Chapter 1 Sections 1.1 and 1.2 Objectives: To use the order of operations to evaluate expressions. To determine the sets of numbers to which a given number belongs. To use the properties of real numbers to simplify expressions. Expressions vs. Equations Expressions Equations (formula) Mathematical Sentence a 2 + b 2 = c 2 Mathematical Phrase b + a Order of Operations PEMDASPEMDAS - Parentheses - Exponents - Multiplication - Division - Addition - Subtraction 150 / x Left to Right + / - Left to Right = 54 Runny Numbers Real Numbers ALL the numbers we use in everyday life! Each real number corresponds to exactly one point on the number line, and every point on the number line represents exactly one real number. -Activity- Operations with Real Numbers For any real numbers a, b, and c: AdditionMultiplication Commutativea + b = b + aa*b = b*a Associative(a + b) + c = a + (b + c)(a*b)*c = a*(b*c) Identitya + 0 = a = 0 + aa*1 = a = 1*a Inversea + (-a) = 0 = (-a) + a Distributivea(b + c) = a*b + a*c and (b + c)a = b*a + c*a Name the property illustrated by each equation: (3 + 4a)2 = 2(3 + 4a) Commutative property of multiplication ( ) = ( ) + 75Associative property of addition. Examples Name the inverses for each number: -2.5 Examples You can use properties to simplify algebraic expressions. Simplify: 4(2b 6c) + 2(3b + c) = 4(2b) 4(6c) + 2(3b) + 2(c) Examples = 8b 24c + 6b + 2c = 14b- 22c Use the distribution property Multiply Combine like terms