs more practice on the properties on Test 1 at the beginning you can practice those problems again because they are all about identifying the different properties!
Section 1.1: Basic Concepts.
ReplyDelete-Natural Numbers
otherwise known as counting numbers {1,2,3,4,5,6,...}
-Whole Numbers
{0,1,2,3,4,5,6,...}
-Integers
{...,-3,-2,-1,0,1,2,3,...}
-Rational Numbers
{p/q⎮p and q are integers, q≠0}
Examples:4/1,1.3,-9/2,16/8 or 2,√
-Irrational Numbers
{x⎮x is a real number that is not rational}
Examples: √x, -√2, pi.
-Real Numbers
{x⎮x is represented by a point on a number line}
This comment has been removed by the author.
ReplyDelete-Absolute Value
ReplyDelete⎮a⎮= {a if a is positive or 0, -a if a is negative.}
-Additive Inverse
ReplyDeleteFor any real number a, the number -a is the additive inverse of a.
For any real number a, -(-a)=a
-Set Builder Notation
ReplyDelete{x⎮x has propert P}
This comment has been removed by the author.
ReplyDeleteThis comment has been removed by the author.
ReplyDelete1.2: Operations on Real Numbers
ReplyDeleteAdding Real Numbers.
Like Signs- to add two numbers with the same sign, add their absolute values, The sign of the answer (either +or -) is the same as the sign of the two numbers.
Unlike Signs-to add two numbers with different signs, subtract the smaller absolute value from the larger. The sign of the answer is the same as the sign of the number with the larger absolute value.
Subtraction
ReplyDeleteFor all real numbers a and b
a-b=a+(-b)
Multiplying Real Numbers
ReplyDeleteLike Signs the product of two numbers with the same sign is positive.
Unlike Signs The product of two numbers with different signs is negative.
Reciprocal
ReplyDeleteThe reciprocal of a nonzero number a is 1/a
Division
ReplyDeleteFor all real numbers a and b (where b isn't equal to 0)
a / b= a/b = a x 1/b
Dividing Real Numbers
ReplyDeleteLike signs The quotient of two nonzero numbers with the same sign is positive.
Unlike signs The quotient of two nonzero numbers with different signs is negative.
1.3 Exponents, Roots, and Order of Operations
ReplyDeleteExponential Expression
If a is a real number and n is a natural number,
a^n= n factors of a.
Where n is the exponent, a is the base, and a^n is an exponential expression. Exponents are also called powers.
Order of Operations
ReplyDelete1. Work separately above and below any fraction bar.
2. If grouping symbols such as parentheses, square brackets, or absolute value bars are present, start with the innermost set and work outward.
3. Evaluate all powers, roots, and absolute values.
4. Do any multiplications or divisions in order, working from left to right.
5. Do any additions or subtractions in order, working from left to right.
1.4 Properties of Real Numbers
ReplyDeleteDistributive Property
For any real numbers a, b, and c,
a(b+c)=ab+ac and (b+c)a=ba+ca
Inverse Properties
ReplyDeleteFor any real number a, there is a single real number -a such that
a+(-a)=0 and -a+a=0
The inverse "undoes" addition with the result 0.
For any nonzero real number a, there is a single real number 1/a such that
a x 1/a=1 and 1/a X a= 1
The inverse "undoes: multiplication with the result 1.
Identity Properties
ReplyDeleteFor any real number a, a+0=0+a=a
Start with a number a; add o. The answer is identical to a.
Also, a x 1=1 x a=a
Start with a number a;multiply by 1. The answer is identical to a.
Commutative and Associative Properties
ReplyDeleteFor any real numbers a, b, and c,
a+b=b+a
and ab=ba, these two are the commutative property.
Interchange the order of the two terms or factors.
Associative
ReplyDeletea+b(b+c)=(a+b)+c
and a(bc)=(ab)c
Multiplication Property of 0
ReplyDeleteFor any real number a,
a x 0=0 and 0 x a=0
KEY TERMS FOR CHAPTER 1.
ReplyDeleteset
elements
empty set
variable
set-builder notation
number line
coordinate
graph
additiv inverse
signed numbers
absolute value
equation
inequality
sum
difference
product
reciprocals
quotient
factors
exponent
base
exponential expression
square root
algebraic expression
term
like terms
coefficient
combining like terms
Thanks so much for posting about the different properties because they are really important to remember! Also if anyone needs more practice on the properties on Test 1 at the beginning you can practice those problems again because they are all about identifying the different properties!
ReplyDelete