VARIABLES AND EXPRESSIONS VARIABLES are symbols used to represent unspecified numbers or values. EXAMPLES 3m 5x + 2 3ab + 7c An ALGEBRAIC EXPRESSION consists of one or more numbers and variables along with one or more arithmetic operations. EXAMPLES x y z a b c θ (Theta)

VARIABLES AND EXPRESSIONS Quantities being multiplied are called FACTORS. The answer to the problem is called the PRODUCT. Example: 5(6) = 30 The 5 and 6 are factors. Their product is 30.

VARIABLES AND EXPRESSIONS Writing an algebraic expression for a verbal expression. 2 Two more than a number. +x 2 + x

VARIABLES AND EXPRESSIONS Writing an algebraic expression for a verbal expression. 2/32/3 Two-thirds of a number. · x

VARIABLES AND EXPRESSIONS Writing an algebraic expression for a verbal expression. – The difference of seven and a number squared. 7x2x2 7 – x 2

VARIABLES AND EXPRESSIONS Evaluate = 81 = 3 · 3 ·3 ·3 3 · 3 · 3 · 3

ORDER OF OPERATIONS Step 1: Evaluate in grouping symbols. Step 2: Evaluate all powers. Step 3: Mult./Div. from left to right Step 4: Add./Subt. from left to right

ORDER OF OPERATIONS Evaluate: ·

ORDER OF OPERATIONS Evaluate: (2 + 5) (7) (7)

OPEN SENTENCES An OPEN SENTENCE is a mathematical statement with one or more variables. The process of finding a value for a variable that results in a true sentence is called SOLVING THE OPEN SENTENCE. EXAMPLES x + 3 = 7 2a + 1 = 11

OPEN SENTENCES The replacement value for a variable that results in a true sentence is called the SOLUTION. EXAMPLE The solution for x + 3 = 7 is ? x = 4 A set of numbers from which replacements for a variable may be chosen is called the REPLACEMENT SET.

OPEN SENTENCES Finding the solution set of an inequality. Solve: 2x + 3 > 7 If the replacement set is {1, 2, 3} If x = 1, then 2(1) + 3 = 5 > 7 is false If x = 2, then 2(2) + 3 = 7 > 7 is false If x = 3, then 2(3) + 3 = 9 > 7 is true The solution set is {3}.

IDENTITY & EQUALITY PROPERTIES Multiplicative Identity a(1) = a Multiplicative Property of Zero a(0) = 0 Multiplicative Inverse

IDENTITY & EQUALITY PROPERTIES Reflexive Property a = a Symmetric Property If a = b, then b = a Transitive Property If a = b and b = c, then a = c

IDENTITY & EQUALITY PROPERTIES Substitution Property If a = b, then a may replace b and b may replace a in any expression

IDENTITY & EQUALITY PROPERTIES Name the properties illustrated by the following = Reflexive Prop (0) = Mult. Prop. Of Zero If x = y + 2, then y + 2 = x Symmetric Prop.

COMPREHENSION QUIZ Which quiz do you want?

COMPREHENSION QUIZ 1. 6(0) = 0 2. If 7 = x, then x = 7 NEXT LEFT DESKS 1. 8(1) = 8 2. If x = y and y = 3, then x = 3. RIGHT DESKS Name the property illustrated:

COMPREHENSION QUIZ 1. If 5 = x, then x = (1) = 9 NEXT LEFT DESKS 1. If a = b and b = c, then a = c. 2. 3(0) = 0. RIGHT DESKS Name the property illustrated:

COMPREHENSION QUIZ 1. 6(1) = 6 2. If a = m and m = 2, then a = 2. NEXT LEFT DESKS 1. 8(0) = 0 2. If 5 = a, then a = 5. RIGHT DESKS Name the property illustrated:

COMPREHENSION QUIZ 1. If y = 3, then 3 = y 2. 2(1) = 2 NEXT LEFT DESKS 1. If m = n and n = p, then m = p. 2. 5(0) = 0 RIGHT DESKS Name the property illustrated: