Algebra II (Algebra I Review) Guided Notes
Chapter 1 Section 1.2
1.
Classifying Real Numbers
a. Youtube Video Link: http://www.youtube.com/watch?v=skDLentDAH4
b. Vocabulary
I. Set- a well-defined collection of objects
II. Element of the set- each object in the set
III. Subset- consists of the elements from the given set
2.
Subset of Real Numbers

Natural Numbers
{1, 2, 3, 4, 5,…} Number we used for counting

Whole Numbers
{0, 1, 2, 3, 4, 5,…} All natural numbers includes 0

Integers
{…,-3,-2,-1, 0, 1, 2, 3} The set of integers includes the negatives of the natural numbers
and the whole numbers.

Rational numbers
{a/b | a and b are integers and b ≠ 0 } example: 2/3, 4/5, 17, 5, -4/5

Irrational numbers
Set of all numbers whose decimal representations are neither terminating nor repeating.
Irrational numbers cannot be expressed as a quotient of integers; Inaddition, not all
square roots are irrational!!
Which of these are irrational?

25, 3 , π
Real Numbers
The set of real numbers is the set of numbers that are either rational or irrational. 0 is
the additive identity for the real numbers, and 0 is the one real number that has NO
multiplicative inverse.
Examples:
To which subsets of the real numbers does each number belong?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
15
-1.4583
√57
3/10
√64
If you add two rational numbers together, will you sum be rational or irrational?
If you add a rational and irrational number together, will your sum be rational or irrational?
The product of two rational numbers is ___________?
The product of a nonzero rational number and irrational number is _____________?
Your school is sponsoring a charity race. Which set of numbers best describes the number of
people p who participate in the race?
Properties of Real Numbers
Examples: Which property does the equation illustrate?
2
3
1. (− 3) (− 2) = 1
2. (3 ∙ 4) ∙ 5 = (4 ∙ 3) ∙ 5
3. 3(𝑔 + ℎ)2𝑔 = (3𝑔 + 3ℎ) + 2
4. 𝑎 + [3 + (−𝑎)] = 3
5.(2√7)√3 = 2(√7√3)
6. 7 ∙ 7 = 1
1
Algebraic Expressions
To evaluate an algebraic expression, substitute a number for each variable in the expression. Then
simplify using the order of operations. What is the value of the expression
2(𝑥 2 −𝑦 2 )
3
for x = 6, y = -3
Will the value of the expression change if the parentheses are removed? Explain.
In basketball, team can score by making 2-point shots, 3-points shots, and 1-point free throws. What
algebraic expression models the total number of points that a basketball team scores in a game?
An expression that is a number, a variable, or the product of a number and one or more variables is term.
A coefficient is the numerical factor of a term.
A constant term is a term with no variables.
Like terms have the same variables raised to the same powers.
Examples: Combine like terms. What is a simpler form of each expression?
1. −4𝑗 2 − 7𝑘 + 5𝑗 + 𝑗 2
1
2. −𝑎2 + 2𝑏 2 + 4 𝑎2
3.
𝑦2
4
𝑦
+3+
𝑦2
3
𝑦
−5
Solving Equations: An equation is a statement that two expressions are equal.
Solving an equation that contains a variable means finding all values of the variable that make the
equation true.
Inverse operations are operations that “undo” each other.
Example: addition and subtraction, multiplication and division.
One Step Equations
Multi-Step Equations
An equation does not always have one solution!!

An equation has NO solution if no value of the variable makes the equation true.

An equation that is true for every value of the variable is an identity.

An equation is sometimes true if it is true for some, but not all value of the variables.
Example: Equations with No Solution and Identities
A ) 2x + 1 = 2x -1
B) 4 = 4
C) Is the equation always, sometimes, or never true?
1. 7𝑥 + 6 − 4𝑥 = 12 + 3𝑥 − 8
Classwork:
2. 2𝑥 + 3(𝑥 − 4) = 2(2𝑥 − 6) + 𝑥