ALGEBRA REVIEW #1 – TEACHER NOTES
This Algebra Review sheet is #1 in a series of 12 topics that review the most important topics of Algebra. Review 1
consists of topics that are building blocks in an Algebra course: Sets of Numbers, Properties, Vocabulary, Absolute
Value, Order of Operations, Translating, and Inequalities.
REVIEW # 1 - ALGEBRA BASICS
PROPERTIES
SETS OF NUMBERS
Real Numbers
[All #s on a number line]
Commutative – Changing the ORDER doesn’t change the value
2+3=3+2
5+1= 1+5
Associative – Changing the GROUPING doesn’t change the
value
Rational Numbers
[#s that can be written as
a fraction or decimal that
repeats or ends]
Irrational Numbers
[#s that can NOT be
written as a fraction or
decimal that repeats or
ends]
2 + 3 + 1 = (2 + 3) + 1
2 4+5 = 2+4 5
Distributive – Multiply each term on the inside of the ( ) by the
term on the outside of the ( )
3 x+4 = 3+x+3+4
Identity – Adding or multiplying a value by the identity does not
change the initial value [Additive Identity: 0, Multiplicative
Identity: 1]
2 + 0 = 2
6+1= 6
Integers
[“counting” numbers]
…,-2,-1,0,1,2,…
Inverse – Adding or multiplying a value by the inverse will result
in the identify [Additive Inverse: opposite #, Multiplicative
Inverse: reciprocal]
7−7=0
Whole Numbers
3
4
5+ =1
Multiplication Property of Zero – The product of a # and 0 is 0
[Positive “counting” #s & 0]
0,1,2,3,…
4+0= 0
Closure – A set is closed under an operation if the resulting
term is a member of the original set of #s
Natural Numbers
Ex: The set of Whole #s is closed under addition &
multiplication.
Ex: The set of Whole #s is NOT closed under subtraction &
division.
[Positive “counting” #s]
1,2,3,…
ORDER OF OPERATIONS
P
E
M/D
A/S
ABSOLUTE VALUE
Parenthesis/Grouping
Exponents
Distance a # is away from 0
Multiplication/Division
TRANSLATING
Addition/Subtraction
VOCABULARY
Variable – a letter or symbol used to represent an unknown
value
Constant – A # alone or a fixed value
Coefficient – A # that is multiplied by a variable (# in front of a
variable)
Term – A #, a variable, or the product of a # and variable
Expression – 2 or more terms that are connected with + or Equation – An expression with an = sign
Like Terms – Terms that have the same variable and exponent
Addition – Sum, Plus, Total of, Together, Make, Combined, In
all
Subtraction – Difference, Less, Decreased by, Fewer, Minus
Multiplication – Product, Times, Double, Triple, Twice
Division – Quotient of, Per, A Third, Half
Equals – Is, Are, Totals, Altogether, Was
Parentheses ( ) – Times the sum of, The quantity of, Twice
the sum, Plus of the difference of, Times the difference of
Flipping Words – From, Into, Than, To
INEQUALITY SYMBOLS
*Can be combined by adding or subtracting the coefficients*
Equation
Terms
2$ + 7 = 13
Coe!cient
Variable
Less than (Under, fewer than, below)
> Greater than (Above, over, more than, exceeds)
≤ Less than or equal to (Maximum, at most, no more than)
≥ Greater than or equal to
<
Expression
Constant
(Minimum, at least, no less than, no fewer than)
REVIEW # 1 - ALGEBRA BASICS
PROPERTIES
SETS OF NUMBERS
Real Numbers
[All #s on a number line]
Rational Numbers
[#s that can be written as
a fraction or decimal that
repeats or ends]
Irrational Numbers
[#s that can NOT be
written as a fraction or
decimal that repeats or
ends]
Integers
[“counting” numbers]
Commutative – Changing the ORDER doesn’t change the value
Associative – Changing the GROUPING doesn’t change the value
Distributive – Multiply each term on the inside of the ( ) by the
term on the outside of the ( )
Identity – Adding or multiplying a value by the identity does not
change the initial value [Additive Identity: 0, Multiplicative
Identity: 1]
Inverse – Adding or multiplying a value by the inverse will result
in the identify [Additive Inverse: opposite #, Multiplicative
Inverse: reciprocal]
Whole Numbers
[Positive “counting” #s & 0]
Multiplication Property of Zero – The product of a # and 0 is 0
Closure – A set is closed under an operation if the resulting
term is a member of the original set of #s
Natural Numbers
[Positive “counting” #s]
ORDER OF OPERATIONS
P
E
M/D
A/S
ABSOLUTE VALUE
Parenthesis/Grouping
Exponents
Distance a # is away from 0
Multiplication/Division
TRANSLATING
Addition/Subtraction
VOCABULARY
Variable – a letter or symbol used to represent an unknown
value
Constant – A # alone or a fixed value
Coe!cient – A # that is multiplied by a variable (# in front of a
variable)
Term – A #, a variable, or the product of a # and variable
Expression – 2 or more terms that are connected with + or Equation – An expression with an = sign
Like Terms – Terms that have the same variable and exponent
Addition – Sum, Plus, Total of, Together, Make, Combined, In
all
Subtraction – Difference, Less, Decreased by, Fewer, Minus
Multiplication – Product, Times, Double, Triple, Twice
Division – Quotient of, Per, A Third, Half
Equals – Is, Are, Totals, Altogether, Was
Parentheses ( ) – Times the sum of, The quantity of, Twice
the sum, Plus of the difference of, Times the difference of
Flipping Words – From, Into, Than, To
INEQUALITY SYMBOLS
*Can be combined by adding or subtracting the coefficients*
Less than (Under, fewer than, below)
> Greater than (Above, over, more than, exceeds)
≤ Less than or equal to (Maximum, at most, no more than)
≥ Greater than or equal to
<
2$ + 7 = 13
(Minimum, at least, no less than, no fewer than)
REVIEW # 1 - ALGEBRA BASICS
PROPERTIES
SETS OF NUMBERS
Real Numbers
[All #s on a number line]
Commutative – Changing the ORDER doesn’t change the value
2+3=3+2
5+1= 1+5
Associative – Changing the GROUPING doesn’t change the value
2 + 3 + 1 = (2 + 3) + 1
Rational Numbers
[#s that can be written as
a fraction or decimal that
repeats or ends]
Irrational Numbers
[#s that can NOT be
written as a fraction or
decimal that repeats or
ends]
Integers
2 4+5 = 2+4 5
Distributive – Multiply each term on the inside of the ( ) by the
term on the outside of the ( )
3 x+4 = 3+x+3+4
Identity – Adding or multiplying a value by the identity does not
change the initial value [Additive Identity: 0, Multiplicative
Identity: 1]
2 + 0 = 2
6+1= 6
Inverse – Adding or multiplying a value by the inverse will result
[“counting” numbers]
…,-2,-1,0,1,2,…
in the identify [Additive Inverse: opposite #, Multiplicative
Inverse: reciprocal]
7−7=0
3
4
5+ =1
Multiplication Property of Zero – The product of a # and 0 is 0
Whole Numbers
4+0= 0
[Positive “counting” #s & 0]
0,1,2,3,…
Closure – A set is closed under an operation if the resulting
term is a member of the original set of #s
Ex: The set of Whole #s is closed under addition &
multiplication.
Ex: The set of Whole #s is NOT closed under subtraction &
division.
Natural Numbers
[Positive “counting” #s]
1,2,3,…
ORDER OF OPERATIONS
P
E
M/D
A/S
ABSOLUTE VALUE
Parenthesis/Grouping
Exponents
Distance a # is away from 0
Multiplication/Division
TRANSLATING
Addition/Subtraction
VOCABULARY
Variable – a letter or symbol used to represent an unknown
value
Constant – A # alone or a fixed value
Coe!cient – A # that is multiplied by a variable (# in front of a
variable)
Term – A #, a variable, or the product of a # and variable
Expression – 2 or more terms that are connected with + or Equation – An expression with an = sign
Like Terms – Terms that have the same variable and exponent
Addition – Sum, Plus, Total of, Together, Make, Combined, In
all
Subtraction – Difference, Less, Decreased by, Fewer, Minus
Multiplication – Product, Times, Double, Triple, Twice
Division – Quotient of, Per, A Third, Half
Equals – Is, Are, Totals, Altogether, Was
Parentheses ( ) – Times the sum of, The quantity of, Twice
the sum, Plus of the difference of, Times the difference of
Flipping Words – From, Into, Than, To
INEQUALITY SYMBOLS
*Can be combined by adding or subtracting the coefficients*
Equation
Terms
2$ + 7 = 13
Coe!cient
Variable
Less than (Under, fewer than, below)
> Greater than (Above, over, more than, exceeds)
≤ Less than or equal to (Maximum, at most, no more than)
≥ Greater than or equal to
<
Expression
Constant
(Minimum, at least, no less than, no fewer than)
REVIEW # 1 - ALGEBRA BASICS
PROPERTIES
SETS OF NUMBERS
Real Numbers
Commutative –
Associative –
Rational Numbers
Irrational Numbers
Distributive –
Identity –:
Integers
Inverse –
Whole Numbers
Multiplication Property of Zero –
Closure –
Natural Numbers
ORDER OF OPERATIONS
ABSOLUTE VALUE
P
E
M/D
A/S
TRANSLATING
VOCABULARY
Addition –
Subtraction –
Multiplication –
Division –
Equals –
Parentheses ( ) –
Variable –
Constant –
Coe!cient –
Term –
Expression –
Equation –
Like Terms –
Flipping Words –
INEQUALITY SYMBOLS
Less than
> Greater than
≤ Less than or equal to
≥ Greater than or equal to
<
2$ + 7 = 13
REVIEW # 1 - ALGEBRA BASICS
SETS OF NUMBERS
ORDER OF OPERATIONS
PROPERTIES
ABSOLUTE VALUE
TRANSLATING
VOCABULARY
INEQUALITY SYMBOLS