Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Unit 1 Algebraic Expressions and Properties Monday, June 01, 2009 8:49 PM Make sure you get a good start on Unit 1 Variables and Expressions. Algebra is one of those classes where it's important to learn the stuff as you go. Each new unit builds on the last one. So here we go…… In Unit 1 it's important to know: Algebraic Expressions o What's an Algebraic Expression? An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Some examples might be: o 6x 5-2x Convert a word phrase to an expression? Example: four times the sum of a variable x plus 3 --- >>> 4(x+3) And back again…. Example: Important Properties of Algebra o Understand each of the following properties: Commutative Property a + b = b + a …. Examples: 3+ 4 = 4 + 3 ab = ba …. Examples: 3(4) = 4(3) x+7 = 7 + x x(7) = 7(x) = 7x Remember just Addition and Multiplication are commutative. Subtraction and Division are NOT!!!! Associative Property (a + b) + c = a + (b + c) ….Examples: (x + 3) + 4 = x + (3 + 4) (ab)c = a(bc) ….Examples: (3x)4 = 3(4x) Addition (4 + 5) + 8 = 4 + (5 + 8) 9 + 8 = 4 + 13 17 = 17 Multiplication (4 ∙ 5) ∙ 8 = 4 ∙ (5 ∙ 8) 20 ∙ 8 = 4 ∙ 40 160 = 160 Distributed Property by multiplying the sum of numbers or by multiplying each number individually and then adding. a(b + c) = ab + ac a(b – c) = ab – ac Example Addition 2(4 + 5) = 2(4) + 2(5) 2(9) = 8 + 10 18 = 18 Subtraction 8(6 – 3) = 8(6) – 8(3) 8(3) = 48 – 24 24 = 24 Another Example: Simplify: 4(x + 3) + 5x 4x + 12 + 5x 9x + 12 Order of Operations Always do: Parentheses (Groups, Brackets, Division Bars, etc.) First!!! then Exponents and then Multiplication & Division, Left to Right finally Addition & Subtraction, Left to Right Laws of Algebra