1. ALGEBRA 1 BASICS CHEAT SHEET THINGS YOU SHOULD KNOW . . .

2. Algebra 1 Basics
Real Numbers – Any number that can exist on a number line
5 Subsets of Real Numbers
Natural Numbers
Whole Numbers
Integers
Rational Numbers
Irrational Numbers

3. 5 Subsets of Real Numbers
Natural Numbers – Any number that occurs in nature; positive whole numbers 1, 2, 3, 4, 5,…
Whole Numbers – Natural Numbers subset with the addition of the number 0.
Integers – Any positive or negative whole number …-4, -3, -2, -1, 0, 1, 2, 3, 4, …

4. 5 Subsets of Real Numbers (cont.)
Rational Numbers – Any number that can be represented by a fraction i.e. 0.75, ½, ¾, …, 0.666…
Irrational Numbers – Any number that cannot be represented by a fraction or a decimal that repeats or terminates. i.e. , e, 2, 7

5. How the Numbers Sets are Related
RATIONAL NUMBERS
INTEGERS
IRRATIONAL NUMBERS
WHOLE NUMBERS
NATURAL NUMBERS

6. Natural – N Whole – W Integers – Z Rational – Q Irrational – I
Real Number Symbols
Natural – N
Whole – W
Integers – Z
Rational – Q
Irrational – I
Real – R

7. Addition Properties Commutative: a + b = b + a 3 + 7 = 7 + 3
Associative: (a + b) + c = a + (b + c)
(2 + 4) + 5 = 2 + (4 + 5)
Identity: a + 0 = 0 + a = a
6 + 0 = = 6
Inverse: a + (-a) = (-a) + a = 0
3 + (-3) = (-3) + 3 = 0

8. Multiplication Properties
Commutative: a ● b = b ● a
6 ● 7 = 7 ● 6
Associative: (a ● b) ● c = a ● (b ● c)
(3 ● 2) ● 5 = 3 ● (2 ● 5)
Identity: a ● 1 = 1 ● a = a
9 ● 1 = 1 ● 9 = 9
Inverse: a ● (1/a) = (1/a) ● a = 1
5 ● (1/5) = (1/5) ● 5 = 1

9. Distributive Property
a ● (b + c) = a ● b + a ● c
(or)
(b + c) ● a = b ● a + c ● a
7 ● (x + 3) = 7 ● x + 7 ● 3 = 7x + 21

10. Algebra 1 Basics
In math whether you evaluate, simplify, or solve you always need to follow the order of operations.
PEMDAS
P – Parentheses (Brackets, braces, fraction bars, or radical signs)
E – Exponents
M or D – Multiplication or Division (Always done left to right)
A or S - Addition or Subtraction (Always done left to right)

11. Algebra 1 Basics
Numerical Expression – combination of numbers, operations and grouping symbols. NO EQUAL SIGN
Power – Numerical expression where a base value is raised to an exponent
34 = 3 ● 3 ● 3 ● 3
Variable – a letter that is used to represent one or more numbers (i.e. x, y, a, b)
BASE
EXPONENT

12. Algebra 1 Basics
Algebraic Expression – a numerical expression that contains variables. NO EQUAL SIGN
Mathematical Model – an expression that represents a real-life situation.
Term – variables or numbers that make up a numerical or algebraic expression.
Coefficient – is the number part of a term that is the product of a number and a power.

13. Algebra 1 Basics
Like Terms – numbers or terms that have the same variable
Constant Term - numbers
Equivalent – When two algebraic expressions are identical when simplified
Identity – When two expressions are identical

14. Algebra 1 Basics
Equation – is a statement in which two expressions are equal
Linear Equation – is an equation with one variable that can be written in the form ax = b, where a and b are coefficients and
a ≠ 0.
Solution – is a number that makes the statement true when substituted for the variable.

15. Algebra 1 Basics
Equivalent – when two equations have the same solution.
Rewrite equations with more than one variable and rewrite common formulas for solving.
d = r  t r = t = d d t r