Sect. 1.1 Some Basics of Algebra  Numbers, Variables, and Constants  Operations and Exponents English phrases for operations  Algebraic Expressions vs. Equations  Evaluating Algebraic Expressions  Sets and Set Notation  Important Sets of Numbers 11.1

Numbers, Variables, and Constants  Numbers: 127, 4.39, 0, -11¾, square root of 3 Integers, Decimals, Fractions, Mixed Numbers  Variables: x, a, b, y, Q, B 2 etc  Constants: π, e, C=speed of light in vacuum 21.1

Operations and Exponents  Operations combine two numbers Addition Subtraction⅔ – 5 Multiplication356 · 0.03 or 356(0.03) Division19 / 3 or 19 ÷ 3  Exponents7 4 Short for 7·7·7·7 31.1

Class Exercise: Op’s + –  = 30  = 23  (-6) + (-2) + (-5) = -13  -6 – 2 – 5 = -13  8 + (-2) + (-9) (-4) = 14 + (-15) = -1  = 60  -3 7 (-2) = 42  2 (-5) (-3) (-4) =

Class Exercise: Op ÷, fractions 51.1

Algebraic Expressions vs. Equations  Algebraic expressions have one or more terms  Sometimes expressions can be simplified  If each variable is replaced with a number, we can evaluate an expression (reduce it to a single number)  Today we will review how to evaluate expressions  Tomorrow we’ll look at equations An equation is two expressions separated by an equal sign – equations are not evaluated, they are solved 61.1

Evaluating Algebraic Expressions  Substitution is replacing a variable with a number  When every variable in an expression is substituted with a number, we can evaluate that expression  Evaluate 3xz + y for x = 2, y = 5, and z = 7 3xz + y (write original problem) 3(2)(7) + (5) (put parentheses for each variable) (insert the corresponding numbers) (simplify according to “order of operations”) 47 (final answer) 71.1

Class Exercise: mixed + – ÷  = ? 5 6 = 30 or = 15  -3 – 3 = ? -6 or 0  = ? 6 2 = 36 or 3 4 = 12  ÷ 2 = ? 10 ÷ 2 = =

Rules for Order of Operations  To make sure an expression is always evaluated in the same way by different people, the Order of Operations convention was defined  Mnemonic: “Please Excuse My Dear Aunt Sally”  Parentheses  Exponents  Multiply/Divide  Add/Subtract  Always: Evaluate & Eliminate the innermost grouping first 91.1

Order of Ops Example  2 { 9 – 3 [ -2x – 4 ] }  2 { 9 + 6x + 12 }  2 { 6x + 21}  12x + 42  Remember: It’s an INSIDE job 101.1

Class Exercise – Evaluate expressions  7x + 3 for x = 5 7(5)  3z – 2y for y = 1 and z = 6 3(6) – 2(1) 18 – 2 16  [17 – (a – b)] for a = -3 and b = 7 [17 – (-3 – 7)] [17 – (-10)]

Sets and Set Notation  Finite sets and Infinite sets  Roster notation: {1, 2, 3, … } with ellipsis  Set-Builder notation: { x | x is an integer > 0}  Set of all real numbers:  Empty Set (no members):  Element of a set: 5 {1, 2, 3, 4, 5, 6}  Union of sets: {1, 2, 3} {3, 4, 5} = {1, 2, 3, 4, 5}  Intersection of sets: {1, 2, 3} {3, 4, 5} = { 3 }  Subset of a set: {1, 2, 3} {1, 2, 3, 4, 5} 121.1

Different Sets of Numbers 131.1

Next time:  1.2 Operations and Properties of Real Numbers