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

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

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, …

5 Subsets of Real Numbers (cont.) Rational Numbers – Any number that can be represented by a fraction i.e. 0.75, ½, ¾, 0.3333…, 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

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

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

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 = 0 + 6 = 6 Inverse: a + (-a) = (-a) + a = 0 3 + (-3) = (-3) + 3 = 0

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

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

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)

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

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.

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

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.

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